diff --git a/LeanPool/PersistentSOS.lean b/LeanPool/PersistentSOS.lean
new file mode 100644
index 0000000000..2f48bc12da
--- /dev/null
+++ b/LeanPool/PersistentSOS.lean
@@ -0,0 +1,72 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.Contracts
+
+/-!
+# Persistent failure of quartic sum-of-squares exactness
+
+Source: url:https://github.com/JD-Jones-ASES/persistent-sos
+Authors: JD Jones
+Status: verified
+Main declarations: `PersistentSOS.persistent_failure`, `PersistentSOS.unique_persistent_failure`
+Tags: sum-of-squares, polynomial-optimization, exact-certificates
+MSC: 90C22, 90C26, 14P10
+-/
+
+/-!
+## Mathematical context and certificate data
+
+This explicit example addresses the zero-gradient, negative-definite-Hessian case in
+Cartis and Zhu, [Remark 2.3](https://arxiv.org/html/2601.20418v2#S2.SS3).
+It does not contradict their sufficient conditions with nonzero gradient or
+positive-definite Hessian at the origin. Positive curvature in the companion
+example is proved at its unique global minimizer.
+
+The analytic construction uses the classical Choi–Lam quartic
+([1977](https://doi.org/10.1007/BF01360024)) and a contraction variant of
+Tkachev's cubic normal form ([2010](https://doi.org/10.1090/S0002-9939-10-10385-2)).
+The polynomial inequalities and exact moment certificate are proved here;
+these published results are not assumptions of the Lean theorems.
+
+The eight integer matrix certificates and the sparse moment table were generated
+from exact rational data by the upstream `scripts/generate_moments.py` at the
+commit recorded in the retained MIT notice. Their proofs check every Schur
+identity, positive pivot, basis-coverage identity, and sphere localizer in Lean.
+The port only factors repeated large integers and wraps the generated data;
+it preserves every matrix entry. Python and numerical optimization are not
+part of the formal proof's trusted base.
+-/
diff --git a/LeanPool/PersistentSOS/Contracts.lean b/LeanPool/PersistentSOS/Contracts.lean
new file mode 100644
index 0000000000..7e6c5e627f
--- /dev/null
+++ b/LeanPool/PersistentSOS/Contracts.lean
@@ -0,0 +1,124 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.Main
+public import LeanPool.PersistentSOS.UniqueMain
+
+/-!
+# Contracts
+
+Part of the explicit persistent quartic SOS counterexample.
+-/
+
+@[expose] public section
+namespace PersistentSOS
+
+/-- The norm polynomial uses every Euclidean coordinate once. -/
+theorem qPoly_definition : qPoly = ∑ i : Fin 14, MvPolynomial.X i ^ 2 := rfl
+
+/-- Literal coefficients of the fixed cubic. -/
+theorem cubicPoly_definition : cubicPoly =
+  MvPolynomial.X 0 ^ 3
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 5 ^ 2
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 6 ^ 2
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 7 ^ 2
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 8 ^ 2
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 9 ^ 2
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 10 ^ 2
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 11 ^ 2
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 12 ^ 2
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 13 ^ 2
+  + MvPolynomial.C (3 / 2) * MvPolynomial.X 0 * MvPolynomial.X 1 ^ 2
+  + MvPolynomial.C (3 / 2) * MvPolynomial.X 0 * MvPolynomial.X 2 ^ 2
+  + MvPolynomial.C (3 / 2) * MvPolynomial.X 0 * MvPolynomial.X 3 ^ 2
+  + MvPolynomial.C (3 / 2) * MvPolynomial.X 0 * MvPolynomial.X 4 ^ 2
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 5 * MvPolynomial.X 1 ^ 2
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 6 * MvPolynomial.X 2 ^ 2
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 7 * MvPolynomial.X 3 ^ 2
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 8 * MvPolynomial.X 1 * MvPolynomial.X 2
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 8 * MvPolynomial.X 3 * MvPolynomial.X 4
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 9 * MvPolynomial.X 1 * MvPolynomial.X 3
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 9 * MvPolynomial.X 2 * MvPolynomial.X 4
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 10 * MvPolynomial.X 2 * MvPolynomial.X 3
+  + MvPolynomial.C (1813 / 500) * MvPolynomial.X 11 * MvPolynomial.X 1 * MvPolynomial.X 4
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 12 * MvPolynomial.X 2 * MvPolynomial.X 4
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 13 * MvPolynomial.X 3 * MvPolynomial.X 4 := rfl
+
+/-- Ordinary finite sums of squares, without a restriction on summand degree. -/
+theorem sos_definition (p : Poly) : IsSOS p ↔
+    ∃ (m : ℕ) (f : Fin m → Poly), p = ∑ i, (f i) ^ 2 := Iff.rfl
+
+/-- The exact quartic polynomial, with ordinary polynomial scalar coefficients. -/
+theorem quarticPoly_definition (σ a b : ℝ) : quarticPoly σ a b =
+    MvPolynomial.C (σ / 4) * qPoly ^ 2 - MvPolynomial.C (a / 2) * qPoly -
+      MvPolynomial.C b * cubicPoly := rfl
+
+/-- Ordinary polynomial evaluation defines the objective function. -/
+theorem objective_definition (σ a b : ℝ) (z : Fin 14 → ℝ) :
+    objective σ a b z = MvPolynomial.eval z (quarticPoly σ a b) := rfl
+
+/-- Explicit positive minimizing root. -/
+theorem minimizingRadius_definition (σ a b : ℝ) : minimizingRadius σ a b =
+    (3 * b + Real.sqrt (9 * b ^ 2 + 4 * a * σ)) / (2 * σ) := rfl
+
+/-- Explicit attained minimum. -/
+theorem minimumValue_definition (σ a b : ℝ) : minimumValue σ a b =
+    -(b * minimizingRadius σ a b ^ 3 + a * minimizingRadius σ a b ^ 2) / 4 := rfl
+
+/-- Exact rational separation constant. -/
+theorem separation_definition : separation = 753357629 / 500000000000 := rfl
+
+/-- Literal rational coefficients defining the companion cubic. -/
+theorem uniqueCubicPoly_definition : uniqueCubicPoly =
+    MvPolynomial.C (1 / 1001) * (1000 * cubicPoly + MvPolynomial.X 0 * qPoly) := rfl
+
+/-- The companion cubic uses ordinary polynomial evaluation. -/
+theorem uniqueCubic_definition (z : Fin 14 → ℝ) :
+    uniqueCubic z = MvPolynomial.eval z uniqueCubicPoly := rfl
+
+/-- Literal quartic regularization of the companion cubic. -/
+theorem uniqueQuarticPoly_definition (σ a b : ℝ) : uniqueQuarticPoly σ a b =
+    MvPolynomial.C (σ / 4) * qPoly ^ 2 - MvPolynomial.C (a / 2) * qPoly
+      - MvPolynomial.C b * uniqueCubicPoly := rfl
+
+/-- The companion objective uses ordinary polynomial evaluation. -/
+theorem uniqueObjective_definition (σ a b : ℝ) (z : Fin 14 → ℝ) :
+    uniqueObjective σ a b z = MvPolynomial.eval z (uniqueQuarticPoly σ a b) := rfl
+
+/-- Exact rational separation for the companion cubic. -/
+theorem uniqueSeparation_definition : uniqueSeparation = 132860603 / 143000000000 := rfl
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/Definitions.lean b/LeanPool/PersistentSOS/Definitions.lean
new file mode 100644
index 0000000000..faef9d897a
--- /dev/null
+++ b/LeanPool/PersistentSOS/Definitions.lean
@@ -0,0 +1,145 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import Mathlib.Algebra.MvPolynomial.CommRing
+public import Mathlib.Analysis.InnerProductSpace.PiL2
+public import Mathlib.Analysis.SpecialFunctions.Sqrt
+public import Mathlib.Data.Fin.VecNotation
+
+/-!
+# Definitions
+
+Part of the explicit persistent quartic SOS counterexample.
+-/
+
+@[expose] public section
+
+namespace PersistentSOS
+
+/-- Ordinary real multivariate polynomials in fourteen variables. -/
+abbrev Poly := MvPolynomial (Fin 14) ℝ
+
+/-- The squared Euclidean norm polynomial, the sum of all coordinate squares. -/
+noncomputable def qPoly : Poly := ∑ i, MvPolynomial.X i ^ 2
+
+/-- The fixed sparse rational cubic, in coordinate order `(t, x₁, …, x₄, y₁, …, y₉)`. -/
+noncomputable def cubicPoly : Poly :=
+  MvPolynomial.X 0 ^ 3
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 5 ^ 2
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 6 ^ 2
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 7 ^ 2
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 8 ^ 2
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 9 ^ 2
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 10 ^ 2
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 11 ^ 2
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 12 ^ 2
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 13 ^ 2
+  + MvPolynomial.C (3 / 2) * MvPolynomial.X 0 * MvPolynomial.X 1 ^ 2
+  + MvPolynomial.C (3 / 2) * MvPolynomial.X 0 * MvPolynomial.X 2 ^ 2
+  + MvPolynomial.C (3 / 2) * MvPolynomial.X 0 * MvPolynomial.X 3 ^ 2
+  + MvPolynomial.C (3 / 2) * MvPolynomial.X 0 * MvPolynomial.X 4 ^ 2
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 5 * MvPolynomial.X 1 ^ 2
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 6 * MvPolynomial.X 2 ^ 2
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 7 * MvPolynomial.X 3 ^ 2
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 8 * MvPolynomial.X 1 * MvPolynomial.X 2
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 8 * MvPolynomial.X 3 * MvPolynomial.X 4
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 9 * MvPolynomial.X 1 * MvPolynomial.X 3
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 9 * MvPolynomial.X 2 * MvPolynomial.X 4
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 10 * MvPolynomial.X 2 * MvPolynomial.X 3
+  + MvPolynomial.C (1813 / 500) * MvPolynomial.X 11 * MvPolynomial.X 1 * MvPolynomial.X 4
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 12 * MvPolynomial.X 2 * MvPolynomial.X 4
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 13 * MvPolynomial.X 3 * MvPolynomial.X 4
+
+/-- Evaluation of the squared Euclidean norm polynomial at a real vector. -/
+noncomputable def Q (z : Fin 14 → ℝ) : ℝ := MvPolynomial.eval z qPoly
+/-- Evaluation of the fixed cubic polynomial at a real vector. -/
+noncomputable def C (z : Fin 14 → ℝ) : ℝ := MvPolynomial.eval z cubicPoly
+/-- Euclidean radius, written as the square root of the sum of coordinate squares. -/
+noncomputable def radius (z : Fin 14 → ℝ) : ℝ := Real.sqrt (Q z)
+
+/-- Ordinary SOS: a finite sum of squares of arbitrary real polynomials. -/
+def IsSOS (p : Poly) : Prop :=
+  ∃ (m : ℕ) (f : Fin m → Poly), p = ∑ i, (f i) ^ 2
+
+/-- Euclidean quartic regularization with quadratic coefficient -a / 2 and cubic -bC. -/
+noncomputable def quarticPoly (σ a b : ℝ) : Poly :=
+  MvPolynomial.C (σ / 4) * qPoly ^ 2 - MvPolynomial.C (a / 2) * qPoly
+    - MvPolynomial.C b * cubicPoly
+
+/-- The real - valued function obtained by evaluating the quartic polynomial. -/
+noncomputable def objective (σ a b : ℝ) (z : Fin 14 → ℝ) : ℝ :=
+  MvPolynomial.eval z (quarticPoly σ a b)
+
+/-- The point on the distinguished coordinate axis with first coordinate `r`. -/
+def axis (r : ℝ) : Fin 14 → ℝ := fun i => if i = 0 then r else 0
+
+/-- Positive minimizing radius for quartic regularization with negative quadratic
+strength `a` and positive cubic strength `b`. -/
+noncomputable def minimizingRadius (σ a b : ℝ) : ℝ :=
+  (3 * b + Real.sqrt (9 * b ^ 2 + 4 * a * σ)) / (2 * σ)
+
+/-- Exact minimum, once the cubic has sphere maximum one. -/
+noncomputable def minimumValue (σ a b : ℝ) : ℝ :=
+  -(b * minimizingRadius σ a b ^ 3 + a * minimizingRadius σ a b ^ 2) / 4
+
+/-- A second literal rational cubic selecting the positive first coordinate axis. -/
+noncomputable def uniqueCubicPoly : Poly :=
+  MvPolynomial.C (1 / 1001) * (1000 * cubicPoly + MvPolynomial.X 0 * qPoly)
+
+/-- Evaluation of the cubic with a unique sphere maximizer. -/
+noncomputable def uniqueCubic (z : Fin 14 → ℝ) : ℝ := MvPolynomial.eval z uniqueCubicPoly
+
+/-- Quartic regularization using the cubic with a unique sphere maximizer. -/
+noncomputable def uniqueQuarticPoly (σ a b : ℝ) : Poly :=
+  MvPolynomial.C (σ / 4) * qPoly ^ 2 - MvPolynomial.C (a / 2) * qPoly
+    - MvPolynomial.C b * uniqueCubicPoly
+
+/-- Evaluation of the quartic with a unique global minimizer. -/
+noncomputable def uniqueObjective (σ a b : ℝ) (z : Fin 14 → ℝ) : ℝ :=
+  MvPolynomial.eval z (uniqueQuarticPoly σ a b)
+
+/-- The strict rational moment separation for the selected cubic. -/
+noncomputable def uniqueSeparation : ℝ := 132860603 / 143000000000
+
+
+@[simp] theorem Q_eq_sum (z : Fin 14 → ℝ) : Q z = ∑ i, z i ^ 2 := by
+  simp [Q, qPoly, map_sum]
+
+@[simp] theorem objective_eq (σ a b : ℝ) (z : Fin 14 → ℝ) :
+    objective σ a b z = σ / 4 * Q z ^ 2 - a / 2 * Q z - b * C z := by
+  simp [objective, quarticPoly, Q, C]
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/Derivatives.lean b/LeanPool/PersistentSOS/Derivatives.lean
new file mode 100644
index 0000000000..c36619320c
--- /dev/null
+++ b/LeanPool/PersistentSOS/Derivatives.lean
@@ -0,0 +1,78 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.Definitions
+public import Mathlib.Algebra.MvPolynomial.PDeriv
+
+/-!
+# Derivatives
+
+Part of the explicit persistent quartic SOS counterexample.
+-/
+
+@[expose] public section
+namespace PersistentSOS
+open MvPolynomial
+
+theorem cubic_first_at_zero (i : Fin 14) : eval (0 : Fin 14 → ℝ) (pderiv i cubicPoly) = 0 := by
+  simp [cubicPoly]
+
+theorem cubic_second_at_zero (i j : Fin 14) :
+    eval (0 : Fin 14 → ℝ) (pderiv j (pderiv i cubicPoly)) = 0 := by
+  simp [cubicPoly]
+
+theorem q_first (i : Fin 14) : pderiv i qPoly = 2 * X i := by
+  simp [qPoly, Pi.single_apply, mul_ite]
+
+theorem stationary_origin (σ a b : ℝ) (i : Fin 14) :
+    eval (0 : Fin 14 → ℝ) (pderiv i (quarticPoly σ a b)) = 0 := by
+  have hc : constantCoeff (pderiv i cubicPoly) = 0 := by simpa using cubic_first_at_zero i
+  have hq : constantCoeff qPoly = 0 := by simp [qPoly]
+  simp [quarticPoly, q_first, hc, hq]
+
+theorem hessian_origin (σ a b : ℝ) (i j : Fin 14) :
+    eval (0 : Fin 14 → ℝ) (pderiv j (pderiv i (quarticPoly σ a b))) =
+      if i = j then -a else 0 := by
+  have hc : constantCoeff (pderiv j (pderiv i cubicPoly)) = 0 := by
+    simpa using cubic_second_at_zero i j
+  have hq : constantCoeff qPoly = 0 := by simp [qPoly]
+  have htwo : constantCoeff (2 : Poly) = 2 := by
+    rw [← map_ofNat MvPolynomial.C 2]
+    simp
+  simp [quarticPoly, q_first, hc, hq, Pi.single_apply, htwo]
+  split_ifs <;> simp_all
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/Geometry.lean b/LeanPool/PersistentSOS/Geometry.lean
new file mode 100644
index 0000000000..2313506eed
--- /dev/null
+++ b/LeanPool/PersistentSOS/Geometry.lean
@@ -0,0 +1,101 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.Transfer
+public import Mathlib.Tactic.Linarith
+public import Mathlib.Tactic.Ring
+
+/-!
+# Geometry
+
+Part of the explicit persistent quartic SOS counterexample.
+-/
+
+@[expose] public section
+
+namespace PersistentSOS
+
+/-- The objective separates into its radial envelope and a nonnegative cubic deficit. -/
+theorem objective_radial_decomposition (σ a b : ℝ) (z : Fin 14 → ℝ) :
+    objective σ a b z = radialValue σ a b (radius z) +
+      b * (radius z ^ 3 - C z) := by
+  rw [objective_eq, ← radius_sq]
+  unfold radialValue
+  ring
+
+/-- Equality in the global lower bound requires the unique radial minimum and
+    equality in the sharp cubic bound. -/
+theorem objective_minimizer_radius_iff {σ a b : ℝ} (hσ : 0 < σ)
+    (ha : 0 < a) (hb : 0 < b) (z : Fin 14 → ℝ) :
+    objective σ a b z = minimumValue σ a b ↔
+      radius z = minimizingRadius σ a b ∧ C z = radius z ^ 3 := by
+  constructor
+  · intro hobj
+    have hrad := radial_global_minimum hσ ha hb (radius_nonneg z)
+    have hc := (le_abs_self (C z)).trans (cubic_abs_le z)
+    have hdef := mul_nonneg (le_of_lt hb) (sub_nonneg.mpr hc)
+    have hid := objective_radial_decomposition σ a b z
+    have heq : radialValue σ a b (radius z) = minimumValue σ a b := by linarith
+    have hr := (radial_minimum_eq_iff hσ ha hb (radius_nonneg z)).mp heq
+    have hzero : b * (radius z ^ 3 - C z) = 0 := by linarith
+    have hd := (mul_eq_zero.mp hzero).resolve_left (ne_of_gt hb)
+    exact ⟨hr, by linarith⟩
+  · rintro ⟨hr, hc⟩
+    rw [objective_radial_decomposition, hc, sub_self, mul_zero, add_zero, hr]
+    exact radial_at_minimizingRadius hσ ha
+
+/-- Complete coordinate description of all global minimizers. Besides the
+    distinguished axis point, they form a sphere in the nine `y` coordinates
+    at first coordinate `-r / 2`, with squared radius `3 * r² / 4`. -/
+theorem objective_all_minimizers {σ a b : ℝ} (hσ : 0 < σ)
+    (ha : 0 < a) (hb : 0 < b) (z : Fin 14 → ℝ) :
+    objective σ a b z = minimumValue σ a b ↔
+      Q z = minimizingRadius σ a b ^ 2 ∧
+      (z 1 = 0 ∧ z 2 = 0 ∧ z 3 = 0 ∧ z 4 = 0) ∧
+      (z 0 = minimizingRadius σ a b ∨ z 0 = -minimizingRadius σ a b / 2) := by
+  rw [objective_minimizer_radius_iff hσ ha hb z]
+  constructor
+  · rintro ⟨hr, hc⟩
+    obtain ⟨hx, ht⟩ := (cubic_upper_equality_coordinates z).mp hc
+    exact ⟨by rw [← radius_sq, hr], hx, by simpa only [hr] using ht⟩
+  · rintro ⟨hQ, hx, ht⟩
+    have hp := minimizingRadius_pos hσ ha hb
+    have hn := radius_nonneg z
+    have hs := radius_sq z
+    have hr : radius z = minimizingRadius σ a b := by nlinarith
+    exact ⟨hr, (cubic_upper_equality_coordinates z).mpr ⟨hx, by simpa only [hr] using ht⟩⟩
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/Imports.lean b/LeanPool/PersistentSOS/Imports.lean
new file mode 100644
index 0000000000..fd830d8364
--- /dev/null
+++ b/LeanPool/PersistentSOS/Imports.lean
@@ -0,0 +1,38 @@
+/-
+Copyright (c) 2026 Lean Pool contributors. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Lean Pool contributors
+-/
+module  -- shake: keep-all --deprecated_module: ignore
+
+-- Generated project imports; run `lake exe mk_all`.
+public import LeanPool.PersistentSOS
+public import LeanPool.PersistentSOS.Contracts
+public import LeanPool.PersistentSOS.Definitions
+public import LeanPool.PersistentSOS.Derivatives
+public import LeanPool.PersistentSOS.Geometry
+public import LeanPool.PersistentSOS.Localizers
+public import LeanPool.PersistentSOS.Main
+public import LeanPool.PersistentSOS.MomentBlock1
+public import LeanPool.PersistentSOS.MomentBlock2
+public import LeanPool.PersistentSOS.MomentBlock3
+public import LeanPool.PersistentSOS.MomentBlock4
+public import LeanPool.PersistentSOS.MomentBlock5
+public import LeanPool.PersistentSOS.MomentBlock6
+public import LeanPool.PersistentSOS.MomentBlock7
+public import LeanPool.PersistentSOS.MomentBlockFull0
+public import LeanPool.PersistentSOS.MomentBridge
+public import LeanPool.PersistentSOS.MomentData
+public import LeanPool.PersistentSOS.MomentGeneral
+public import LeanPool.PersistentSOS.Moments
+public import LeanPool.PersistentSOS.PSD
+public import LeanPool.PersistentSOS.Polynomial
+public import LeanPool.PersistentSOS.QuadraticMonomials
+public import LeanPool.PersistentSOS.Radial
+public import LeanPool.PersistentSOS.SOSDegree
+public import LeanPool.PersistentSOS.Sphere
+public import LeanPool.PersistentSOS.Transfer
+public import LeanPool.PersistentSOS.UniqueDerivatives
+public import LeanPool.PersistentSOS.UniqueGeometry
+public import LeanPool.PersistentSOS.UniqueMain
+public import LeanPool.PersistentSOS.UniqueMoments
diff --git a/LeanPool/PersistentSOS/Localizers.lean b/LeanPool/PersistentSOS/Localizers.lean
new file mode 100644
index 0000000000..8a70ad6266
--- /dev/null
+++ b/LeanPool/PersistentSOS/Localizers.lean
@@ -0,0 +1,103 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.Moments
+public import LeanPool.PersistentSOS.Polynomial
+public import Mathlib.Tactic.FieldSimp
+public import Mathlib.Tactic.NormNum
+public import Mathlib.Tactic.Positivity
+public import Mathlib.Tactic.Ring
+
+/-! # The full truncated sphere relation
+
+The sphere relation annihilates every polynomial of degree at most two.
+This follows from positivity and its zero square, without enumerating
+individual localizer equations.
+-/
+
+
+@[expose] public section
+namespace PersistentSOS
+open MvPolynomial
+
+/-- A null square of a positive truncated functional is orthogonal to
+every other polynomial in its domain of quadratic - square positivity. -/
+theorem mul_eq_zero_of_square_eq_zero (L : Poly →ₗ[ℝ] ℝ)
+    (hL : ∀ p : Poly, p.totalDegree ≤ 2 → 0 ≤ L (p ^ 2))
+    (h k : Poly) (hh : h.totalDegree ≤ 2) (hk : k.totalDegree ≤ 2)
+    (hk0 : L (k ^ 2) = 0) : L (k * h) = 0 := by
+  have hscale (c : ℝ) (p : Poly) : L (MvPolynomial.C c * p) = c * L p := by
+    rw [← MvPolynomial.smul_eq_C_mul, map_smul, smul_eq_mul]
+  have hpos (t : ℝ) : 0 ≤ L (h ^ 2) + 2 * t * L (k * h) := by
+    have hd : (h + MvPolynomial.C t * k).totalDegree ≤ 2 := by
+      apply (totalDegree_add _ _).trans
+      apply max_le hh
+      apply (totalDegree_mul _ _).trans
+      simpa only [totalDegree_C, zero_add] using hk
+    have he : (h + MvPolynomial.C t * k) ^ 2 =
+        h ^ 2 + MvPolynomial.C (2 * t) * (k * h) + MvPolynomial.C (t ^ 2) * k ^ 2 := by
+      simp only [map_mul, map_pow, map_ofNat]
+      ring
+    have hp := hL _ hd
+    rw [he] at hp
+    simpa only [map_add, hscale, hk0, mul_zero, add_zero] using hp
+  by_contra hn
+  have hv : L (h ^ 2) + 2 * (-(L (h ^ 2) + 1) / (2 * L (k * h))) * L (k * h) = -1 := by
+    field_simp
+    ring
+  have hp := hpos (-(L (h ^ 2) + 1) / (2 * L (k * h)))
+  rw [hv] at hp
+  norm_num at hp
+
+/-- The sphere relation has zero square under the exact moment functional. -/
+theorem moment_sphere_relation_square : sphereFunctional ((qPoly - 1) ^ 2) = 0 := by
+  have he : (qPoly - 1) ^ 2 = qPoly ^ 2 - (2 : ℝ) • qPoly + 1 := by
+    rw [MvPolynomial.smul_eq_C_mul]
+    simp only [map_ofNat]
+    ring
+  rw [he]
+  simp only [map_add, map_sub, map_smul, smul_eq_mul, moment_q_sq, moment_q, moment_one]
+  norm_num
+
+/-- All sphere localizer identities through degree four, for arbitrary
+quadratic multipliers. -/
+theorem moment_sphere_localizer (h : Poly) (hh : h.totalDegree ≤ 2) :
+    sphereFunctional ((qPoly - 1) * h) = 0 := by
+  apply mul_eq_zero_of_square_eq_zero sphereFunctional moment_square_nonneg h (qPoly - 1)
+    hh _ moment_sphere_relation_square
+  exact (totalDegree_sub _ _).trans (max_le totalDegree_qPoly_le (by simp))
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/Main.lean b/LeanPool/PersistentSOS/Main.lean
new file mode 100644
index 0000000000..3991b71bf1
--- /dev/null
+++ b/LeanPool/PersistentSOS/Main.lean
@@ -0,0 +1,105 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.Localizers
+public import LeanPool.PersistentSOS.Geometry
+public import LeanPool.PersistentSOS.Derivatives
+public import Mathlib.Tactic.Linarith
+public import Mathlib.Tactic.NormNum
+public import Mathlib.Tactic.Positivity
+
+/-!
+# Main
+
+Part of the explicit persistent quartic SOS counterexample.
+-/
+
+@[expose] public section
+namespace PersistentSOS
+
+/-- Every ordinary polynomial SOS lower bound satisfies the displayed quantitative bound. -/
+theorem quantitative_sos_gap {σ a b γ : ℝ} (hσ : 0 < σ) (ha : 0 < a)
+    (hsos : IsSOS (quarticPoly σ a b - MvPolynomial.C γ)) :
+    γ ≤ minimumValue σ a b - b * separation * minimizingRadius σ a b ^ 3 := by
+  apply moment_quantitative_transfer sphereFunctional moment_one moment_q moment_q_sq
+    ?_ moment_square_nonneg hσ ha hsos
+  rw [moment_cubic]
+  norm_num [separation]
+
+/-- A strict gap holds for every positive regularization parameter and every
+positive fixed quadratic and cubic strength. -/
+theorem quantitative_sos_strict {σ a b γ : ℝ} (hσ : 0 < σ) (ha : 0 < a)
+    (hb : 0 < b) (hsos : IsSOS (quarticPoly σ a b - MvPolynomial.C γ)) :
+    γ < minimumValue σ a b := by
+  have h := quantitative_sos_gap hσ ha hsos
+  have hr := minimizingRadius_pos hσ ha hb
+  have hd := separation_pos
+  have hp : 0 < b * separation * minimizingRadius σ a b ^ 3 := by positivity
+  linarith
+
+/-- The exact minimum shift is not a finite sum of squares of real polynomials. -/
+theorem minimum_shift_not_sos {σ a b : ℝ} (hσ : 0 < σ) (ha : 0 < a) (hb : 0 < b) :
+    ¬ IsSOS (quarticPoly σ a b - MvPolynomial.C (minimumValue σ a b)) := by
+  intro h
+  exact (lt_irrefl _) (quantitative_sos_strict hσ ha hb h)
+
+/-- The exact minimum shift is globally nonnegative. -/
+theorem minimum_shift_nonnegative {σ a b : ℝ} (hσ : 0 < σ) (ha : 0 < a)
+    (hb : 0 < b) (z : Fin 14 → ℝ) :
+    0 ≤ MvPolynomial.eval z
+      (quarticPoly σ a b - MvPolynomial.C (minimumValue σ a b)) := by
+  simpa only [map_sub, MvPolynomial.eval_C, sub_nonneg, objective]
+    using objective_global_lower_bound hσ ha hb z
+
+/-- Explicit persistent failure, including actual global optimality and attainment. -/
+theorem persistent_failure {σ a b : ℝ} (hσ : 0 < σ) (ha : 0 < a) (hb : 0 < b) :
+    (∀ z : Fin 14 → ℝ, minimumValue σ a b ≤ objective σ a b z) ∧
+    objective σ a b (axis (minimizingRadius σ a b)) = minimumValue σ a b ∧
+    ¬ IsSOS (quarticPoly σ a b - MvPolynomial.C (minimumValue σ a b)) :=
+  ⟨objective_global_lower_bound hσ ha hb, objective_axis_attainment hσ ha,
+    minimum_shift_not_sos hσ ha hb⟩
+
+/-- The finite certificate is a functional on ordinary real polynomials, positive
+on every quadratic square, with normalized radial moments and a strict cubic gap. -/
+theorem sphere_moment_gap : ∃ L : Poly →ₗ[ℝ] ℝ,
+    L 1 = 1 ∧ L qPoly = 1 ∧ L (qPoly ^ 2) = 1 ∧
+    (∀ h : Poly, h.totalDegree ≤ 2 → 0 ≤ L (h ^ 2)) ∧
+    (∀ h : Poly, h.totalDegree ≤ 2 → L ((qPoly - 1) * h) = 0) ∧
+    L cubicPoly = 500753357629 / 500000000000 :=
+  ⟨sphereFunctional, moment_one, moment_q, moment_q_sq, moment_square_nonneg,
+    moment_sphere_localizer, moment_cubic⟩
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/MomentBlock1.lean b/LeanPool/PersistentSOS/MomentBlock1.lean
new file mode 100644
index 0000000000..80cb150b3a
--- /dev/null
+++ b/LeanPool/PersistentSOS/MomentBlock1.lean
@@ -0,0 +1,336 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.PSD
+
+/-!
+# Exact moment block certificate
+
+Generated by `scripts/generate_moments.py`; all identities below are checked
+by the Lean kernel with integer arithmetic. No external verifier is trusted.
+-/
+
+@[expose] public section
+
+
+namespace PersistentSOS
+
+
+/-- Exact integer matrix after 0 fraction-free Schur steps in moment block 1. -/
+def momentBlock1Stage0 : Fin 11 → Fin 11 → ℤ :=
+  ![![148973087, 79751621, 27438237, 3349856, 3349854, 7457187, 4162390, 7457187, 4162390,
+    4143478, 7594848],
+  ![79751621, 45340304, 14265654, 1432129, 1432127, 3269119, 1964655, 3269121, 1964657, 2022744,
+    3598238],
+  ![27438237, 14265654, 6365418, 202667, 202668, 608339, 318998, 608339, 318997, 331233, 900626],
+  ![3349856, 1432129, 202667, 307820, 305587, 604148, 317179, 604133, 317182, 297189, 454472],
+  ![3349854, 1432127, 202668, 305587, 307807, 604133, 317183, 604148, 317179, 297189, 454472],
+  ![7457187, 3269119, 608339, 604148, 604133, 1203533, 630687, 1201302, 630690, 591740, 918271],
+  ![4162390, 1964655, 318998, 317179, 317183, 630687, 340281, 630691, 338068, 318788, 486285],
+  ![7457187, 3269121, 608339, 604133, 604148, 1201302, 630691, 1203525, 630686, 591740, 918271],
+  ![4162390, 1964657, 318997, 317182, 317179, 630690, 338068, 630686, 340280, 318788, 486284],
+  ![4143478, 2022744, 331233, 297189, 297189, 591740, 318788, 591740, 318788, 305822, 461335],
+  ![7594848, 3598238, 900626, 454472, 454472, 918271, 486285, 918271, 486284, 461335, 739380]]
+
+/-- Exact integer matrix after 1 fraction-free Schur steps in moment block 1. -/
+def momentBlock1Stage1 : Fin 10 → Fin 10 → ℤ :=
+  ![![394164000270807, -63045363678279, -53807768004353, -53807906447285, -107712002149774,
+    -39276629494205, -107711704203600, -39276331548031, -29114669187110, -69660816627902],
+  ![-63045363678279, 195419119837197, -61722214220843, -61722010371282, -113985925486826,
+    -66686526499604, -113985925486826, -66686675472691, -64344928842015, -74220203950514],
+  ![-53807768004353, -61722214220843, 34635360419604, 34302710216045, 65021289949804,
+    33307727645733, 65019055353499, 33308174564994, 30393108113275, 42262449653176],
+  ![-53807906447285, -61722010371282, 34302710216045, 34633437168893, 65019070267873,
+    33308331862861, 65021304864178, 33307735970513, 30393116400231, 42262464842872],
+  ![-107712002149774, -113985925486826, 65021289949804, 65019070267873, 123684388363402,
+    62915668723839, 123352029406305, 62916115643100, 57254644224994, 80161463800001],
+  ![-39276629494205, -66686526499604, 33307727645733, 33308331862861, 62915668723839,
+    33367220505347, 62916264616187, 33037543063816, 30244061066136, 40830658245075],
+  ![-107711704203600, -113985925486826, 65019055353499, 65021304864178, 123352029406305,
+    62916264616187, 123683196578706, 62915519750752, 57254644224994, 80161463800001],
+  ![-39276331548031, -66686675472691, 33308174564994, 33307735970513, 62916115643100,
+    33037543063816, 62915519750752, 33367071532260, 30244061066136, 40830509271988],
+  ![-29114669187110, -64344928842015, 30393108113275, 30393116400231, 57254644224994,
+    30244061066136, 57254644224994, 30244061066136, 28390837476030, 37257413489801],
+  ![-69660816627902, -74220203950514, 42262449653176, 42262464842872, 80161463800001,
+    40830658245075, 80161463800001, 40830509271988, 37257413489801, 52466004922956]]
+
+/-- Exact integer matrix after 2 fraction-free Schur steps in moment block 1. -/
+def momentBlock1Stage2 : Fin 9 → Fin 9 → ℤ :=
+  ![![490373567429017047174, -186080625189770468124, -186080144418546196047,
+    -347176068872799429144, -193065996140418724329, -347175942782072072586,
+    -193066264213691638578, -182569885638358230285, -225857735018149537488],
+  ![-186080625189770468124, 72205903313274394837, 71325702822894004330, 133133505694376550938,
+    73941673780013411818, 133127700849908497539, 73942963887550232945, 69900368711887496185,
+    86660237875258001398],
+  ![-186080144418546196047, 71325702822894004330, 72200714625580276798, 133127532597540335183,
+    73943235961969528246, 133133552673357291858, 73941766921781339588, 69900363581427660541,
+    86660213328432565582],
+  ![-347176068872799429144, 133133505694376550938, 133127532597540335183, 249374290547215855774,
+    138068745688176504269, 248495126086615984905, 138070143604181616238, 130437790362319217414,
+    161730267485108146157],
+  ![-193065996140418724329, 73941673780013411818, 73943235961969528246, 138068745688176504269,
+    77930206869383177092, 138070400897436575907, 77058000490042869611, 72345913190039940646,
+    89666756402860260145],
+  ![-347175942782072072586, 133127700849908497539, 133133552673357291858, 248495126086615984905,
+    138070400897436575907, 249371568082626396066, 138068645500843629072, 130437848591657591634,
+    161730406806741401961],
+  ![-193066264213691638578, 73942963887550232945, 73941766921781339588, 138070143604181616238,
+    77058000490042869611, 138068645500843629072, 77929969811304990757, 72345971419378314866,
+    89666501560493245142],
+  ![-182569885638358230285, 69900368711887496185, 69900363581427660541, 130437790362319217414,
+    72345913190039940646, 130437848591657591634, 72345971419378314866, 69428527776399464530,
+    84964202355947631301],
+  ![-225857735018149537488, 86660237875258001398, 86660213328432565582, 161730267485108146157,
+    89666756402860260145, 161730406806741401961, 89666501560493245142, 84964202355947631301,
+    106244566210768005424]]
+
+/-- Exact integer matrix after 3 fraction-free Schur steps in moment block 1. -/
+def momentBlock1Stage3 : Fin 8 → Fin 8 → ℤ :=
+  ![![1983609171847332477984066, 888791806450867328033256, 1731289981927854358116708,
+    845336175434431364456448, 1724127787392449738657046, 846814624487559281377794,
+    772710621041152958336550, 1187681941255603213265820],
+  ![888791806450867328033256, 1977607936056179816333349, 1724282399960433563794782,
+    847515149956543248355563, 1731831412638573174020250, 845560984709112988488678,
+    772926923152667034740877, 1187926886977058350382076],
+  ![1731289981927854358116708, 1724282399960433563794782, 4453318115154302473653420,
+    1718497376862947357978490, 3359673751584938788189098, 1720000386861134956471740,
+    1469818138259514635274228, 2272778993491518995385378],
+  ![845336175434431364456448, 847515149956543248355563, 1718497376862947357978490,
+    2385896953254035178163281, 1720618358741073366106632, 1300666670145889973982336,
+    579674206018121414525577, 925398107160633602067354],
+  ![1724127787392449738657046, 1731831412638573174020250, 3359673751584938788189098,
+    1720618358741073366106632, 4450153256562740551488984, 1718198379544243076230260,
+    1469948983537180043595558, 2273024572012999203165978],
+  ![846814624487559281377794, 845560984709112988488678, 1720000386861134956471740,
+    1300666670145889973982336, 1718198379544243076230260, 2385339421987486178639862,
+    579622481410148464616622, 924927454379666643263292],
+  ![772710621041152958336550, 772926923152667034740877, 1469818138259514635274228,
+    579674206018121414525577, 1469948983537180043595558, 579622481410148464616622,
+    1811813622156643457511285, 1089338853750612068062242],
+  ![1187681941255603213265820, 1187926886977058350382076, 2272778993491518995385378,
+    925398107160633602067354, 2273024572012999203165978, 924927454379666643263292,
+    1089338853750612068062242, 2759791570124841361802976]]
+
+/-- Exact integer matrix after 4 fraction-free Schur steps in moment block 1. -/
+def momentBlock1Stage4 : Fin 7 → Fin 7 → ℤ :=
+  ![![6388701539298208968258340727, 3836964628320547655398172186, 1896127809632242774168018905,
+    3880482452329512721633214326, 1885543361657211113613801066, 1726043411418072396716851943,
+    2652632149921893241204577604],
+  ![3836964628320547655398172186, 11901697082592072773671087244, 3966986060951734345637487294,
+    7503084885820699016996835850, 3967846140718111902810435912, 3217462538067429628784836952,
+    5000439610387889732488128462],
+  ![1896127809632242774168018905, 3966986060951734345637487294, 8193944569903493237516266683,
+    3987912272975865234796740696, 3801533003144797114415358336, 1012792824940068467188311843,
+    1695926775744948244815446046],
+  ![3880482452329512721633214326, 7503084885820699016996835850, 3987912272975865234796740696,
+    11939363329229270452260767522, 3972925070334038424319162314, 3229277713405522757927486572,
+    5018779793290138678116711522],
+  ![1885543361657211113613801066, 3967846140718111902810435912, 3801533003144797114415358336,
+    3972925070334038424319162314, 8186587560632525972682653244, 1010253914249320953138465048,
+    1690442144041308751050458208],
+  ![1726043411418072396716851943, 3217462538067429628784836952, 1012792824940068467188311843,
+    3229277713405522757927486572, 1010253914249320953138465048, 6111357980468335959498984065,
+    2534981845860472950687857178],
+  ![2652632149921893241204577604, 5000439610387889732488128462, 1695926775744948244815446046,
+    5018779793290138678116711522, 1690442144041308751050458208, 2534981845860472950687857178,
+    8287068772095160817902922184]]
+
+/-- Exact integer matrix after 5 fraction-free Schur steps in moment block 1. -/
+def momentBlock1Stage5 : Fin 6 → Fin 6 → ℤ :=
+  ![![30910369735653223417949121811512, 9108908586471128600269979137188,
+    16659378529867100384474552357429, 9132152553111458125305642689178,
+    7023883812784242661746054790041, 10974067277872033740588326976205],
+  ![9108908586471128600269979137188, 24578110601697782748440362059326,
+    9134708006729155153290827218257, 10441385752058049772346963254387,
+    1612027314677383154724829427931, 2926504120335916135547315920967],
+  ![16659378529867100384474552357429, 9134708006729155153290827218257,
+    30862372329039645102608275293973, 9107144109198882876018250051557,
+    7024070329092434509137562758461, 10974941026442257804267794349115],
+  ![9132152553111458125305642689178, 10441385752058049772346963254387,
+    9107144109198882876018250051557, 24574594367359960123348199569152,
+    1613060216764024204165705361313, 2922993838109656780945379722172],
+  ![7023883812784242661746054790041, 1612027314677383154724829427931,
+    7024070329092434509137562758461, 1613060216764024204165705361313,
+    18181210689469626476359625365091, 5856337196018697807164788233149],
+  ![10974067277872033740588326976205, 2926504120335916135547315920967,
+    10974941026442257804267794349115, 2922993838109656780945379722172,
+    5856337196018697807164788233149, 23143244319142747269387066438772]]
+
+/-- Exact integer matrix after 6 fraction-free Schur steps in moment block 1. -/
+def momentBlock1Stage6 : Fin 5 → Fin 5 → ℤ :=
+  ![![105928609483909163009389834691827584, 20443660574195181264682375102637916,
+    37497940680292044387973737524883840, -2215090995399726959885384710076868,
+    -1487383814218449834259658212210068],
+  ![20443660574195181264682375102637916, 105879487787578960217221708185780505,
+    20249686838657465620457623390132986, 15668766355533316139320066243769709,
+    24483589223547230933205943117851905],
+  ![37497940680292044387973737524883840, 20249686838657465620457623390132986,
+    105845230613133102216525870609458820, -2235648464679397203615324104118846,
+    -1544294435722564946115527023401438],
+  ![-2215090995399726959885384710076868, 15668766355533316139320066243769709,
+    -2235648464679397203615324104118846, 80243692350376820334814092439452993,
+    16269499188964114464497532019095429],
+  ![-1487383814218449834259658212210068, 24483589223547230933205943117851905,
+    -1544294435722564946115527023401438, 16269499188964114464497532019095429,
+    93123161648485719773585326557627457]]
+
+/-- Exact integer matrix after 7 fraction-free Schur steps in moment block 1. -/
+def momentBlock1Stage7 : Fin 4 → Fin 4 → ℤ :=
+  ![![349323665451965264283586650187605360322, 44594290187816015560664354844532120032,
+    55161268383475024443974654854009359762, 84888021525038038066651065966398066234],
+  ![44594290187816015560664354844532120032, 317237956968842946548522942445683365440,
+    -4974310683641765843566986833905578912, -3487862911296267424287321140207185056],
+  ![55161268383475024443974654854009359762, -4974310683641765843566986833905578912,
+    274833209536585530728217894243784859874, 55648339062374115739709093375458375626],
+  ![84888021525038038066651065966398066234, -3487862911296267424287321140207185056,
+    55648339062374115739709093375458375626, 319057804804681848889483082026913725522]]
+
+/-- Exact integer matrix after 8 fraction-free Schur steps in moment block 1. -/
+def momentBlock1Stage8 : Fin 3 → Fin 3 → ℤ :=
+  ![![1027390765929250487667117036395703368307359, -39625952525742478153319454076821262737822,
+    -47238551950266101258519097711251342023780],
+  ![-39625952525742478153319454076821262737822, 877600291993785071511487467969136482002176,
+    139308454171099711761775036613463008355896],
+  ![-47238551950266101258519097711251342023780, 139308454171099711761775036613463008355896,
+    984138904257299960968477274638393989292742]]
+
+/-- Exact integer matrix after 9 fraction-free Schur steps in moment block 1. -/
+def momentBlock1Stage9 : Fin 2 → Fin 2 → ℤ :=
+  ![![2576602472360758911423274480933654344737594750,
+    404359511776974814588039016464831077827114632],
+  ![404359511776974814588039016464831077827114632, 2888048654047028442742867641207330953640496149]]
+
+/-- Exact integer matrix after 10 fraction-free Schur steps in moment block 1. -/
+def momentBlock1Stage10 : Fin 1 → Fin 1 → ℤ :=
+  ![![7083815553830273222944915207836617157660525052714]]
+
+/-- Exact integer matrix after 11 fraction-free Schur steps in moment block 1. -/
+def momentBlock1Stage11 : Fin 0 → Fin 0 → ℤ := fun i => Fin.elim0 i
+
+theorem momentBlock1Stage10_psd : IsPSD (fun i j => (momentBlock1Stage10 i j : ℝ)) := by
+  apply integer_schur_step momentBlock1Stage10 momentBlock1Stage11
+    (2576602472360758911423274480933654344737594750)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact quadraticForm_zero _
+
+theorem momentBlock1Stage9_psd : IsPSD (fun i j => (momentBlock1Stage9 i j : ℝ)) := by
+  apply integer_schur_step momentBlock1Stage9 momentBlock1Stage10
+    (1027390765929250487667117036395703368307359)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock1Stage10_psd
+
+theorem momentBlock1Stage8_psd : IsPSD (fun i j => (momentBlock1Stage8 i j : ℝ)) := by
+  apply integer_schur_step momentBlock1Stage8 momentBlock1Stage9
+    (349323665451965264283586650187605360322)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock1Stage9_psd
+
+theorem momentBlock1Stage7_psd : IsPSD (fun i j => (momentBlock1Stage7 i j : ℝ)) := by
+  apply integer_schur_step momentBlock1Stage7 momentBlock1Stage8
+    (105928609483909163009389834691827584)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock1Stage8_psd
+
+theorem momentBlock1Stage6_psd : IsPSD (fun i j => (momentBlock1Stage6 i j : ℝ)) := by
+  apply integer_schur_step momentBlock1Stage6 momentBlock1Stage7 (30910369735653223417949121811512)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock1Stage7_psd
+
+theorem momentBlock1Stage5_psd : IsPSD (fun i j => (momentBlock1Stage5 i j : ℝ)) := by
+  apply integer_schur_step momentBlock1Stage5 momentBlock1Stage6 (6388701539298208968258340727)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock1Stage6_psd
+
+theorem momentBlock1Stage4_psd : IsPSD (fun i j => (momentBlock1Stage4 i j : ℝ)) := by
+  apply integer_schur_step momentBlock1Stage4 momentBlock1Stage5 (1983609171847332477984066)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock1Stage5_psd
+
+theorem momentBlock1Stage3_psd : IsPSD (fun i j => (momentBlock1Stage3 i j : ℝ)) := by
+  apply integer_schur_step momentBlock1Stage3 momentBlock1Stage4 (490373567429017047174)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock1Stage4_psd
+
+theorem momentBlock1Stage2_psd : IsPSD (fun i j => (momentBlock1Stage2 i j : ℝ)) := by
+  apply integer_schur_step momentBlock1Stage2 momentBlock1Stage3 (394164000270807)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock1Stage3_psd
+
+theorem momentBlock1Stage1_psd : IsPSD (fun i j => (momentBlock1Stage1 i j : ℝ)) := by
+  apply integer_schur_step momentBlock1Stage1 momentBlock1Stage2 (148973087)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock1Stage2_psd
+
+theorem momentBlock1Stage0_psd : IsPSD (fun i j => (momentBlock1Stage0 i j : ℝ)) := by
+  apply integer_schur_step momentBlock1Stage0 momentBlock1Stage1 (1)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock1Stage1_psd
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/MomentBlock2.lean b/LeanPool/PersistentSOS/MomentBlock2.lean
new file mode 100644
index 0000000000..28e2f09854
--- /dev/null
+++ b/LeanPool/PersistentSOS/MomentBlock2.lean
@@ -0,0 +1,336 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.PSD
+
+/-!
+# Exact moment block certificate
+
+Generated by `scripts/generate_moments.py`; all identities below are checked
+by the Lean kernel with integer arithmetic. No external verifier is trusted.
+-/
+
+@[expose] public section
+
+
+namespace PersistentSOS
+
+
+/-- Exact integer matrix after 0 fraction-free Schur steps in moment block 2. -/
+def momentBlock2Stage0 : Fin 11 → Fin 11 → ℤ :=
+  ![![162381159, 86495040, 7457187, 4162390, 3349614, 30621436, 3504174, 3462345, 5800689,
+    10073399, 5911137],
+  ![86495040, 48848306, 3269119, 1964655, 1411787, 15833908, 1503644, 1400984, 2688879, 4832959,
+    2789333],
+  ![7457187, 3269119, 1189529, 623959, 608339, 604148, 604133, 583593, 883143, 1220643, 651390],
+  ![4162390, 1964655, 623959, 335974, 318998, 317179, 317183, 301842, 470216, 651390, 344016],
+  ![3349614, 1411787, 608339, 318998, 315848, 196997, 310742, 299603, 451763, 615867, 326209],
+  ![30621436, 15833908, 604148, 317179, 196997, 7147237, 236820, 297238, 449043, 1128524, 777072],
+  ![3504174, 1503644, 604133, 317183, 310742, 236820, 310383, 297238, 449043, 615337, 326753],
+  ![3462345, 1400984, 583593, 301842, 299603, 297238, 297238, 293173, 429020, 591740, 318788],
+  ![5800689, 2688879, 883143, 470216, 451763, 449043, 449043, 429020, 665471, 918271, 486284],
+  ![10073399, 4832959, 1220643, 651390, 615867, 1128524, 615337, 591740, 918271, 1311685, 705658],
+  ![5911137, 2789333, 651390, 344016, 326209, 777072, 326753, 318788, 486284, 705658, 389139]]
+
+/-- Exact integer matrix after 1 fraction-free Schur steps in moment block 2. -/
+def momentBlock2Stage1 : Fin 10 → Fin 10 → ℤ :=
+  ![![450652598865054, -114166355723559, -41003133610455, -60477387593427, -77473999138068,
+    -58930214853564, -71982263608344, -65107538651799, -86517565621479, -58348905883533],
+  ![-114166355723559, 137547459731142, 70279464991551, 73804093909083, -130247522013000,
+    71968535931609, 68945153600772, 100148961300894, 123090204996624, 61693009169391],
+  ![-41003133610455, 70279464991551, 37230357001766, 37856865141222, -75954465361579,
+    36918804339237, 34601823590328, 52209489173634, 63844047897400, 31257259257114],
+  ![-60477387593427, 73804093909083, 37856865141222, 40067850358836, -70581389546181,
+    38721015821142, 37052363095047, 53927730449271, 66263198931867, 33170168245113],
+  ![-77473999138068, -130247522013000, -75954465361579, -70581389546181, 222904285005587,
+    -68847733799484, -57756124888578, -104709304188567, -125210907701648, -54825651346284],
+  ![-58930214853564, 71968535931609, 36918804339237, 38721015821142, -68847733799484,
+    38121115851621, 36133191610812, 52589499204951, 64620192368157, 32344878260889],
+  ![-71982263608344, 68945153600772, 34601823590328, 37052363095047, -57756124888578,
+    36133191610812, 35617938628482, 49580778278475, 61209844366005, 31298769279027],
+  ![-65107538651799, 100148961300894, 52209489173634, 53927730449271, -104709304188567,
+    52589499204951, 49580778278475, 74411959386168, 90677254484178, 44674692149763],
+  ![-86517565621479, 123090204996624, 63844047897400, 66263198931867, -125210907701648,
+    64620192368157, 61209844366005, 90677254484178, 111519563129714, 55040322352959],
+  ![-58348905883533, 61693009169391, 31257259257114, 33170168245113, -54825651346284,
+    32344878260889, 31298769279027, 44674692149763, 55040322352959, 28247301199332]]
+
+/-- Exact integer matrix after 2 fraction-free Schur steps in moment block 2. -/
+def momentBlock2Stage2 : Fin 9 → Fin 9 → ℤ :=
+  ![![301464552398762538693, 166216606495192061751, 162306538172855483571, -415943012426799800868,
+    158300138024355818790, 140732829332995712688, 232165477189856421765, 280780885444244985465,
+    130191415672872290913],
+  ![166216606495192061751, 92970762535589386021, 89792019878802583017, -230357722404209330234,
+    87579321004440436542, 77853264701328588888, 128455351615808365149, 155338186767095835545,
+    72013755817882934199],
+  ![162306538172855483571, 89792019878802583017, 88675105989482017785, -224737352101169506590,
+    85513498310660513760, 76021408781670853350, 125415646451687197179, 151676010996004736115,
+    70324865261495286129],
+  ![-415943012426799800868, -230357722404209330234, -224737352101169506590, 581657227815938351686,
+    -219187803539929546632, -194632812111910900356, -321660848912406196050,
+    -388773446101504191796, -179995299502698325620],
+  ![158300138024355818790, 87579321004440436542, 85513498310660513760, -219187803539929546632,
+    84410099003429300682, 74156303100508117848, 122322031513432057602, 147940555709351726958,
+    68590407635016521166],
+  ![140732829332995712688, 77853264701328588888, 76021408781670853350, -194632812111910900356,
+    74156303100508117848, 66940465272576884388, 108738715030495226766, 131521694732749968066,
+    60997134478540724334],
+  ![232165477189856421765, 128455351615808365149, 125415646451687197179, -321660848912406196050,
+    122322031513432057602, 108738715030495226766, 180408561406572771369, 216964793578562195949,
+    100589333000663059065],
+  ![280780885444244985465, 155338186767095835545, 151676010996004736115, -388773446101504191796,
+    147940555709351726958, 131521694732749968066, 216964793578562195949, 263400582007387595485,
+    121663493096580428481],
+  ![130191415672872290913, 72013755817882934199, 70324865261495286129, -179995299502698325620,
+    68590407635016521166, 60997134478540724334, 100589333000663059065, 121663493096580428481,
+    57427382191535722521]]
+
+/-- Exact integer matrix after 3 fraction-free Schur steps in moment block 2. -/
+def momentBlock2Stage3 : Fin 8 → Fin 8 → ℤ :=
+  ![![886334707026019035703788, 202082701617548993686740, -683567910157418986844061,
+    199597330823719926200154, 172785604625233657970124, 299515224344444639160273,
+    351736564527657982888305, 154485642415908136525986],
+  ![202082701617548993686740, 863167777918241564336166, -532727060453868102806523,
+    191147454767044031940585, 168426044742867297975513, 280475105975236468929708,
+    338103593232504908354670, 154300787453444143625631],
+  ![-683567910157418986844061, -532727060453868102806523, 5193460000564225186373481,
+    -518174772745356954162264, -306348184087754299282806, -891453591395931551050845,
+    -915484768111792786820352, -244074419308775174013744],
+  ![199597330823719926200154, 191147454767044031940585, -518174772745356954162264,
+    860350115477851307537769, 171907171877892638350836, 274999845494127780767034,
+    335470134866262316752936, 151463602138006344087792],
+  ![172785604625233657970124, 168426044742867297975513, -306348184087754299282806,
+    171907171877892638350836, 830902006634885998653510, 238684026192585016762917,
+    297436212462500259024867, 147047994033225375060117],
+  ![299515224344444639160273, 280475105975236468929708, -891453591395931551050845,
+    274999845494127780767034, 238684026192585016762917, 1078385913600173673631398,
+    487218154406696488537758, 217830993689687594508900],
+  ![351736564527657982888305, 338103593232504908354670, -915484768111792786820352,
+    335470134866262316752936, 297436212462500259024867, 487218154406696488537758,
+    1260467435463556324824720, 270650874018907705214922],
+  ![154485642415908136525986, 154300787453444143625631, -244074419308775174013744,
+    151463602138006344087792, 147047994033225375060117, 217830993689687594508900,
+    270650874018907705214922, 804423082903201858728546]]
+
+/-- Exact integer matrix after 4 fraction-free Schur steps in moment block 2. -/
+def momentBlock2Stage4 : Fin 7 → Fin 7 → ℤ :=
+  ![![2402332663989154152910936856, -1108048128281066334499621088, 428194474090142027269377140,
+    379364228163566411059252588, 623847724964937508678637388, 758275134558375396484602820,
+    350101749678667532912443516],
+  ![-1108048128281066334499621088, 13719287151159723008777240999, -1070898560101111002294713366,
+    -508903392162286480742313148, -1941811258185411341087551299, -1894053847617048504396487447,
+    -367307533552242765544907182],
+  ![428194474090142027269377140, -1070898560101111002294713366, 2397360045548347288112323592,
+    391023576059379220504185304, 610219233751525346744811750, 753432343745016656165615086,
+    343033782003342887585190364],
+  ![379364228163566411059252588, -508903392162286480742313148, 391023576059379220504185304,
+    2343898862502734248047864728, 530085597204807833532963408, 672891793237571033242217432,
+    343791151413255532173931124],
+  ![623847724964937508678637388, -1941811258185411341087551299, 610219233751525346744811750,
+    530085597204807833532963408, 2872979546968614039130329915, 1083005950488364968151665723,
+    486957312091403513888767254],
+  ![758275134558375396484602820, -1894053847617048504396487447, 753432343745016656165615086,
+    672891793237571033242217432, 1083005950488364968151665723, 3295503290176505346709408595,
+    615491979143967927027674942],
+  ![350101749678667532912443516, -367307533552242765544907182, 343033782003342887585190364,
+    343791151413255532173931124, 486957312091403513888767254, 615491979143967927027674942,
+    2285914805949667393515520964]]
+
+/-- Exact integer matrix after 5 fraction-free Schur steps in moment block 2. -/
+def momentBlock2Stage5 : Fin 6 → Fin 6 → ℤ :=
+  ![![35799704946405830565911300019550, -2367271064262160009575892059052,
+    -905077294721532914274365507288, -4483208518589852780080384399350,
+    -4185712296389158313621400084894, -557876492055224911276625008668],
+  ![-2367271064262160009575892059052, 6290970885966110286789468124004,
+    876561683562026943594571963708, 1352560651669073078861560118360,
+    1675784435893810102394884867232, 760626453452058176595203933588],
+  ![-905077294721532914274365507288, 876561683562026943594571963708,
+    6190559319602646279128014743748, 1169734667935046779625707217108,
+    1499261466953342762946024873964, 781967158784178070604701190572],
+  ![-4483208518589852780080384399350, 1352560651669073078861560118360,
+    1169734667935046779625707217108, 7347863705533931156258537561242,
+    2401680015108114280893343697506, 1073435654973543541900311282032],
+  ![-4185712296389158313621400084894, 1675784435893810102394884867232,
+    1499261466953342762946024873964, 2401680015108114280893343697506,
+    8283455403907247377602450418090, 1368718865410015303622369114664],
+  ![-557876492055224911276625008668, 760626453452058176595203933588,
+    781967158784178070604701190572, 1073435654973543541900311282032,
+    1368718865410015303622369114664, 6057482041198732628941501132156]]
+
+/-- Exact integer matrix after 6 fraction-free Schur steps in moment block 2. -/
+def momentBlock2Stage6 : Fin 5 → Fin 5 → ℤ :=
+  ![![91415702972481670310185491673575191, 12170706741163621018320414139954879,
+    15738162752188478863998161771749675, 20848017223827449016245220033373777,
+    10785166483944262300604127038915419],
+  ![12170706741163621018320414139954879, 91911097699071194956417662364531101,
+    15742409994617456735128328912757475, 20765119560881892639511834020129113,
+    11442741726863052680874295279870811],
+  ![15738162752188478863998161771749675, 15742409994617456735128328912757475,
+    101131786477869406359192854954129975, 27978645880542076162670654099710775,
+    14955298915947280926716143519878925],
+  ![20848017223827449016245220033373777, 20765119560881892639511834020129113,
+    27978645880542076162670654099710775, 116147557809548523302373193717115519,
+    19424712381884582783143591279981743],
+  ![10785166483944262300604127038915419, 11442741726863052680874295279870811,
+    14955298915947280926716143519878925, 19424712381884582783143591279981743,
+    90139407775898496645471613298363621]]
+
+/-- Exact integer matrix after 7 fraction-free Schur steps in moment block 2. -/
+def momentBlock2Stage7 : Fin 4 → Fin 4 → ℤ :=
+  ![![230560322128640981995614972808417029443, 34848301529441414263056591324712009048,
+    45936772402500502713934200623612972472, 25552813405375944744383283128360491932],
+  ![34848301529441414263056591324712009048, 251324517908527565862701119650015994212,
+    62279230976810031073860648408133374021, 33447495165776961090198579853398728287],
+  ![45936772402500502713934200623612972472, 62279230976810031073860648408133374021,
+    284445663414725196401913767555511677148, 43320871027593036132592889310766056377],
+  ![25552813405375944744383283128360491932, 33447495165776961090198579853398728287,
+    43320871027593036132592889310766056377, 226924705760351602730999289458383164531]]
+
+/-- Exact integer matrix after 8 fraction-free Schur steps in moment block 2. -/
+def momentBlock2Stage8 : Fin 3 → Fin 3 → ℤ :=
+  ![![620583289781254120751888124686652423276532, 139563561238557148110195081821893729809417,
+    74617301968294747570129174844580910506955],
+  ![139563561238557148110195081821893729809417, 694319407523906574871114096848460568837580,
+    96419541925112656404259559654624399306477],
+  ![74617301968294747570129174844580910506955, 96419541925112656404259559654624399306477,
+    565186125644920708018030247449874013176799]]
+
+/-- Exact integer matrix after 9 fraction-free Schur steps in moment block 2. -/
+def momentBlock2Stage9 : Fin 2 → Fin 2 → ℤ :=
+  ![![1784370487759058228490618359410623583351466997,
+    214358219480647245879310590684659113816959403],
+  ![214358219480647245879310590684659113816959403, 1497123703903514595754913732378980425045337201]]
+
+/-- Exact integer matrix after 10 fraction-free Schur steps in moment block 2. -/
+def momentBlock2Stage10 : Fin 1 → Fin 1 → ℤ :=
+  ![![4230655176739430507011639448708130569138958702359]]
+
+/-- Exact integer matrix after 11 fraction-free Schur steps in moment block 2. -/
+def momentBlock2Stage11 : Fin 0 → Fin 0 → ℤ := fun i => Fin.elim0 i
+
+theorem momentBlock2Stage10_psd : IsPSD (fun i j => (momentBlock2Stage10 i j : ℝ)) := by
+  apply integer_schur_step momentBlock2Stage10 momentBlock2Stage11
+    (1784370487759058228490618359410623583351466997)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact quadraticForm_zero _
+
+theorem momentBlock2Stage9_psd : IsPSD (fun i j => (momentBlock2Stage9 i j : ℝ)) := by
+  apply integer_schur_step momentBlock2Stage9 momentBlock2Stage10
+    (620583289781254120751888124686652423276532)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock2Stage10_psd
+
+theorem momentBlock2Stage8_psd : IsPSD (fun i j => (momentBlock2Stage8 i j : ℝ)) := by
+  apply integer_schur_step momentBlock2Stage8 momentBlock2Stage9
+    (230560322128640981995614972808417029443)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock2Stage9_psd
+
+theorem momentBlock2Stage7_psd : IsPSD (fun i j => (momentBlock2Stage7 i j : ℝ)) := by
+  apply integer_schur_step momentBlock2Stage7 momentBlock2Stage8
+    (91415702972481670310185491673575191)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock2Stage8_psd
+
+theorem momentBlock2Stage6_psd : IsPSD (fun i j => (momentBlock2Stage6 i j : ℝ)) := by
+  apply integer_schur_step momentBlock2Stage6 momentBlock2Stage7 (35799704946405830565911300019550)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock2Stage7_psd
+
+theorem momentBlock2Stage5_psd : IsPSD (fun i j => (momentBlock2Stage5 i j : ℝ)) := by
+  apply integer_schur_step momentBlock2Stage5 momentBlock2Stage6 (2402332663989154152910936856)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock2Stage6_psd
+
+theorem momentBlock2Stage4_psd : IsPSD (fun i j => (momentBlock2Stage4 i j : ℝ)) := by
+  apply integer_schur_step momentBlock2Stage4 momentBlock2Stage5 (886334707026019035703788)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock2Stage5_psd
+
+theorem momentBlock2Stage3_psd : IsPSD (fun i j => (momentBlock2Stage3 i j : ℝ)) := by
+  apply integer_schur_step momentBlock2Stage3 momentBlock2Stage4 (301464552398762538693)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock2Stage4_psd
+
+theorem momentBlock2Stage2_psd : IsPSD (fun i j => (momentBlock2Stage2 i j : ℝ)) := by
+  apply integer_schur_step momentBlock2Stage2 momentBlock2Stage3 (450652598865054)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock2Stage3_psd
+
+theorem momentBlock2Stage1_psd : IsPSD (fun i j => (momentBlock2Stage1 i j : ℝ)) := by
+  apply integer_schur_step momentBlock2Stage1 momentBlock2Stage2 (162381159)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock2Stage2_psd
+
+theorem momentBlock2Stage0_psd : IsPSD (fun i j => (momentBlock2Stage0 i j : ℝ)) := by
+  apply integer_schur_step momentBlock2Stage0 momentBlock2Stage1 (1)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock2Stage1_psd
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/MomentBlock3.lean b/LeanPool/PersistentSOS/MomentBlock3.lean
new file mode 100644
index 0000000000..80a7def34d
--- /dev/null
+++ b/LeanPool/PersistentSOS/MomentBlock3.lean
@@ -0,0 +1,873 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.PSD
+
+/-!
+# Exact moment block certificate
+
+Generated by `scripts/generate_moments.py`; all identities below are checked
+by the Lean kernel with integer arithmetic. No external verifier is trusted.
+-/
+
+@[expose] public section
+
+
+namespace PersistentSOS
+
+
+/-- Exact integer matrix after 0 fraction-free Schur steps in moment block 3. -/
+def momentBlock3Stage0 : Fin 16 → Fin 16 → ℤ :=
+  ![![21035273, 11656848, -2998234, -1514923, 7457187, 10073398, 1370160, 455296, 1065984, 270523,
+    2353567, 1717705, 2833858, 3953065, 1418658, 2037393],
+  ![11656848, 7733555, -1514923, -1319691, 4162390, 5911137, 455296, 126537, 270523, 19998,
+    1717705, 1403748, 1418815, 2037568, 752865, 1065899],
+  ![-2998234, -1514923, 4872560, 2735066, 3269119, 4832959, -166144, 37680, -18413, 127362,
+    -416068, -377759, -906164, -1199593, -442446, -607622],
+  ![-1514923, -1319691, 2735066, 1803955, 1964655, 2789334, 37680, 78319, 127362, 131135, -377759,
+    -364529, -442523, -607709, -233311, -315518],
+  ![7457187, 4162390, 3269119, 1964655, 6925782, 9655915, 608339, 318998, 604148, 317179, 604133,
+    317183, 583593, 883142, 301842, 470215],
+  ![10073398, 5911137, 4832959, 2789334, 9655915, 13722105, 615867, 326209, 615337, 326753,
+    1128523, 777071, 591740, 918271, 318788, 486284],
+  ![1370160, 455296, -166144, 37680, 608339, 615867, 320428, 127678, 309873, 125148, -128470,
+    -210023, 312527, 399703, 124516, 197247],
+  ![455296, 126537, 37680, 78319, 318998, 326209, 127678, 149893, 125148, 156445, -210023,
+    -120298, 124519, 197239, 78020, 105630],
+  ![1065984, 270523, -18413, 127362, 604148, 615337, 309873, 125148, 323490, 131237, -195351,
+    -262558, 231540, 278253, 82775, 129317],
+  ![270523, 19998, 127362, 131135, 317179, 326753, 125148, 156445, 131237, 179693, -262558,
+    -143251, 79784, 130616, 54692, 68507],
+  ![2353567, 1717705, -416068, -377759, 604133, 1128523, -128470, -210023, -195351, -262558,
+    947187, 739214, 231538, 278254, 79776, 130613],
+  ![1717705, 1403748, -377759, -364529, 317183, 777071, -210023, -120298, -262558, -143251,
+    739214, 807060, 82777, 129312, 54684, 68496],
+  ![2833858, 1418815, -906164, -442523, 583593, 591740, 312527, 124519, 231540, 79784, 231538,
+    82777, 673907, 920821, 305305, 478133],
+  ![3953065, 2037568, -1199593, -607709, 883142, 918271, 399703, 197239, 278253, 130616, 278254,
+    129312, 920821, 1395424, 478133, 775732],
+  ![1418658, 752865, -442446, -233311, 301842, 318788, 124516, 78020, 82775, 54692, 79776, 54684,
+    305305, 478133, 185908, 270806],
+  ![2037393, 1065899, -607622, -315518, 470215, 486284, 197247, 105630, 129317, 68507, 130613,
+    68496, 478133, 775732, 270806, 469720]]
+
+/-- Exact integer matrix after 1 fraction-free Schur steps in moment block 3. -/
+def momentBlock3Stage1 : Fin 15 → Fin 15 → ℤ :=
+  ![![26795335390411, 3083139127453, -10100833317939, 629714615894, 6918311205897, -6394471199872,
+    -2645575927407, -6735488300653, -2732782102050, 8697220831649, 9505196309364, -3188691098089,
+    -3219478703056, -700359862839, -1328104061837],
+  ![3083139127453, 93506222690124, 52990766337036, 91125202242245, 131865016341939, 613175900128,
+    2157693033904, 2808746990507, 3490185696208, -1695559365886, -2796182160237, -10564837716000,
+    -13381552356679, -5053503747786, -6672913686844],
+  ![-10100833317939, 52990766337036, 35651694208786, 52624118377416, 73934824496536,
+    2868295984320, 2337199928295, 4293978119058, 3168282039584, -4380790912866, -5065776219702,
+    -5015515450845, -6794735630562, -2758602945569, -3550513750675],
+  ![629714615894, 91125202242245, 52624118377416, 90076077155517, 127995595478369, 2579037601627,
+    3314982604102, 4759176085396, 4654606256066, -4842886652720, -6137216399876, -8856570961557,
+    -10901611860389, -4229869122180, -5302119699796],
+  ![6918311205897, 131865016341939, 73934824496536, 127995595478369, 187174877543261,
+    -847236526989, 2275517554249, 2205700688369, 4148252711415, 30372281113, -957225486207,
+    -16099167064464, -20504715891887, -7584914050760, -10294353875882],
+  ![-6394471199872, 613175900128, 2868295984320, 2579037601627, -847236526989, 4862952031244,
+    2061913218734, 5057694512889, 2261862551724, -5927164883030, -6771421824079, 2691251887591,
+    2991530183519, 675439607588, 1357590100551],
+  ![-2645575927407, 2157693033904, 2337199928295, 3314982604102, 2275517554249, 2061913218734,
+    2945745728173, 2147184094140, 3167695244677, -5489460782111, -3312565487034, 1329046946719,
+    2349161529007, 995262686692, 1294339003662],
+  ![-6735488300653, 2808746990507, 4293978119058, 4759176085396, 2205700688369, 5057694512889,
+    2147184094140, 5668378574514, 2472232933069, -6618126380751, -7354025255054, 1849659824148,
+    1639223777109, 228927993103, 548390058829],
+  ![-2732782102050, 3490185696208, 3168282039584, 4654606256066, 4148252711415, 2261862551724,
+    3167695244677, 2472232933069, 3706708617660, -6159673213875, -3478002602238, 911654453298,
+    1678148215173, 766681532782, 889901780872],
+  ![8697220831649, -1695559365886, -4380790912866, -4842886652720, 30372281113, -5927164883030,
+    -5489460782111, -6618126380751, -6159673213875, 14385059503562, 11506834491687,
+    -1799209631612, -3450654479513, -1660796714238, -2047660818482],
+  ![9505196309364, -2796182160237, -5065776219702, -6137216399876, -957225486207, -6771421824079,
+    -3312565487034, -7354025255054, -3478002602238, 11506834491687, 14026216960355,
+    -3126495262769, -4070086293649, -1286543071158, -2058808083657],
+  ![-3188691098089, -10564837716000, -5015515450845, -8856570961557, -16099167064464,
+    2691251887591, 1329046946719, 1849659824148, 911654453298, -1799209631612, -3126495262769,
+    6145066557447, 8167296244363, 2401898700701, 4283975733115],
+  ![-3219478703056, -13381552356679, -6794735630562, -10901611860389, -20504715891887,
+    2991530183519, 2349161529007, 1639223777109, 1678148215173, -3450654479513, -4070086293649,
+    8167296244363, 13726401896527, 4449610898539, 8263787435291],
+  ![-700359862839, -5053503747786, -2758602945569, -4229869122180, -7584914050760, 675439607588,
+    995262686692, 228927993103, 766681532782, -1660796714238, -1286543071158, 2401898700701,
+    4449610898539, 1898035011920, 2806114261444],
+  ![-1328104061837, -6672913686844, -3550513750675, -5302119699796, -10294353875882,
+    1357590100551, 1294339003662, 548390058829, 889901780872, -2047660818482, -2058808083657,
+    4283975733115, 8263787435291, 2806114261444, 5729718197111]]
+
+/-- Exact integer matrix after 2 fraction-free Schur steps in moment block 3. -/
+def momentBlock3Stage2 : Fin 14 → Fin 14 → ℤ :=
+  ![![118659018648966430435, 68981640077511674931, 115985604694961431281, 166959431578068198156,
+    1718318476444000288, 3136293366358849355, 4565082904304963682, 4846442626646304506,
+    -3434603569415254191, -4955033455080728763, -12990427633413859171, -16573927169006313237,
+    -6334646615815648923, -8305489102607323651],
+  ![68981640077511674931, 40563879054196625525, 67336494464348910954, 97502377447074368123,
+    583185450103498944, 1706825220686181264, 2235508862633783127, 2723606361325316938,
+    -1404097956594900555, -1888673812054102662, -7920071013358042842, -10201276582448330742,
+    -3850290384755568160, -5160482800251559016],
+  ![115985604694961431281, 67336494464348910954, 114722645032329551587, 162837361210126174717,
+    3476677934988022305, 4301918426218506860, 6264009733475451306, 6010980155727389362,
+    -6429369335626137462, -8102311429053304324, -11186297602786373657, -13790407821202598655,
+    -5367162810025866018, -6714234186405479886],
+  ![166959431578068198156, 97502377447074368123, 162837361210126174717, 236153369176104660094,
+    1023849553185396585, 3768725684591823866, 5024926175348594800, 6182950880952864855,
+    -2821748254979311270, -4345514512147742145, -19458850077320995527, -25060639042797472525,
+    -9431539510341298849, -12676442445897011281],
+  ![1718318476444000288, 583185450103498944, 3476677934988022305, 1023849553185396585,
+    4250725376308211300, 1822300911760008490, 4395128830488757531, 2050492486281068868,
+    -4906341972749709474, -5736165858022746557, 2458870087212996741, 2832014148456096749,
+    647493372147714220, 1325609555583905189],
+  ![3136293366358849355, 1706825220686181264, 4301918426218506860, 3768725684591823866,
+    1822300911760008490, 3419645315446611998, 1888032175284726153, 3691403194610218289,
+    -5898796022358200086, -3024186312506851362, 1291941125646244382, 2587520290342265645,
+    1179710969181372443, 1481732496503671551],
+  ![4565082904304963682, 2235508862633783127, 6264009733475451306, 5024926175348594800,
+    4395128830488757531, 1888032175284726153, 5063842165285375765, 2274165337821461933,
+    -5645512034409182168, -6324207660228295174, 1335131888264034607, 1057214220558810847,
+    67360033456640042, 273296485409884246],
+  ![4846442626646304506, 2723606361325316938, 6010980155727389362, 6182950880952864855,
+    2050492486281068868, 3691403194610218289, 2274165337821461933, 4366684596270351120,
+    -6716475713664597975, -3195519062908657266, 747035176318268436, 1719417213303462111,
+    885634234952285324, 961042800497108654],
+  ![-3434603569415254191, -1404097956594900555, -6429369335626137462, -2821748254979311270,
+    -4906341972749709474, -5898796022358200086, -5645512034409182168, -6716475713664597975,
+    14728158926888832197, 10727728522277265777, -973492232437771827, -3064420739949797163,
+    -1826000574585630459, -2059252764811860593],
+  ![-4955033455080728763, -1888673812054102662, -8102311429053304324, -4345514512147742145,
+    -5736165858022746557, -3024186312506851362, -6324207660228295174, -3195519062908657266,
+    10727728522277265777, 13571890929670193833, -2541747582984500431, -3729808984170345635,
+    -1322364349747401654, -2022439322705926983],
+  ![-12990427633413859171, -7920071013358042842, -11186297602786373657, -19458850077320995527,
+    2458870087212996741, 1291941125646244382, 1335131888264034607, 747035176318268436,
+    -973492232437771827, -2541747582984500431, 7344395695941700252, 9915702972793790433,
+    2953441583524119280, 5255727034010102164],
+  ![-16573927169006313237, -10201276582448330742, -13790407821202598655, -25060639042797472525,
+    2832014148456096749, 2587520290342265645, 1057214220558810847, 1719417213303462111,
+    -3064420739949797163, -3729808984170345635, 9915702972793790433, 16992339457709127357,
+    5560851181741029665, 10323381739859534673],
+  ![-6334646615815648923, -3850290384755568160, -5367162810025866018, -9431539510341298849,
+    647493372147714220, 1179710969181372443, 67360033456640042, 885634234952285324,
+    -1826000574585630459, -1322364349747401654, 2953441583524119280, 5560851181741029665,
+    2394453392150569063, 3530290384185808217],
+  ![-8305489102607323651, -5160482800251559016, -6714234186405479886, -12676442445897011281,
+    1325609555583905189, 1481732496503671551, 273296485409884246, 961042800497108654,
+    -2059252764811860593, -2022439322705926983, 5255727034010102164, 10323381739859534673,
+    3530290384185808217, 7214827227821685524]]
+
+/-- Exact integer matrix after 3 fraction-free Schur steps in moment block 3. -/
+def momentBlock3Stage3 : Fin 13 → Fin 13 → ℤ :=
+  ![![2045259467160214510966274, -402864329999712810336111, 1955601838276526422475879,
+    -1841074678192509334874208, -515629092990198230308515, -1852696272849802631418627,
+    -415561243941962464055696, 2624176954431151504863636, 4392486661174064374444653,
+    -1630390139834101988315679, -2507032982343465570063993, -742568264525067764540317,
+    -1470836782400203469499389],
+  ![-402864329999712810336111, 5979248908801644913868344, -1596141638284529919911231,
+    7958063643107878269831177, 5474704235930695290018395, 7978901683008548656262388,
+    5640512631168687709920244, -13604535218525663449377609, -14431607806142715349428067,
+    6693236185799259440879896, 10672779491943104285807352, 3652335187130854394928303,
+    6217975400850230920882011],
+  ![1955601838276526422475879, -1596141638284529919911231, 5458981650379603594506814,
+    -6172734562270524449275023, -2852752738667884923339970, -6192527006716441674054872,
+    -2817521077156384244672601, 8905041767855117293254086, 11630945350504018482563523,
+    -5228284645080437638372179, -7706467315002287054513473, -2295482535499412990860957,
+    -4384885627635445354342189],
+  ![-1841074678192509334874208, 7958063643107878269831177, -6172734562270524449275023,
+    18713491583760721757592196, 7868656389688212682286810, 19170404104903820121512179,
+    8769500020622600310829732, -21506727662619807674031762, -25083973616689734132044741,
+    11721771673206841250403853, 13603983664558948555123061, 3273549935629741785271084,
+    6402868329820953677641773],
+  ![-515629092990198230308515, 5474704235930695290018395, -2852752738667884923339970,
+    7868656389688212682286810, 14776281595648676425615555, 7826534089301146234008495,
+    15779552988951529249780735, -25719902840971691132268055, -12812175570726373123112055,
+    7241643193005342415104625, 13398351279807004257397610, 5965615049143858507102670,
+    7533750608866159041144890],
+  ![-1852696272849802631418627, 7978901683008548656262388, -6192527006716441674054872,
+    19170404104903820121512179, 7826534089301146234008495, 21646699007559827256825841,
+    9245109689444057567874233, -24415132641714866631334238, -27161598299656663591592884,
+    8125586620392760348663897, 7505386686133284350985589, 1377518209755597521390396,
+    2625245702217475707036472],
+  ![-415561243941962464055696, 5640512631168687709920244, -2817521077156384244672601,
+    8769500020622600310829732, 15779552988951529249780735, 9245109689444057567874233,
+    18460619940090117140540324, -29121666008250811589488989, -13254652929358115101892712,
+    5657694555052144406038526, 10611882335434034070659037, 5067635415139816270985798,
+    5758034738534290997460136],
+  ![2624176954431151504863636, -13604535218525663449377609, 8905041767855117293254086,
+    -21506727662619807674031762, -25719902840971691132268055, -24415132641714866631334238,
+    -29121666008250811589488989, 64781140366423243184512874, 46870962609559295028030042,
+    -5976062614939904373666546, -15694747649785976076132852, -8898132179967734970144978,
+    -10183674537544774086969536],
+  ![4392486661174064374444653, -14431607806142715349428067, 11630945350504018482563523,
+    -25083973616689734132044741, -12812175570726373123112055, -27161598299656663591592884,
+    -13254652929358115101892712, 46870962609559295028030042, 59184737913451423427931526,
+    -13657947252291534733621978, -19581760398566192036801696, -7027299311665661550785649,
+    -10491924716650510782498738],
+  ![-1630390139834101988315679, 6693236185799259440879896, -5228284645080437638372179,
+    11721771673206841250403853, 7241643193005342415104625, 8125586620392760348663897,
+    5657694555052144406038526, -5976062614939904373666546, -13657947252291534733621978,
+    26225742858312990029117889, 35875094245691292489791148, 10007813210204606870123197,
+    19247661933708048133095129],
+  ![-2507032982343465570063993, 10672779491943104285807352, -7706467315002287054513473,
+    13603983664558948555123061, 13398351279807004257397610, 7505386686133284350985589,
+    10611882335434034070659037, -15694747649785976076132852, -19581760398566192036801696,
+    35875094245691292489791148, 64996359904552638468975066, 20707155344096789459906084,
+    40578248380123186626275388],
+  ![-742568264525067764540317, 3652335187130854394928303, -2295482535499412990860957,
+    3273549935629741785271084, 5965615049143858507102670, 1377518209755597521390396,
+    5067635415139816270985798, -8898132179967734970144978, -7027299311665661550785649,
+    10007813210204606870123197, 20707155344096789459906084, 9105903636247343269596916,
+    13669858904916925389458702],
+  ![-1470836782400203469499389, 6217975400850230920882011, -4384885627635445354342189,
+    6402868329820953677641773, 7533750608866159041144890, 2625245702217475707036472,
+    5758034738534290997460136, -10183674537544774086969536, -10491924716650510782498738,
+    19247661933708048133095129, 40578248380123186626275388, 13669858904916925389458702,
+    29375380373977915264293049]]
+
+/-- Exact integer matrix after 4 fraction-free Schur steps in moment block 3. -/
+def momentBlock3Stage4 : Fin 12 → Fin 12 → ℤ :=
+  ![![101693203822505537150860699301, -20872257334551476142722120935,
+    130918002411405796037088797286, 92613795600940191466894475299, 131237719133073628129985568489,
+    95811487284022230539860337960, -225584346358402444771555356642,
+    -233836472035509823327579040225, 109832179568058272626876258421,
+    175449025039382247516637378035, 60432143582516249842889822841,
+    102182080370536466281440959841],
+  ![-20872257334551476142722120935, 61863442283627779166846834617, -76053509285885399653768029162,
+    -40673304052723766891301205637, -76203126843049496608139448457,
+    -41715239016526906484094868694, 110242574513558045658577153792,
+    128084205263033203333742532249, -63246812574722269443869927343,
+    -91514046290934912196991009873, -27327796582180146996697212645,
+    -51339188510326072673366200933],
+  ![130918002411405796037088797286, -76053509285885399653768029162,
+    293988524865756744772508744024, 127627318014472877456244558172,
+    301683754830446471459299581698, 144707278481524061577149421080,
+    -329983620828227396260747154700, -364206101140903262368035253966,
+    176745052531884300451650993854, 195585988356294622154277519982, 44902911123716690178757654568,
+    87541653647461176360043522494],
+  ![92613795600940191466894475299, -40673304052723766891301205637, 127627318014472877456244558172,
+    252449892157006527094763659487, 126850778085130924267661928135,
+    270177564553732719254425047770, -431916371638773439629548376038,
+    -201748925117060486518501578765, 117735363635500353915661248599,
+    220045690195910038484288201827, 99599179148255170155615380695,
+    123463590772664053374760135615],
+  ![131237719133073628129985568489, -76203126843049496608139448457,
+    301683754830446471459299581698, 126850778085130924267661928135,
+    344184816826845931392615818003, 152864397127187803045402534870,
+    -379857164064447423926679130624, -399586756571317000575851776811,
+    114599929959435940139846562407, 90222324725979154543104707765, 12149339511486376325512550827,
+    22284819404932246184984141555],
+  ![95811487284022230539860337960, -41715239016526906484094868694, 144707278481524061577149421080,
+    270177564553732719254425047770, 152864397127187803045402534870,
+    316740075744564787686606066456, -492763698276674157255469277118,
+    -213079944994107839261881407360, 91808667562209919612272506884,
+    174131113685647385256742474446, 84747428654895790784991852692, 94096954664069967158267464192],
+  ![-225584346358402444771555356642, 110242574513558045658577153792,
+    -329983620828227396260747154700, -431916371638773439629548376038,
+    -379857164064447423926679130624, -492763698276674157255469277118,
+    1058562066076790443000142646508, 710747642306992691367828139920,
+    -66949537408236698126448995496, -215077904146926552087167964540,
+    -136950050146103218206668113056, -143002369002277192086275828116],
+  ![-233836472035509823327579040225, 128084205263033203333742532249,
+    -364206101140903262368035253966, -201748925117060486518501578765,
+    -399586756571317000575851776811, -213079944994107839261881407360,
+    710747642306992691367828139920, 857534535670768806263355873089,
+    -175061105464266600455073775691, -244715254140662014732515777865,
+    -93637461149792676478293583395, -126396438962419096497386367897],
+  ![109832179568058272626876258421, -63246812574722269443869927343,
+    176745052531884300451650993854, 117735363635500353915661248599,
+    114599929959435940139846562407, 91808667562209919612272506884, -66949537408236698126448995496,
+    -175061105464266600455073775691, 429636764543137606015441424907,
+    583912079128061251553359143003, 162296123433129225307575327581,
+    311551750757775786112235452389],
+  ![175449025039382247516637378035, -91514046290934912196991009873,
+    195585988356294622154277519982, 220045690195910038484288201827, 90222324725979154543104707765,
+    174131113685647385256742474446, -215077904146926552087167964540,
+    -244715254140662014732515777865, 583912079128061251553359143003,
+    1067337379772641970419107592161, 341228697453229607396167384081,
+    668348779874180446341368994561],
+  ![60432143582516249842889822841, -27327796582180146996697212645, 44902911123716690178757654568,
+    99599179148255170155615380695, 12149339511486376325512550827, 84747428654895790784991852692,
+    -136950050146103218206668113056, -93637461149792676478293583395,
+    162296123433129225307575327581, 341228697453229607396167384081,
+    152306400283558634677341312277, 226415252114957267510307690161],
+  ![102182080370536466281440959841, -51339188510326072673366200933, 87541653647461176360043522494,
+    123463590772664053374760135615, 22284819404932246184984141555, 94096954664069967158267464192,
+    -143002369002277192086275828116, -126396438962419096497386367897,
+    311551750757775786112235452389, 668348779874180446341368994561,
+    226415252114957267510307690161, 488095339320032298625590038083]]
+
+/-- Exact integer matrix after 5 fraction-free Schur steps in moment block 3. -/
+def momentBlock3Stage5 : Fin 11 → Fin 11 → ℤ :=
+  ![![2862932851840624615711760636137958, -2445445609947284576026664418405348,
+    -1077193216817131298059384864661778, -2449622038016415522861721252286983,
+    -1096366657442947208717958670106731, 3179286626705773707534522704210953,
+    3982183338839158338709023125317451, -2023863257053246361199153882993692,
+    -2759717998130137642630491812277752, -742055450708193745052439707360565,
+    -1509869986851434762325464858479177],
+  ![-2445445609947284576026664418405348, 6237404999264556069143221458474122,
+    417559611415939933289235610799917, 6599557541088701246680084817822906,
+    1062113769334055736629828372310980, -1967495897249578200786024721946712,
+    -3140863821949115521652273304471184, 1757606386829039488578925472860652,
+    -1505760102270942134829196282117622, -1635652923185934258419174342445367,
+    -2188026843965878877853653575849368],
+  ![-1077193216817131298059384864661778, 417559611415939933289235610799917,
+    8358412943182890047281001716199289, 364471475575458285742886049991476,
+    9095059546021508781524657131888645, -11260545393249097090104726423087020,
+    557380948747728943851467440818865, 880529503124779802951474892184330,
+    2996270731597575232083006384892363, 2215713705260134356085140464559364,
+    1511758212213681250471767522238444],
+  ![-2449622038016415522861721252286983, 6599557541088701246680084817822906,
+    364471475575458285742886049991476, 8692255477793630712100044581339543,
+    1452719952682770013068462163840195, -4412015719928159138355266122364839,
+    -4863486711799475799891225109835639, -1349506379427090704515022231923213,
+    -6772017357690976525550740975065025, -3273653800091152321765599299707253,
+    -5448662461238305343449566554858581],
+  ![-1096366657442947208717958670106731, 1062113769334055736629828372310980,
+    9095059546021508781524657131888645, 1452719952682770013068462163840195,
+    11260415783748299184111811415740444, -13933267602548440626502859250430227,
+    359581706871611425963179699435860, -580301400405165713785231868061274,
+    439024397020045535011350663407079, 1382780045585072546491489110531518,
+    -108150729967472961816046605203732],
+  ![3179286626705773707534522704210953, -1967495897249578200786024721946712,
+    -11260545393249097090104726423087020, -4412015719928159138355266122364839,
+    -13933267602548440626502859250430227, 27752112401260262892699614986414156,
+    9548107450503338266743382514213655, 8785245966101821771174150364799489,
+    8657381996222916917092806745370445, -143915116217339204911808886279591,
+    4160014359299380218217894590834719],
+  ![3982183338839158338709023125317451, -3140863821949115521652273304471184,
+    557380948747728943851467440818865, -4863486711799475799891225109835639,
+    359581706871611425963179699435860, 9548107450503338266743382514213655,
+    15903086717868967766308055607811986, 3852931539163610130345474643705791,
+    7891665130335282812673136653586115, 2253477323906759544145961662035045,
+    5397964672218368418730736042426322],
+  ![-2023863257053246361199153882993692, 1757606386829039488578925472860652,
+    880529503124779802951474892184330, -1349506379427090704515022231923213,
+    -580301400405165713785231868061274, 8785245966101821771174150364799489,
+    3852931539163610130345474643705791, 15464067960810640488785041901930959,
+    19611174962420910373452752665965132, 4824335920542248578322356221758930,
+    10003530319594263330435044068911522],
+  ![-2759717998130137642630491812277752, -1505760102270942134829196282117622,
+    2996270731597575232083006384892363, -6772017357690976525550740975065025,
+    439024397020045535011350663407079, 8657381996222916917092806745370445,
+    7891665130335282812673136653586115, 19611174962420910373452752665965132,
+    38018940173539025035655021637949614, 11782308892605273042945665493542029,
+    24465738026011411105107772847663049],
+  ![-742055450708193745052439707360565, -1635652923185934258419174342445367,
+    2215713705260134356085140464559364, -3273653800091152321765599299707253,
+    1382780045585072546491489110531518, -143915116217339204911808886279591,
+    2253477323906759544145961662035045, 4824335920542248578322356221758930,
+    11782308892605273042945665493542029, 5787276391862792320450104924633004,
+    8238470717230485147298948375015070],
+  ![-1509869986851434762325464858479177, -2188026843965878877853653575849368,
+    1511758212213681250471767522238444, -5448662461238305343449566554858581,
+    -108150729967472961816046605203732, 4160014359299380218217894590834719,
+    5397964672218368418730736042426322, 10003530319594263330435044068911522,
+    24465738026011411105107772847663049, 8238470717230485147298948375015070,
+    19163730522590933557431562057229623]]
+
+/-- Exact integer matrix after 6 fraction-free Schur steps in moment block 3. -/
+def momentBlock3Stage6 : Fin 10 → Fin 10 → ℤ :=
+  ![![116793128793042370409386692146419042172, -14148165658318409599832213660116739858,
+    126888249637802480421504543059857645664, 3536670689518734812582173995915077852,
+    21062999329658724538072884678025586148, 7337073834903506737715185066240538876,
+    812852238459915148188055314735423800, -108754861792982924665981477308718493972,
+    -63892379117197550470317137568374526406, -97907023173485957822067558624963547140],
+  ![-14148165658318409599832213660116739858, 223901194200475412726005396877377415178,
+    -15686976338336078217342010227766965966, 244436649676174943447108223466404573592,
+    -283337315221785827750023838391112098926, 57873337535435533414448862205849869148,
+    3351306246998463987437638620965488564, 55120422918023840906480832589728060298,
+    54517925000517615836793271893948833542, 26566579084180321292610560510719252846],
+  ![126888249637802480421504543059857645664, -15686976338336078217342010227766965966,
+    185702632280053858407360774522424014405, 14488242044304210350753341186852335137,
+    -47626134091749474195994141722815078063, -40995776106487757764098297370283335129,
+    -86743713957878244575853423661533633290, -257127280984649057646493577354558777366,
+    -110036914707199107886338828848928083069, -189764554835767846928413614952412492889],
+  ![3536670689518734812582173995915077852, 244436649676174943447108223466404573592,
+    14488242044304210350753341186852335137, 305190447921128477876376083349544450691,
+    -357982090567113574353694743230384477923, 53055574170608450358823748253230019261,
+    -38156533490858510609187031549156280144, -17393152753787355985702793332603465030,
+    30928729226926479613777805172261667529, -19322819171493999357694379939633219743],
+  ![21062999329658724538072884678025586148, -283337315221785827750023838391112098926,
+    -47626134091749474195994141722815078063, -357982090567113574353694743230384477923,
+    681899755738100870785883747372507442539, 144307463105421780632549760725060886587,
+    310600998768941975820190030192203588538, 330006692595002629983502346366415885166,
+    19147667527657098272982428851389670167, 164319252442806992473294793472676197583],
+  ![7337073834903506737715185066240538876, 57873337535435533414448862205849869148,
+    -40995776106487757764098297370283335129, 53055574170608450358823748253230019261,
+    144307463105421780632549760725060886587, 291776482112982551948233601248927588087,
+    187722267606104878167699259162691042870, 330238493105457660365387058182958608722,
+    92499348631139910975436476850325755425, 211091682548322141147299930502129930403],
+  ![812852238459915148188055314735423800, 3351306246998463987437638620965488564,
+    -86743713957878244575853423661533633290, -38156533490858510609187031549156280144,
+    310600998768941975820190030192203588538, 187722267606104878167699259162691042870,
+    395076211533019498786899723519512871458, 497183521674785151920539828255220670472,
+    121049692320997528331582136076768580960, 251576941578982863057606111681115494992],
+  ![-108754861792982924665981477308718493972, 55120422918023840906480832589728060298,
+    -257127280984649057646493577354558777366, -17393152753787355985702793332603465030,
+    330006692595002629983502346366415885166, 330238493105457660365387058182958608722,
+    497183521674785151920539828255220670472, 995441441322569620388537714473470290308,
+    311565514953631968397606187361090998302, 647800907881957562976506477797519250438],
+  ![-63892379117197550470317137568374526406, 54517925000517615836793271893948833542,
+    -110036914707199107886338828848928083069, 30928729226926479613777805172261667529,
+    19147667527657098272982428851389670167, 92499348631139910975436476850325755425,
+    121049692320997528331582136076768580960, 311565514953631968397606187361090998302,
+    157512368682744000536437827058173001507, 220917233081710343016794176846099460555],
+  ![-97907023173485957822067558624963547140, 26566579084180321292610560510719252846,
+    -189764554835767846928413614952412492889, -19322819171493999357694379939633219743,
+    164319252442806992473294793472676197583, 211091682548322141147299930502129930403,
+    251576941578982863057606111681115494992, 647800907881957562976506477797519250438,
+    220917233081710343016794176846099460555, 517092237466849230879325785408671436005]]
+
+/-- Exact integer matrix after 7 fraction-free Schur steps in moment block 3. -/
+def momentBlock3Stage7 : Fin 9 → Fin 9 → ℤ :=
+  ![![9064114236208252019014403923233385481674894, -12887159355932130420586861638567680995180,
+    9989252277355036606814239894275566548006980, -11454634265596600917873831470031015152551136,
+    2397197089729339600428259983531836117311308, 140733272873322111743027459258696245417776,
+    1711183987094712866247801142927198535341160, 1908308491604406360156624105492793925914122,
+    599940410231296225718673353007443764061824],
+  ![-12887159355932130420586861638567680995180, 1951901718321237668020827255388995590969458,
+    434297704512162004627259879286205190791242, -2876439216749551101450420232010130341667926,
+    -1997606549337381399240649521118213713235194, -3574729720762369158476399083792195363580260,
+    -5669356017657567897623225809133995473443868, -1657168940221778799239068318939315272312898,
+    -3402086531402517055853407715896210248678906],
+  ![9989252277355036606814239894275566548006980, 434297704512162004627259879286205190791242,
+    12445852241342092792946229670188294503462406, -14629872046996110336126904363349191509690694,
+    2155334411476254239924994398853489061077130, -1557597034842641194721806545282455644850896,
+    -575204059216934781523275553114580980710452, 1340663424238298671180332076100357889002550,
+    -667325329602813484890148305397015024114702],
+  ![-11454634265596600917873831470031015152551136, -2876439216749551101450420232010130341667926,
+    -14629872046996110336126904363349191509690694, 27663085428002821751884574284915655411746838,
+    5833032141241484044977935358533340544443302, 12664963945278492207921883321840924387295092,
+    14262722824813893880648255333463788530718276, 1251192858350438566661999607829194281386314,
+    7423707183190467415246991667943862052849262],
+  ![2397197089729339600428259983531836117311308, -1997606549337381399240649521118213713235194,
+    2155334411476254239924994398853489061077130, 5833032141241484044977935358533340544443302,
+    11884196159148205315653130648276756730633486, 7656032521635791699011269233284966294927980,
+    13750769349429829952400279603235355604017532, 3937246182275209224344540965605675482646982,
+    8862383589846809032749555374214389196765382],
+  ![140733272873322111743027459258696245417776, -3574729720762369158476399083792195363580260,
+    -1557597034842641194721806545282455644850896, 12664963945278492207921883321840924387295092,
+    7656032521635791699011269233284966294927980, 16116873330862969684729526868433408391501172,
+    20313442097045328358275821413557697677879648, 4956353537899980291138796601294120469381240,
+    10290860319409777896266593693602206690022128],
+  ![1711183987094712866247801142927198535341160, -5669356017657567897623225809133995473443868,
+    -575204059216934781523275553114580980710452, 14262722824813893880648255333463788530718276,
+    13750769349429829952400279603235355604017532, 20313442097045328358275821413557697677879648,
+    36477663257650664476393207210897315247761424, 10283197678215509778612787270354125270911064,
+    22707773272054186608308781723543044938937732],
+  ![1908308491604406360156624105492793925914122, -1657168940221778799239068318939315272312898,
+    1340663424238298671180332076100357889002550, 1251192858350438566661999607829194281386314,
+    3937246182275209224344540965605675482646982, 4956353537899980291138796601294120469381240,
+    10283197678215509778612787270354125270911064, 4999812078583126687827898408776426429627896,
+    6827300263263823654386247675026792236358890],
+  ![599940410231296225718673353007443764061824, -3402086531402517055853407715896210248678906,
+    -667325329602813484890148305397015024114702, 7423707183190467415246991667943862052849262,
+    8862383589846809032749555374214389196765382, 10290860319409777896266593693602206690022128,
+    22707773272054186608308781723543044938937732, 6827300263263823654386247675026792236358890,
+    17746499038211815681228678785389221600138970]]
+
+/-- Exact integer matrix after 8 fraction-free Schur steps in moment block 3. -/
+def momentBlock3Stage8 : Fin 8 → Fin 8 → ℤ :=
+  ![![151482319693558654989275257032404079755559095541,
+    34807330997783075504088927600833052654107466609,
+    -224499434360850584307166720211448001163033640467,
+    -154766304217424891773141569112433939998546753593,
+    -277413108418882233195425363293067590533529673330,
+    -439800173348158827785261255675464832394379315286,
+    -128399470604199949204455537371790521394402093191,
+    -263963897131795618897588694380876333862233668277],
+  ![34807330997783075504088927600833052654107466609,
+    111525956676198026379802567291872732841333639887,
+    -155690666558167933509153214660223025531926210123,
+    -37759149108940861220791575136632569868972449335,
+    -132919271748007221461317700684542655765567031032,
+    -190997227940186948799745243508241648375042280354,
+    -59169992168793474172685255473656022665684016755,
+    -103102547674301759478184046156684115856876152239],
+  ![-224499434360850584307166720211448001163033640467,
+    -155690666558167933509153214660223025531926210123,
+    1023456786560088074690652658116758188144124155283,
+    687799756948328606250551172713998971962804469883,
+    996708705128567910787389942562381737149116100522,
+    1274731975034411553876429341805903047182449499282,
+    284262706033909216229279571492061556207138132589,
+    634981087597745974024726285930960198730351583711],
+  ![-154766304217424891773141569112433939998546753593,
+    -37759149108940861220791575136632569868972449335,
+    687799756948328606250551172713998971962804469883,
+    873109221054574850781845539340491435278768378835,
+    591282969244216847101149136102964122759362290646,
+    1032051287526674623311315081794327995725694306374,
+    266394589573585602301038330249930078881401674281,
+    675480507058315144858996347141006092767167122603],
+  ![-277413108418882233195425363293067590533529673330,
+    -132919271748007221461317700684542655765567031032,
+    996708705128567910787389942562381737149116100522,
+    591282969244216847101149136102964122759362290646,
+    1250633292016473141647106171239982673430737114986,
+    1574429429843158777505372380377559569089958579216,
+    382354618155800178368098738068761346559293947604,
+    797933088269861269712867706669491035817685051064],
+  ![-439800173348158827785261255675464832394379315286,
+    -190997227940186948799745243508241648375042280354,
+    1274731975034411553876429341805903047182449499282,
+    1032051287526674623311315081794327995725694306374,
+    1574429429843158777505372380377559569089958579216,
+    2805897569370665822297677459442634578663201378648,
+    770101909804685396056561869911379922282873871568,
+    1753521330244704585588144067412031600863963095794],
+  ![-128399470604199949204455537371790521394402093191,
+    -59169992168793474172685255473656022665684016755,
+    284262706033909216229279571492061556207138132589,
+    266394589573585602301038330249930078881401674281,
+    382354618155800178368098738068761346559293947604,
+    770101909804685396056561869911379922282873871568,
+    356846562562545304668778109095372221443189540245,
+    520052495891652915858114228146450938675382043181],
+  ![-263963897131795618897588694380876333862233668277,
+    -103102547674301759478184046156684115856876152239,
+    634981087597745974024726285930960198730351583711,
+    675480507058315144858996347141006092767167122603,
+    797933088269861269712867706669491035817685051064,
+    1753521330244704585588144067412031600863963095794,
+    520052495891652915858114228146450938675382043181,
+    1374193565476639620293626747081504986440213854757]]
+
+/-- Exact integer matrix after 9 fraction-free Schur steps in moment block 3. -/
+def momentBlock3Stage9 : Fin 7 → Fin 7 → ℤ :=
+  ![![1730192264073342495895793425776371098083210814673019,
+    -1739845371901611204078986234191356324644711107637310,
+    -36720799165155602958085510774896208535320113099867,
+    -1156087561942545080382320725378813191901092462865893,
+    -1503117964067782814963819303823594575028721097587110,
+    -495797457932080123876822486084970487609304698374244,
+    -709427769941451017622205243875961765430047197382749],
+  ![-1739845371901611204078986234191356324644711107637310,
+    11543942339992765446837292188196223544666633513926981,
+    7661482755243589482821369866474198461365360838438738,
+    9786357329099774379222549559532772761832160790856818,
+    10410776382356530192585678417326611687389042859904500,
+    1570497151574305352368724767831583150035999915596458,
+    4074161197743206567270512233856854322663023661916818],
+  ![-36720799165155602958085510774896208535320113099867,
+    7661482755243589482821369866474198461365360838438738,
+    11949099317107740285626129729893489888060673971832169,
+    5144983065047880865696875729646046057753212196708634,
+    9738544037912887313164037446591707224776483678846644,
+    2259697784005702460959068902050273061470731114142257,
+    6781758891067660276926035380267592900878195545078123],
+  ![-1156087561942545080382320725378813191901092462865893,
+    9786357329099774379222549559532772761832160790856818,
+    5144983065047880865696875729646046057753212196708634,
+    12410567266314410044295467357747259746032872842098929,
+    12851988183183376406689002084883444692273892109151854,
+    2460281022833206465392599936413230838274847426041861,
+    5256521345168040560919078359966284057190922012782281],
+  ![-1503117964067782814963819303823594575028721097587110,
+    10410776382356530192585678417326611687389042859904500,
+    9738544037912887313164037446591707224776483678846644,
+    12851988183183376406689002084883444692273892109151854,
+    25553482019066893726060715189285368128188133086863238,
+    6640109855156910225040132383418583908950819200916173,
+    16497597793288408346817684420277200365867985808879978],
+  ![-495797457932080123876822486084970487609304698374244,
+    1570497151574305352368724767831583150035999915596458,
+    2259697784005702460959068902050273061470731114142257,
+    2460281022833206465392599936413230838274847426041861,
+    6640109855156910225040132383418583908950819200916173,
+    4144864025447724298910519591798734482335064443776556,
+    4952048553232415488794374703987703955962867971495481],
+  ![-709427769941451017622205243875961765430047197382749,
+    4074161197743206567270512233856854322663023661916818,
+    6781758891067660276926035380267592900878195545078123,
+    5256521345168040560919078359966284057190922012782281,
+    16497597793288408346817684420277200365867985808879978,
+    4952048553232415488794374703987703955962867971495481,
+    15278833254786058031972090330293196860275458333437832]]
+
+/-- Exact integer matrix after 10 fraction-free Schur steps in moment block 3. -/
+def momentBlock3Stage10 : Fin 6 → Fin 6 → ℤ :=
+  ![![111869014481148939340736808825730391515375768350704349879,
+    87085738511665404535770771566630747257012572798410091372,
+    98499060354312752800346060481295497539408424729813372432,
+    101645208217655479629560967764489325863999215773801095400,
+    12243350336667923282322610175478590010039342699999010782,
+    38385915771919762985462510671177133210101718977991453472],
+  ![87085738511665404535770771566630747257012572798410091372,
+    136470651002920961467529820237803461987206796041827785842,
+    58484432088687442920006809552257295092362237888471578715,
+    110866785634313930096066418276702734617150551040934687826,
+    25689503263637291401809099752819005720022564082151158435,
+    77287541141156073260121476552303774519816443307902774194],
+  ![98499060354312752800346060481295497539408424729813372432,
+    58484432088687442920006809552257295092362237888471578715,
+    132927255582005814343088979250403723233372245067412345322,
+    135320574649124356099362460235404736755081400816921499756,
+    24316857084352448932720080241787005087155946835732060487,
+    54624407410444809379644542416010414865699538120718229402],
+  ![101645208217655479629560967764489325863999215773801095400,
+    110866785634313930096066418276702734617150551040934687826,
+    135320574649124356099362460235404736755081400816921499756,
+    276950296117015774428421992034521050814121540879470452742,
+    70921970697083477630225945184132112033404696374814852267,
+    181391877996847949280700951526862927215234206953354503712],
+  ![12243350336667923282322610175478590010039342699999010782,
+    25689503263637291401809099752819005720022564082151158435,
+    24316857084352448932720080241787005087155946835732060487,
+    70921970697083477630225945184132112033404696374814852267,
+    45718844068296403828734933325405380281754357947235408708,
+    54239092917351791826769910346599056268296104544731669363],
+  ![38385915771919762985462510671177133210101718977991453472,
+    77287541141156073260121476552303774519816443307902774194,
+    54624407410444809379644542416010414865699538120718229402,
+    181391877996847949280700951526862927215234206953354503712,
+    54239092917351791826769910346599056268296104544731669363,
+    171188501689124517654902196807344400496355335844172970227]]
+
+/-- Exact integer matrix after 11 fraction-free Schur steps in moment block 3. -/
+def momentBlock3Stage11 : Fin 5 → Fin 5 → ℤ :=
+  ![![4440495741836092287513057898722264213706671688021808838746986,
+    -1176324548242811518894330673122438728642172189730567105397801,
+    2052205467291615237636430402776850445884213050471225149135066,
+    1044761466238392748840809559337734685375988314812716544758919,
+    3065101691763987457930591158770186348901808806094007986803418],
+  ![-1176324548242811518894330673122438728642172189730567105397801,
+    2987168707362317681531002591701264828864822466237136998430706,
+    2962804731304390729756056375686980809044778397288701129695196,
+    875246274648012992025655357756492495304816695049952453657171,
+    1346556702180804253997912165778153124068493575843379523296866],
+  ![2052205467291615237636430402776850445884213050471225149135066,
+    2962804731304390729756056375686980809044778397288701129695196,
+    11935325779717519825067446449660500618237364883329060001492222,
+    3866329315877563462680873877287286955585171541859885666689047,
+    9473158888447804320977131276344166181871564171181566194789792],
+  ![1044761466238392748840809559337734685375988314812716544758919,
+    875246274648012992025655357756492495304816695049952453657171,
+    3866329315877563462680873877287286955585171541859885666689047,
+    2869405039404802707928011974758384041975132097472443381797832,
+    3235306140513921906588049083540114497597342973630092159196367],
+  ![3065101691763987457930591158770186348901808806094007986803418,
+    1346556702180804253997912165778153124068493575843379523296866,
+    9473158888447804320977131276344166181871564171181566194789792,
+    3235306140513921906588049083540114497597342973630092159196367,
+    10216905260691079233007949535817007310431883187614834533558671]]
+
+/-- Exact integer matrix after 12 fraction-free Schur steps in moment block 3. -/
+def momentBlock3Stage12 : Fin 4 → Fin 4 → ℤ :=
+  ![![106202513157848289971966274047979937573828660669068410859251719285,
+    139184040680772946240676581739182279595812121761761574088515464718,
+    45727639053160639506059182235273446177160128248399780487716983275,
+    85679968751958751991351603849321807841563223928199535919958031986],
+  ![139184040680772946240676581739182279595812121761761574088515464718,
+    436110179825547023074250878812727510697217863853600514288082035384,
+    134303084194883061695797915919843893551408675016421153217358610672,
+    319796356678147642914654323489995634799622156687908818782659813956],
+  ![45727639053160639506059182235273446177160128248399780487716983275,
+    134303084194883061695797915919843893551408675016421153217358610672,
+    104140135602129638537349255180156960892512490760589847600083056729,
+    99795846549737578726595230236034884493517157067445758502514543680],
+  ![85679968751958751991351603849321807841563223928199535919958031986,
+    319796356678147642914654323489995634799622156687908818782659813956,
+    99795846549737578726595230236034884493517157067445758502514543680,
+    321566039450976934075295382349335057368021699161188133137253788158]]
+
+/-- Exact integer matrix after 13 fraction-free Schur steps in moment block 3. -/
+def momentBlock3Stage13 : Fin 3 → Fin 3 → ℤ :=
+  ![![6067745922401502328625444274038558155606757810069491076784132267901506,
+    1778803077709926216723739900447799225314220890345630989561643918510495,
+    4962935177262557428887450603830629645589413158884974175319040895960892],
+  ![1778803077709926216723739900447799225314220890345630989561643918510495,
+    2019803118752815443652613167496359705142626603410529417400595263745490,
+    1504477745171556409413805309857340656974253879999338968099304531060025],
+  ![4962935177262557428887450603830629645589413158884974175319040895960892,
+    1504477745171556409413805309857340656974253879999338968099304531060025,
+    6037628690414478021674404166227914552135933371853295248221183870072869]]
+
+/-- Exact integer matrix after 14 fraction-free Schur steps in moment block 3. -/
+def momentBlock3Stage14 : Fin 2 → Fin 2 → ℤ :=
+  ![![85605429459877816923429548248790034896558658105883372936446071122404844919,
+    2831423917173100249711044183552150263367900667872544338127280979443251446],
+  ![2831423917173100249711044183552150263367900667872544338127280979443251446,
+    113030011593840958453271581116979686568293961304830837110433947447214542930]]
+
+/-- Exact integer matrix after 15 fraction-free Schur steps in moment block 3. -/
+def momentBlock3Stage15 : Fin 1 → Fin 1 → ℤ :=
+  ![![1593337269982554074603871830129897271732730708218462268566114724191074361019709]]
+
+/-- Exact integer matrix after 16 fraction-free Schur steps in moment block 3. -/
+def momentBlock3Stage16 : Fin 0 → Fin 0 → ℤ := fun i => Fin.elim0 i
+
+theorem momentBlock3Stage15_psd : IsPSD (fun i j => (momentBlock3Stage15 i j : ℝ)) := by
+  apply integer_schur_step momentBlock3Stage15 momentBlock3Stage16
+    (85605429459877816923429548248790034896558658105883372936446071122404844919)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact quadraticForm_zero _
+
+theorem momentBlock3Stage14_psd : IsPSD (fun i j => (momentBlock3Stage14 i j : ℝ)) := by
+  apply integer_schur_step momentBlock3Stage14 momentBlock3Stage15
+    (6067745922401502328625444274038558155606757810069491076784132267901506)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock3Stage15_psd
+
+theorem momentBlock3Stage13_psd : IsPSD (fun i j => (momentBlock3Stage13 i j : ℝ)) := by
+  apply integer_schur_step momentBlock3Stage13 momentBlock3Stage14
+    (106202513157848289971966274047979937573828660669068410859251719285)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock3Stage14_psd
+
+theorem momentBlock3Stage12_psd : IsPSD (fun i j => (momentBlock3Stage12 i j : ℝ)) := by
+  apply integer_schur_step momentBlock3Stage12 momentBlock3Stage13
+    (4440495741836092287513057898722264213706671688021808838746986)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock3Stage13_psd
+
+theorem momentBlock3Stage11_psd : IsPSD (fun i j => (momentBlock3Stage11 i j : ℝ)) := by
+  apply integer_schur_step momentBlock3Stage11 momentBlock3Stage12
+    (111869014481148939340736808825730391515375768350704349879)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock3Stage12_psd
+
+theorem momentBlock3Stage10_psd : IsPSD (fun i j => (momentBlock3Stage10 i j : ℝ)) := by
+  apply integer_schur_step momentBlock3Stage10 momentBlock3Stage11
+    (1730192264073342495895793425776371098083210814673019)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock3Stage11_psd
+
+theorem momentBlock3Stage9_psd : IsPSD (fun i j => (momentBlock3Stage9 i j : ℝ)) := by
+  apply integer_schur_step momentBlock3Stage9 momentBlock3Stage10
+    (151482319693558654989275257032404079755559095541)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock3Stage10_psd
+
+theorem momentBlock3Stage8_psd : IsPSD (fun i j => (momentBlock3Stage8 i j : ℝ)) := by
+  apply integer_schur_step momentBlock3Stage8 momentBlock3Stage9
+    (9064114236208252019014403923233385481674894)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock3Stage9_psd
+
+theorem momentBlock3Stage7_psd : IsPSD (fun i j => (momentBlock3Stage7 i j : ℝ)) := by
+  apply integer_schur_step momentBlock3Stage7 momentBlock3Stage8
+    (116793128793042370409386692146419042172)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock3Stage8_psd
+
+theorem momentBlock3Stage6_psd : IsPSD (fun i j => (momentBlock3Stage6 i j : ℝ)) := by
+  apply integer_schur_step momentBlock3Stage6 momentBlock3Stage7
+    (2862932851840624615711760636137958)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock3Stage7_psd
+
+theorem momentBlock3Stage5_psd : IsPSD (fun i j => (momentBlock3Stage5 i j : ℝ)) := by
+  apply integer_schur_step momentBlock3Stage5 momentBlock3Stage6 (101693203822505537150860699301)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock3Stage6_psd
+
+theorem momentBlock3Stage4_psd : IsPSD (fun i j => (momentBlock3Stage4 i j : ℝ)) := by
+  apply integer_schur_step momentBlock3Stage4 momentBlock3Stage5 (2045259467160214510966274)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock3Stage5_psd
+
+theorem momentBlock3Stage3_psd : IsPSD (fun i j => (momentBlock3Stage3 i j : ℝ)) := by
+  apply integer_schur_step momentBlock3Stage3 momentBlock3Stage4 (118659018648966430435)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock3Stage4_psd
+
+theorem momentBlock3Stage2_psd : IsPSD (fun i j => (momentBlock3Stage2 i j : ℝ)) := by
+  apply integer_schur_step momentBlock3Stage2 momentBlock3Stage3 (26795335390411)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock3Stage3_psd
+
+theorem momentBlock3Stage1_psd : IsPSD (fun i j => (momentBlock3Stage1 i j : ℝ)) := by
+  apply integer_schur_step momentBlock3Stage1 momentBlock3Stage2 (21035273)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock3Stage2_psd
+
+theorem momentBlock3Stage0_psd : IsPSD (fun i j => (momentBlock3Stage0 i j : ℝ)) := by
+  apply integer_schur_step momentBlock3Stage0 momentBlock3Stage1 (1)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock3Stage1_psd
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/MomentBlock4.lean b/LeanPool/PersistentSOS/MomentBlock4.lean
new file mode 100644
index 0000000000..b6e9b611ce
--- /dev/null
+++ b/LeanPool/PersistentSOS/MomentBlock4.lean
@@ -0,0 +1,336 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.PSD
+
+/-!
+# Exact moment block certificate
+
+Generated by `scripts/generate_moments.py`; all identities below are checked
+by the Lean kernel with integer arithmetic. No external verifier is trusted.
+-/
+
+@[expose] public section
+
+
+namespace PersistentSOS
+
+
+/-- Exact integer matrix after 0 fraction-free Schur steps in moment block 4. -/
+def momentBlock4Stage0 : Fin 11 → Fin 11 → ℤ :=
+  ![![162381048, 86494935, 7457187, 4162390, 3462345, 5800689, 3349612, 3504174, 30621436,
+    10073398, 5911137],
+  ![86494935, 48848296, 3269121, 1964657, 1400984, 2688879, 1411790, 1503645, 15833900, 4832959,
+    2789334],
+  ![7457187, 3269121, 1189513, 623959, 583593, 883142, 608339, 604133, 604148, 1220643, 651390],
+  ![4162390, 1964657, 623959, 335978, 301842, 470215, 318997, 317182, 317179, 651390, 344016],
+  ![3462345, 1400984, 583593, 301842, 293178, 429020, 299603, 297238, 297238, 591740, 318788],
+  ![5800689, 2688879, 883142, 470215, 429020, 665467, 451763, 449043, 449043, 918271, 486285],
+  ![3349612, 1411790, 608339, 318997, 299603, 451763, 315841, 310741, 196996, 615867, 326209],
+  ![3504174, 1503645, 604133, 317182, 297238, 449043, 310741, 310382, 236820, 615337, 326753],
+  ![30621436, 15833900, 604148, 317179, 297238, 449043, 196996, 236820, 7147227, 1128523, 777071],
+  ![10073398, 4832959, 1220643, 651390, 591740, 918271, 615867, 615337, 1128523, 1311683, 705659],
+  ![5911137, 2789334, 651390, 344016, 318788, 486285, 326209, 326753, 777071, 705659, 389138]]
+
+/-- Exact integer matrix after 1 fraction-free Schur steps in moment block 4. -/
+def momentBlock4Stage1 : Fin 10 → Fin 10 → ℤ :=
+  ![![450663716839983, -114165610829037, -41002589874114, -71982055571343, -65107228045023,
+    -60476532459300, -58929851438730, -77473840499460, -86516957878098, -58348432449063],
+  ![-114165610829037, 137544729596655, 70279395732102, 68945088821949, 100148700890973,
+    73804041297828, 71968468872846, -130247589073428, 123090076962438, 61692936865101],
+  ![-41002589874114, 70279395732102, 37230969232844, 34601790085866, 52209274598610,
+    37856675676176, 36918606750876, -75954500568448, 63843979755500, 31257221071338],
+  ![-71982055571343, 68945088821949, 34601790085866, 35618717991519, 49580730657255,
+    37052336763804, 36133158617394, -57756157881996, 61209782145210, 31298733893559],
+  ![-65107228045023, 100148700890973, 52209274598610, 49580730657255, 74411235994695,
+    53927691904956, 52589449361178, -104709354032340, 90677158356786, 44674800553287],
+  ![-60476532459300, 73804041297828, 37856675676176, 37052336763804, 53927691904956,
+    40066692030824, 38720825956080, -70581512551024, 66263154067040, 33170143858188],
+  ![-58929851438730, 71968468872846, 36918606750876, 36133158617394, 52589449361178,
+    38720825956080, 38120919018060, -68847760086504, 64620127569924, 32344841991306],
+  ![-77473840499460, -130247589073428, -75954500568448, -57756157881996, -104709354032340,
+    -70581512551024, -68847760086504, 222901867851800, -125211164727424, -54825899982324],
+  ![-86516957878098, 123090076962438, 63843979755500, 61209782145210, 90677158356786,
+    66263154067040, 64620127569924, -125211164727424, 111519112917380, 55040412317106],
+  ![-58348432449063, 61692936865101, 31257221071338, 31298733893559, 44674800553287,
+    33170143858188, 32344841991306, -54825899982324, 55040412317106, 28247095623855]]
+
+/-- Exact integer matrix after 2 fraction-free Schur steps in moment block 4. -/
+def momentBlock4Stage2 : Fin 9 → Fin 9 → ℤ :=
+  ![![301467646494139068177, 166221910203131669376, 140737942788312597462, 232172287255321507596,
+    162312435008134086663, 158305513534759209846, -415951933782137283828, 280789974004778874186,
+    130196128546582263999],
+  ![166221910203131669376, 92975348943700200722, 77855887631207961837, 128458715051268809646,
+    89794565865802467371, 87581649362299678206, -230362878584656375663, 155342918303117556986,
+    72016154130202701939],
+  ![140737942788312597462, 77855887631207961837, 66945297180599639886, 108742273017031424037,
+    76024381141666215759, 74158972804571326269, -194636821617598448226, 131526183145961558517,
+    60999505569194539206],
+  ![232172287255321507596, 128458715051268809646, 108742273017031424037, 180412021015652939847,
+    125419776107671465851, 122325835952209313358, -321668164606562255475, 216971292802753240008,
+    100593062860996462014],
+  ![162312435008134086663, 89794565865802467371, 76024381141666215759, 125419776107671465851,
+    88675332196361388479, 85516126679543412555, -224742212626590571804, 151681209065715587165,
+    70327600363146480873],
+  ![158305513534759209846, 87581649362299678206, 74158972804571326269, 122325835952209313358,
+    85516126679543412555, 84412484290926157710, -219192509261994438984, 147945315629744131599,
+    68592870865680480246],
+  ![-415951933782137283828, -230362878584656375663, -194636821617598448226,
+    -321668164606562255475, -224742212626590571804, -219192509261994438984, 581666330266147416725,
+    -388782623702924620039, -179999583535656914739],
+  ![280789974004778874186, 155342918303117556986, 131526183145961558517, 216971292802753240008,
+    151681209065715587165, 147945315629744131599, -388782623702924620039, 263407795751901091457,
+    121668065098234498938],
+  ![130196128546582263999, 72016154130202701939, 60999505569194539206, 100593062860996462014,
+    70327600363146480873, 68592870865680480246, -179999583535656914739, 121668065098234498938,
+    57429125192725967802]]
+
+/-- Exact integer matrix after 3 fraction-free Schur steps in moment block 4. -/
+def momentBlock4Stage3 : Fin 8 → Fin 8 → ℤ :=
+  ![![886106827615905712014446, 171528167614799773430739, 297395617506728451966162,
+    200312204820271556888213, 197905556980256095676802, -680396155981087154300881,
+    349302882677004825163142, 153310116932552493377613],
+  ![171528167614799773430739, 831379653163385438692566, 237043800298663621959459,
+    167249024335820376576939, 170723064699066630779367, -302853479742210322436502,
+    295310191126469178521319, 146100269762559952437828],
+  ![297395617506728451966162, 237043800298663621959459, 1074895509381609909128841,
+    278601175312592252669913, 273216375861698075893050, -887652292848856375305789,
+    484118172447509322358320, 216615969393407174389878],
+  ![200312204820271556888213, 167249024335820376576939, 278601175312592252669913,
+    859659046372334890815458, 189480686254209732993039, -528852625576286422095568,
+    335666489641388929834889, 153208499930871574458048],
+  ![197905556980256095676802, 170723064699066630779367, 273216375861698075893050,
+    189480686254209732993039, 858727569902357783945238, -514719522635114957526960,
+    333119967025495950033549, 150370118153814256626036],
+  ![-680396155981087154300881, -302853479742210322436502, -887652292848856375305789,
+    -528852625576286422095568, -514719522635114957526960, 5186946110304578660938427,
+    -910323765334336083392065, -241242803577322334119257],
+  ![349302882677004825163142, 295310191126469178521319, 484118172447509322358320,
+    335666489641388929834889, 333119967025495950033549, -910323765334336083392065,
+    1255745095030691045737571, 268975921542438195523164],
+  ![153310116932552493377613, 146100269762559952437828, 216615969393407174389878,
+    153208499930871574458048, 150370118153814256626036, -241242803577322334119257,
+    268975921542438195523164, 803240442981406599945591]]
+
+/-- Exact integer matrix after 4 fraction-free Schur steps in moment block 4. -/
+def momentBlock4Stage4 : Fin 7 → Fin 7 → ℤ :=
+  ![![2346086828715395401650741595, 527533904253164843175290548, 377623662957745582018772731,
+    389204271424284919437039452, -503050433579999206871716129, 669262839843382241884341968,
+    342204028586809732604440753],
+  ![527533904253164843175290548, 2866072384790090226544849146, 621288665492953031333376196,
+    607835211746114803037228488, -1937879334910464642461282436, 1078388594161744148288705908,
+    485462152429667855192965866],
+  ![377623662957745582018772731, 621288665492953031333376196, 2393705524968747746081089587,
+    425442772442903081504506184, -1102367939096235654614443275, 754531175531677494695725024,
+    348459317326993426237871807],
+  ![389204271424284919437039452, 607835211746114803037228488, 425442772442903081504506184,
+    2394146641148308792466498672, -1066258044057679985373884574, 749834678030268752135877610,
+    341340324508954706656154590],
+  ![-503050433579999206871716129, -1937879334910464642461282436, -1102367939096235654614443275,
+    -1066258044057679985373884574, 13710424590531202892706739753, -1887365930553644700277870344,
+    -363074719300853474331593297],
+  ![669262839843382241884341968, 1078388594161744148288705908, 754531175531677494695725024,
+    749834678030268752135877610, -1887365930553644700277870344, 3286295594657369124606046726,
+    612967052696774031417746074],
+  ![342204028586809732604440753, 485462152429667855192965866, 348459317326993426237871807,
+    341340324508954706656154590, -363074719300853474331593297, 612967052696774031417746074,
+    2283007336916854296136585321]]
+
+/-- Exact integer matrix after 5 fraction-free Schur steps in moment block 4. -/
+def momentBlock4Stage5 : Fin 6 → Fin 6 → ℤ :=
+  ![![7274250069042875989425952632721, 1420131106618857681271704119592,
+    1377616893817306881960321986284, -4831310278387975520212698046468,
+    2456740395492426831538448010226, 1081598859792268654731135672331],
+  ![1420131106618857681271704119592, 6176728586837242224744080109724,
+    960553418233405247441952865758, -2704286977878420578831728391281,
+    1712509282644435956538713923432, 776759025570355013254422210107],
+  ![1377616893817306881960321986284, 960553418233405247441952865758,
+    6167874759097769380584711552416, -2602106770679170199090198499857,
+    1691328019557818763424629473409, 753438241314064648908109763089],
+  ![-4831310278387975520212698046468, -2704286977878420578831728391281,
+    -2602106770679170199090198499857, 36014604350897634611060879883039,
+    -4617108526162142938943977697948, -767016922402567728966876654443],
+  ![2456740395492426831538448010226, 1712509282644435956538713923432,
+    1691328019557818763424629473409, -4617108526162142938943977697948,
+    8195425015101755722309954661751, 1364451159961743236261130886081],
+  ![1081598859792268654731135672331, 776759025570355013254422210107,
+    753438241314064648908109763089, -767016922402567728966876654443,
+    1364451159961743236261130886081, 5912413359815714063274479174991]]
+
+/-- Exact integer matrix after 6 fraction-free Schur steps in moment block 4. -/
+def momentBlock4Stage6 : Fin 5 → Fin 5 → ℤ :=
+  ![![18291861777669679652713073591443732, 2144383193074229817466141101677562,
+    -5460397103244522935103362363162611, 3822674933091700570485120160319944,
+    1753697757198164339454250060921481],
+  ![2144383193074229817466141101677562, 18315108614122175856555223169656624,
+    -5231128084125236348252753140876963, 3801519952853699270220994915265339,
+    1700989608939627756772099350828807],
+  ![-5460397103244522935103362363162611, -5231128084125236348252753140876963,
+    101717326170181956984857170530179501, -9256574234735785864629209937898492,
+    -150861088347112467547705315748221],
+  ![3822674933091700570485120160319944, 3801519952853699270220994915265339,
+    -9256574234735785864629209937898492, 22838028394896709791491841325412441,
+    3097989062053094577789041462836401],
+  ![1753697757198164339454250060921481, 1700989608939627756772099350828807,
+    -150861088347112467547705315748221, 3097989062053094577789041462836401,
+    17833320014099524905954597322277810]]
+
+/-- Exact integer matrix after 7 fraction-free Schur steps in moment block 4. -/
+def momentBlock4Stage7 : Fin 4 → Fin 4 → ℤ :=
+  ![![45423109296167824139980454774235873244, -11544542362900320930730137549419872654,
+    8432429056101463657713029984564110220, 3760341829890853752881814045833145762],
+  ![-11544542362900320930730137549419872654, 251680010557415297051367129707946526891,
+    -20407141890402219804025513434379043160, 937052742619550018215881104158270039],
+  ![8432429056101463657713029984564110220, -20407141890402219804025513434379043160,
+    55419763027599888251155182389572298356, 6868635361847179347392441377103005708],
+  ![3760341829890853752881814045833145762, 937052742619550018215881104158270039,
+    6868635361847179347392441377103005708, 44420959665162199676597844919062816679]]
+
+/-- Exact integer matrix after 8 fraction-free Schur steps in moment block 4. -/
+def momentBlock4Stage8 : Fin 3 → Fin 3 → ℤ :=
+  ![![617696126625814500855683467684510473534684, -45353901758791832536527657931219662598630,
+    4700192672754586381886367456171389178952],
+  ![-45353901758791832536527657931219662598630, 133733357660209025797556385252635052211752,
+    15322986935732779436908292662371406642966],
+  ![4700192672754586381886367456171389178952, 15322986935732779436908292662371406642966,
+    109534937426634636846251044113711090395776]]
+
+/-- Exact integer matrix after 9 fraction-free Schur steps in moment block 4. -/
+def momentBlock4Stage9 : Fin 2 → Fin 2 → ℤ :=
+  ![![1773317632164501301514496095551643881856804297,
+    213066034122946037123107539976065143447902666],
+  ![213066034122946037123107539976065143447902666, 1489048544133425418592595771616076190951643920]]
+
+/-- Exact integer matrix after 10 fraction-free Schur steps in moment block 4. -/
+def momentBlock4Stage10 : Fin 1 → Fin 1 → ℤ :=
+  ![![4201352075396594638551035310421959745045825335501]]
+
+/-- Exact integer matrix after 11 fraction-free Schur steps in moment block 4. -/
+def momentBlock4Stage11 : Fin 0 → Fin 0 → ℤ := fun i => Fin.elim0 i
+
+theorem momentBlock4Stage10_psd : IsPSD (fun i j => (momentBlock4Stage10 i j : ℝ)) := by
+  apply integer_schur_step momentBlock4Stage10 momentBlock4Stage11
+    (1773317632164501301514496095551643881856804297)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact quadraticForm_zero _
+
+theorem momentBlock4Stage9_psd : IsPSD (fun i j => (momentBlock4Stage9 i j : ℝ)) := by
+  apply integer_schur_step momentBlock4Stage9 momentBlock4Stage10
+    (617696126625814500855683467684510473534684)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock4Stage10_psd
+
+theorem momentBlock4Stage8_psd : IsPSD (fun i j => (momentBlock4Stage8 i j : ℝ)) := by
+  apply integer_schur_step momentBlock4Stage8 momentBlock4Stage9
+    (45423109296167824139980454774235873244)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock4Stage9_psd
+
+theorem momentBlock4Stage7_psd : IsPSD (fun i j => (momentBlock4Stage7 i j : ℝ)) := by
+  apply integer_schur_step momentBlock4Stage7 momentBlock4Stage8
+    (18291861777669679652713073591443732)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock4Stage8_psd
+
+theorem momentBlock4Stage6_psd : IsPSD (fun i j => (momentBlock4Stage6 i j : ℝ)) := by
+  apply integer_schur_step momentBlock4Stage6 momentBlock4Stage7 (7274250069042875989425952632721)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock4Stage7_psd
+
+theorem momentBlock4Stage5_psd : IsPSD (fun i j => (momentBlock4Stage5 i j : ℝ)) := by
+  apply integer_schur_step momentBlock4Stage5 momentBlock4Stage6 (2346086828715395401650741595)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock4Stage6_psd
+
+theorem momentBlock4Stage4_psd : IsPSD (fun i j => (momentBlock4Stage4 i j : ℝ)) := by
+  apply integer_schur_step momentBlock4Stage4 momentBlock4Stage5 (886106827615905712014446)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock4Stage5_psd
+
+theorem momentBlock4Stage3_psd : IsPSD (fun i j => (momentBlock4Stage3 i j : ℝ)) := by
+  apply integer_schur_step momentBlock4Stage3 momentBlock4Stage4 (301467646494139068177)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock4Stage4_psd
+
+theorem momentBlock4Stage2_psd : IsPSD (fun i j => (momentBlock4Stage2 i j : ℝ)) := by
+  apply integer_schur_step momentBlock4Stage2 momentBlock4Stage3 (450663716839983)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock4Stage3_psd
+
+theorem momentBlock4Stage1_psd : IsPSD (fun i j => (momentBlock4Stage1 i j : ℝ)) := by
+  apply integer_schur_step momentBlock4Stage1 momentBlock4Stage2 (162381048)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock4Stage2_psd
+
+theorem momentBlock4Stage0_psd : IsPSD (fun i j => (momentBlock4Stage0 i j : ℝ)) := by
+  apply integer_schur_step momentBlock4Stage0 momentBlock4Stage1 (1)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock4Stage1_psd
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/MomentBlock5.lean b/LeanPool/PersistentSOS/MomentBlock5.lean
new file mode 100644
index 0000000000..5bceefb7ad
--- /dev/null
+++ b/LeanPool/PersistentSOS/MomentBlock5.lean
@@ -0,0 +1,873 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.PSD
+
+/-!
+# Exact moment block certificate
+
+Generated by `scripts/generate_moments.py`; all identities below are checked
+by the Lean kernel with integer arithmetic. No external verifier is trusted.
+-/
+
+@[expose] public section
+
+
+namespace PersistentSOS
+
+
+/-- Exact integer matrix after 0 fraction-free Schur steps in moment block 5. -/
+def momentBlock5Stage0 : Fin 16 → Fin 16 → ℤ :=
+  ![![21035497, 11656813, -2998344, -1514904, 7457187, 10073399, 1370265, 455102, 2353878,
+    1717831, 1066067, 270288, 2833858, 3953065, 1418815, 2037568],
+  ![11656813, 7733193, -1514904, -1319551, 4162390, 5911137, 455102, 126242, 1717831, 1403322,
+    270288, 19621, 1418658, 2037393, 752865, 1065899],
+  ![-2998344, -1514904, 4872616, 2735057, 3269121, 4832959, -166195, 37777, -416222, -377821,
+    -18453, 127480, -906164, -1199593, -442523, -607709],
+  ![-1514904, -1319551, 2735057, 1803902, 1964657, 2789333, 37777, 78463, -377821, -364320,
+    127480, 131319, -442446, -607622, -233311, -315518],
+  ![7457187, 4162390, 3269121, 1964657, 6925775, 9655915, 608339, 318997, 604133, 317182, 604148,
+    317179, 583593, 883143, 301842, 470216],
+  ![10073399, 5911137, 4832959, 2789333, 9655915, 13722116, 615867, 326209, 1128524, 777072,
+    615337, 326753, 591740, 918271, 318788, 486285],
+  ![1370265, 455102, -166195, 37777, 608339, 615867, 320439, 127655, -128440, -210027, 309875,
+    125128, 312527, 399703, 124519, 197239],
+  ![455102, 126242, 37777, 78463, 318997, 326209, 127655, 149877, -210027, -120319, 125128,
+    156420, 124516, 197247, 78020, 105630],
+  ![2353878, 1717831, -416222, -377821, 604133, 1128524, -128440, -210027, 947241, 739234,
+    -195332, -262559, 231540, 278253, 79784, 130616],
+  ![1717831, 1403322, -377821, -364320, 317182, 777072, -210027, -120319, 739234, 807044, -262559,
+    -143279, 82775, 129317, 54692, 68507],
+  ![1066067, 270288, -18453, 127480, 604148, 615337, 309875, 125128, -195332, -262559, 323500,
+    131225, 231538, 278254, 82777, 129312],
+  ![270288, 19621, 127480, 131319, 317179, 326753, 125128, 156420, -262559, -143279, 131225,
+    179660, 79776, 130613, 54684, 68496],
+  ![2833858, 1418658, -906164, -442446, 583593, 591740, 312527, 124516, 231540, 82775, 231538,
+    79776, 673877, 920821, 305316, 478132],
+  ![3953065, 2037393, -1199593, -607622, 883143, 918271, 399703, 197247, 278253, 129317, 278254,
+    130613, 920821, 1395420, 478132, 775756],
+  ![1418815, 752865, -442523, -233311, 301842, 318788, 124519, 78020, 79784, 54692, 82777, 54684,
+    305316, 478132, 185909, 270824],
+  ![2037568, 1065899, -607709, -315518, 470216, 486285, 197239, 105630, 130616, 68507, 129312,
+    68496, 478132, 775756, 270824, 469789]]
+
+/-- Exact integer matrix after 1 fraction-free Schur steps in moment block 5. -/
+def momentBlock5Stage1 : Fin 15 → Fin 15 → ℤ :=
+  ![![26790268834952, 3084376770384, -10098458460895, 630907992799, 6919976212702, -6399626109751,
+    -2649475697652, 8696713176193, 9495140988431, -6741301251335, -2737959185507, -3191576671528,
+    -3222565142524, -701971687690, -1329833933981],
+  ![3084376770384, 93507832507816, 52991079999353, 91126796886465, 131867209996879, 612531417245,
+    2159210321257, -1697700654302, -2797004240173, 2808267566907, 3492021560632, -10564728972356,
+    -13381386228361, -5054595796571, -6674131058981],
+  ![-10098458460895, 52991079999353, 35651040980078, 52624458844577, 73935238392197,
+    2870477899729, 2339944041319, -4381753314325, -5061303213816, 4296594320128, 3171820802895,
+    -5014048686030, -6793116777374, -2758444321807, -3550358028974],
+  ![630907992799, 91126796886465, 52624458844577, 90077481282206, 127997750946142, 2578390864928,
+    3316479718435, -4845070512085, -6138105991943, 4758692468027, 4656429743107, -8856440236725,
+    -10901393001084, -4230972287931, -5303298343864],
+  ![6919976212702, 131867209996879, 73935238392197, 127997750946142, 187178162538451,
+    -848157649836, 2277544409175, 27510925106, -958301352785, 2205001365756, 4150692882329,
+    -16099037348562, -20504514152248, -7586425584549, -10295988794987],
+  ![-6399626109751, 612531417245, 2870477899729, 2578390864928, -848157649836, 4862967452958,
+    2061676027505, -5927235872350, -6771906023634, 5057580335120, 2261763482296, 2691024338549,
+    2991204645166, 675166514968, 1357012277263],
+  ![-2649475697652, 2159210321257, 2339944041319, 3316479718435, 2277544409175, 2061676027505,
+    2945619353465, -5489276913975, -3312758287305, 2146960444782, 3167363831364, 1329561500936,
+    2350140889129, 995483931810, 1294678276174],
+  ![8696713176193, -1697700654302, -4381753314325, -4845070512085, 27510925106, -5927235872350,
+    -5489276913975, 14384943574893, 11506589990680, -6618297357830, -6159284033687,
+    -1799997025944, -3451842589329, -1661421321922, -2048614012552],
+  ![9495140988431, -2797004240173, -5061303213816, -6138105991943, -958301352785, -6771906023634,
+    -3312758287305, 11506589990680, 14025628296307, -7354381997500, -3478254079991,
+    -3126875857823, -4070450236466, -1286810988341, -2059118682029],
+  ![-6741301251335, 2808267566907, 4296594320128, 4758692468027, 2205001365756, 5057580335120,
+    2146960444782, -6618297357830, -7354381997500, 5668484431011, 2472237976529, 1849434407900,
+    1638979036883, 228703484564, 547958183008],
+  ![-2737959185507, 3492021560632, 3171820802895, 4656429743107, 4150692882329, 2261763482296,
+    3167363831364, -6159284033687, -3478254079991, 2472237976529, 3706181788076, 912169997568,
+    1679043336941, 766816449228, 890117222928],
+  ![-3191576671528, -10564728972356, -5014048686030, -8856440236725, -16099037348562,
+    2691024338549, 1329561500936, -1799997025944, -3126875857823, 1849434407900, 912169997568,
+    6144586447705, 8167502508267, 2401753563782, 4283565874260],
+  ![-3222565142524, -13381386228361, -6793116777374, -10901393001084, -20504514152248,
+    2991204645166, 2350140889129, -3451842589329, -4070450236466, 1638979036883, 1679043336941,
+    8167502508267, 13726630329515, 4449076333629, 8263774264812],
+  ![-701971687690, -5054595796571, -2758444321807, -4230972287931, -7586425584549, 675166514968,
+    995483931810, -1661421321922, -1286810988341, 228703484564, 766816449228, 2401753563782,
+    4449076333629, 1897652207548, 2805985397608],
+  ![-1329833933981, -6674131058981, -3550358028974, -5303298343864, -10295988794987,
+    1357012277263, 1294678276174, -2048614012552, -2059118682029, 547958183008, 890117222928,
+    4283565874260, 8263774264812, 2805985397608, 5730561745509]]
+
+/-- Exact integer matrix after 2 fraction-free Schur steps in moment block 5. -/
+def momentBlock5Stage2 : Fin 14 → Fin 14 → ℤ :=
+  ![![118636920772367302208, 68968787841361068088, 115964240288652338712, 166928035617574920920,
+    1718463768643384792, 3138400118295891656, -3437322970280504128, -4954439052377648600,
+    4564995828702946632, 4848808378371911216, -12986995476801093280, -16569674078794779848,
+    -6334475247966670456, -8305012066763362264],
+  ![68968787841361068088, 40556308644181710423, 67324037929696297697, 97484076807768057722,
+    583514436761287879, 1708165471431006284, -1405479152838910945, -1887637211582176471,
+    2235752559208415823, 2725144307423875075, -7917935891529853960, -10198587888005642324,
+    -3850077650949640062, -5160054872900767419],
+  ![115964240288652338712, 67324037929696297697, 114701444640470242263, 162807101244805542238,
+    3475713442690353665, 4303247916458304644, -6431393914628983791, -8102117577917802465,
+    6262737284630722377, 6012427705558695181, -11183611379890422224, -13787081287823658236,
+    -5367403749881507666, -6714259496033220597],
+  ![166928035617574920920, 97484076807768057722, 162807101244805542238, 236108860354147194484,
+    1025071525342901890, 3772211125281425232, -2825891074903514142, -4344052372149923706,
+    5025896163610300706, 6186913035806716626, -19453398410502040544, -25053906372578366584,
+    -9430951573220281244, -12675235985599141346],
+  ![1718463768643384792, 583514436761287879, 3475713442690353665, 1025071525342901890,
+    4246393182712055495, 1819648053744123964, -4902975658575952081, -5735820299984151871,
+    4390299374932328615, 2047554980078857155, 2456246604144594960, 2829120916795277164,
+    646313995029614218, 1323680812232223285],
+  ![3138400118295891656, 1708165471431006284, 4303247916458304644, 3772211125281425232,
+    1819648053744123964, 3417756799010562808, -5895628423949890212, -3023106124256953884,
+    1885229222668463652, 3689020146145407012, 1291307983560893728, 2587188607455352280,
+    1179407609294446920, 1481372956554250988],
+  ![-3437322970280504128, -1405479152838910945, -6431393914628983791, -2825891074903514142,
+    -4902975658575952081, -5895628423949890212, 14724809472199777871, 10728917956157010441,
+    -5641834943512233665, -6712350526770292109, -972935288148698072, -3063871807161579308,
+    -1825727123859429142, -2059268475544774443],
+  ![-4954439052377648600, -1887637211582176471, -8102117577917802465, -4344052372149923706,
+    -5735820299984151871, -3023106124256953884, 10728917956157010441, 13576700861738227999,
+    -6323419170987219295, -3193937057549382195, -2541673932070805024, -3729398251990407404,
+    -1321988835011707586, -2022171492324593901],
+  ![4564995828702946632, 2235752559208415823, 6262737284630722377, 5025896163610300706,
+    4390299374932328615, 1885229222668463652, -5641834943512233665, -6323419170987219295,
+    5058833610267148751, 2271137797781871579, 1332579171804116360, 1054617658196556308,
+    66308165589504074, 271690080338120173],
+  ![4848808378371911216, 2725144307423875075, 6012427705558695181, 6186913035806716626,
+    2047554980078857155, 3689020146145407012, -6712350526770292109, -3193937057549382195,
+    2271137797781871579, 4363727938173126399, 746303868834869320, 1718940633982454612,
+    885229809003550258, 960540588231399137],
+  ![-12986995476801093280, -7917935891529853960, -11183611379890422224, -19453398410502040544,
+    2456246604144594960, 1291307983560893728, -972935288148698072, -2541673932070805024,
+    1332579171804116360, 746303868834869320, 7341350725555851208, 9912983000841805496,
+    2952306151193825952, 5253672607923241816],
+  ![-16569674078794779848, -10198587888005642324, -13787081287823658236, -25053906372578366584,
+    2829120916795277164, 2587188607455352280, -3063871807161579308, -3729398251990407404,
+    1054617658196556308, 1718940633982454612, 9912983000841805496, 16988198121865239432,
+    5558689749681453584, 10320804764664156340],
+  ![-6334475247966670456, -3850077650949640062, -5367403749881507666, -9430951573220281244,
+    646313995029614218, 1179407609294446920, -1825727123859429142, -1321988835011707586,
+    66308165589504074, 885229809003550258, 2952306151193825952, 5558689749681453584,
+    2393375756471677468, 3529253308247669358],
+  ![-8305012066763362264, -5160054872900767419, -6714259496033220597, -12675235985599141346,
+    1323680812232223285, 1481372956554250988, -2059268475544774443, -2022171492324593901,
+    271690080338120173, 960540588231399137, 5253672607923241816, 10320804764664156340,
+    3529253308247669358, 7214226098176359431]]
+
+/-- Exact integer matrix after 3 fraction-free Schur steps in moment block 5. -/
+def momentBlock5Stage3 : Fin 13 → Fin 13 → ℤ :=
+  ![![2044842456426383762347120, -403001992177180605199840, 1955427317642786796504808,
+    -1839996730631474301861232, -515118392608053160997528, 2625068087603435059244152,
+    4395558338157005114904816, -1851397232280680918231616, -414841191281096369117304,
+    -1629778244365219166935520, -2506086352924550061634984, -742070857977776684578984,
+    -1470175836140347104838960],
+  ![-403001992177180605199840, 5976840902557179926120880, -1595716040543186312130968,
+    7953171214751817382457408, 5471460461698703236794440, -13601738216042215692351096,
+    -14433319904201960220413760, 7973626363158679408205616, 5636655995545279557071128,
+    6690408669604482886021984, 10669276882334837720573944, 3650592568975361662694872,
+    6215889211870765498795296],
+  ![1955427317642786796504808, -1595716040543186312130968, 5459410849797712407720536,
+    -6168226711704645247256760, -2850417619655059153841432, 8903626802588287938328912,
+    11633693689852587996553976, -6187655015210429046178696, -2814669255381112981350656,
+    -5225690093883678432326176, -7703362808214043782870056, -2294024937471303666969016,
+    -4382621840522140088323144],
+  ![-1839996730631474301861232, 7953171214751817382457408, -6168226711704645247256760,
+    18694321320441055593936048, 7856741430538672472145480, -21491647706744616315760136,
+    -25082467019204026667689584, 19148998553754352955537888, 8756280792647565596170184,
+    11710192865045911059002720, 13591225264185711364041464, 3268435601331525986195448,
+    6394459086579858906100784],
+  ![-515118392608053160997528, 5471460461698703236794440, -2850417619655059153841432,
+    7856741430538672472145480, 14767398928254352691745464, -25705285440079614773437664,
+    -12807000622338979121630536, 7813695628374742111068312, 15768281110584079693644400,
+    7239762776329280442760352, 13398087161655350067217864, 5964904867295249772003448,
+    7532958260969041519453944],
+  ![2625068087603435059244152, -13601738216042215692351096, 8903626802588287938328912,
+    -21491647706744616315760136, -25705285440079614773437664, 64765713111316727316219192,
+    46875818608428150421573064, -24398357635374957460245512, -29102570117032409470486312,
+    -5974801729322088058076608, -15693893956580528245439904, -8897718902648307026752752,
+    -10184753329977934728062168],
+  ![4395558338157005114904816, -14433319904201960220413760, 11633693689852587996553976,
+    -25082467019204026667689584, -12807000622338979121630536, 46875818608428150421573064,
+    59206256119799262222333296, -27158144252810963167346080, -13247188158041047530481480,
+    -13657184581673352591292896, -19579414022408087536045816, -7025702406558959680444344,
+    -10490782192913972965099504],
+  ![-1851397232280680918231616, 7973626363158679408205616, -6187655015210429046178696,
+    19148998553754352955537888, 7813695628374742111068312, -24398357635374957460245512,
+    -27158144252810963167346080, 21624465916144855467494192, 9231187879476614186409960,
+    8114090647855280876925920, 7493656963656579742025000, 1373015325012464568979592,
+    2618294740152044275258816],
+  ![-414841191281096369117304, 5636655995545279557071128, -2814669255381112981350656,
+    8756280792647565596170184, 15768281110584079693644400, -29102570117032409470486312,
+    -13247188158041047530481480, 9231187879476614186409960, 18446560056101307483689368,
+    5655435799106131159531520, 10611054336843896335070032, 5066600720106790577754080,
+    5756754092562278736092760],
+  ![-1629778244365219166935520, 6690408669604482886021984, -5225690093883678432326176,
+    11710192865045911059002720, 7239762776329280442760352, -5974801729322088058076608,
+    -13657184581673352591292896, 8114090647855280876925920, 5655435799106131159531520,
+    26214488447358537640375232, 35865840036727596385298464, 10003136258643038317502368,
+    19239164413754011482689504],
+  ![-2506086352924550061634984, 10669276882334837720573944, -7703362808214043782870056,
+    13591225264185711364041464, 13398087161655350067217864, -15693893956580528245439904,
+    -19579414022408087536045816, 7493656963656579742025000, 10611054336843896335070032,
+    35865840036727596385298464, 64981558277619310521470776, 20698024664414378966341192,
+    40567609108419496575702024],
+  ![-742070857977776684578984, 3650592568975361662694872, -2294024937471303666969016,
+    3268435601331525986195448, 5964904867295249772003448, -8897718902648307026752752,
+    -7025702406558959680444344, 1373015325012464568979592, 5066600720106790577754080,
+    10003136258643038317502368, 20698024664414378966341192, 9100959562370494335913304,
+    13665105565032409720836040],
+  ![-1470175836140347104838960, 6215889211870765498795296, -4382621840522140088323144,
+    6394459086579858906100784, 7532958260969041519453944, -10184753329977934728062168,
+    -10490782192913972965099504, 2618294740152044275258816, 5756754092562278736092760,
+    19239164413754011482689504, 40567609108419496575702024, 13665105565032409720836040,
+    29372618448217153934963376]]
+
+/-- Exact integer matrix after 4 fraction-free Schur steps in moment block 5. -/
+def momentBlock5Stage4 : Fin 12 → Fin 12 → ℤ :=
+  ![![101648688693585509423120042500, -20861522597036660546788504430,
+    130831613919669094321102198760, 92557028965549989882990664410,
+    -225524262955139856147363575230, -233843278969775694000428319720,
+    131145454929668375670509919060, 95744997354007261069041833750, 109780561855224135648339627160,
+    175384125111383512298586817590, 60401353941098410913385960510,
+    102143837644876504442990346640],
+  ![-20861522597036660546788504430, 61868927905174918006141359257, -75988755699452843977421292268,
+    -40639780256446560280643395227, 110196591144005718121619286753,
+    128070383422194134558879790124, -76135716421222815328430040374,
+    -41676430609436681008895839861, -63207979594789661505792908620,
+    -91469784801926187139052467181, -27308985599367121235893575081,
+    -51307376983538611041733873200],
+  ![130831613919669094321102198760, -75988755699452843977421292268,
+    293680531613186283566517550192, 127430669892807387893647371188,
+    -329719590965191531923560070332, -364152071884662536644890921696,
+    301340595773407511397988556056, 144490502433040134421112256844,
+    176561501813521080223688802720, 195392156236743139179442541324, 44826078563907447852548947084,
+    87414125608221485559413889920],
+  ![92557028965549989882990664410, -40639780256446560280643395227, 127430669892807387893647371188,
+    252296310003761499825632323937, -431661896105017265421931905603,
+    -201657844038074966986516322084, 126639225784945225540096516674,
+    269983055389688839936127874911, 117709103195142058011899947460,
+    220049931498889868960493693991, 99589877221247442830639708251,
+    123455650783924859106719448800],
+  ![-225524262955139856147363575230, 110196591144005718121619286753,
+    -329719590965191531923560070332, -431661896105017265421931905603,
+    1058226196439169848935398903817, 710698015429267363974364314556,
+    -379567789477225595121328712326, -492436791290907994851825596429,
+    -66920561777959514612644757740, -215050198480631904452726588389,
+    -136942587043686677743157866609, -143015380341050208901979497280],
+  ![-233843278969775694000428319720, 128070383422194134558879790124,
+    -364152071884662536644890921696, -201657844038074966986516322084,
+    710698015429267363974364314556, 857629584730228318880966987008,
+    -399506338800284640193884032168, -212960298969334148931673804892,
+    -175013017712502281403657614400, -244621725777214458052051188572,
+    -93601879984461906773045952492, -126349816536877870244893798640],
+  ![131145454929668375670509919060, -76135716421222815328430040374,
+    301340595773407511397988556056, 126639225784945225540096516674,
+    -379567789477225595121328712326, -399506338800284640193884032168,
+    343830183939523213184239413748, 152636202523947570837088044942,
+    114421969424036955149807934760, 90052797273946956105396743182, 12085041384749881464549035062,
+    22186354441506043553695668320],
+  ![95744997354007261069041833750, -41676430609436681008895839861, 144490502433040134421112256844,
+    269983055389688839936127874911, -492436791290907994851825596429,
+    -212960298969334148931673804892, 152636202523947570837088044942,
+    316496885786478981758166353393, 91778984251296494109427624540, 174130501978915847109296939513,
+    84733813369824010191994599733, 94083406849685554850085757920],
+  ![109780561855224135648339627160, -63207979594789661505792908620,
+    176561501813521080223688802720, 117709103195142058011899947460,
+    -66920561777959514612644757740, -175013017712502281403657614400,
+    114421969424036955149807934760, 91778984251296494109427624540, 429447439238648094599510295680,
+    583761167898852680870651411500, 162221226357591488673454042060,
+    311412327509464490634687752160],
+  ![175384125111383512298586817590, -91469784801926187139052467181,
+    195392156236743139179442541324, 220049931498889868960493693991,
+    -215050198480631904452726588389, -244621725777214458052051188572,
+    90052797273946956105396743182, 174130501978915847109296939513, 583761167898852680870651411500,
+    1067092601681830374616657914033, 341078525002469364457245973773,
+    668172954466283833159588047280],
+  ![60401353941098410913385960510, -27308985599367121235893575081, 44826078563907447852548947084,
+    99589877221247442830639708251, -136942587043686677743157866609,
+    -93601879984461906773045952492, 12085041384749881464549035062, 84733813369824010191994599733,
+    162221226357591488673454042060, 341078525002469364457245973773,
+    152223770066875741261282926953, 226337747237605137691720955520],
+  ![102143837644876504442990346640, -51307376983538611041733873200, 87414125608221485559413889920,
+    123455650783924859106719448800, -143015380341050208901979497280,
+    -126349816536877870244893798640, 22186354441506043553695668320, 94083406849685554850085757920,
+    311412327509464490634687752160, 668172954466283833159588047280,
+    226337747237605137691720955520, 488051779270745368339675703440]]
+
+/-- Exact integer matrix after 5 fraction-free Schur steps in moment block 5. -/
+def momentBlock5Stage5 : Fin 11 → Fin 11 → ℤ :=
+  ![![2862661741483201582491309929483230, -2442638398091412416238544285491360,
+    -1075926320714608506861293390938260, 3177046456589235716869936075448530,
+    3980678150229254687302693091363920, -2446741972579037363500043969828660,
+    -1094934276226582539883827959990250, -2022071947855214938021244595613010,
+    -2757671513179788833283309819533240, -741308143730053003367607869991360,
+    -1508405502738816320318236884356290],
+  ![-2442638398091412416238544285491360, 6228024898674438391100930962376520,
+    412635708010080036133482683131820, -1960963175979847622344934640581460,
+    -3140333368990886417676140766452940, 6588725132095764319293895057790620,
+    1056706136771485799035786356043500, 1752935556146374509979529990772820,
+    -1508395755399548446427422160544820, -1636260291464019261947097825044480,
+    -2189954475750574414620652905897720],
+  ![-1075926320714608506861293390938260, 412635708010080036133482683131820,
+    8352127768821044436374010612952370, -11249771290200480522360324943642860,
+    560230804167116462974504330978960, 359087598791487815939270751022920,
+    9087033085630345381832218778136500, 882226079533056673143924178214870,
+    3000110554563088039826100471958630, 2216606245711271776271082674016070,
+    1513551748069025757343309633021730],
+  ![3177046456589235716869936075448530, -1960963175979847622344934640581460,
+    -11249771290200480522360324943642860, 27731286510396576477103512999988830,
+    9538235147431749777403953562649620, -4404293337831114458077383490256260,
+    -13919279722426884411092424919787250, 8781015325362951987759220591791390,
+    8652893926042300937464079024090360, -145763586481911905612336706567460,
+    4156108847837812648900796307593810],
+  ![3980678150229254687302693091363920, -3140333368990886417676140766452940,
+    560230804167116462974504330978960, 9538235147431749777403953562649620,
+    15890829854004197082333515357554180, -4861896440893642385847721703551640,
+    362956564137404096819958442747000, 3854381432572983051070784732141460,
+    7896413336553239388209914869864040, 2254424190791677095114098123233560,
+    5400101469471385118566956290796340],
+  ![-2446741972579037363500043969828660, 6588725132095764319293895057790620,
+    359087598791487815939270751022920, -4404293337831114458077383490256260,
+    -4861896440893642385847721703551640, 8680745514761471217278553283272220,
+    1446932299942275778714358986398000, -1352856582448736077739444219917580,
+    -6771710982218044504033950802014920, -3273080725789734016574447182531880,
+    -5448090235664757904472210771106820],
+  ![-1094934276226582539883827959990250, 1056706136771485799035786356043500,
+    9087033085630345381832218778136500, -13919279722426884411092424919787250,
+    362956564137404096819958442747000, 1446932299942275778714358986398000,
+    11249956604326017645907512260103250, -577905746167631031003146169253750,
+    444036453827898070533546229059500, 1383946980798895645909331901037000,
+    -105781514004376252991485052881250],
+  ![-2022071947855214938021244595613010, 1752935556146374509979529990772820,
+    882226079533056673143924178214870, 8781015325362951987759220591791390,
+    3854381432572983051070784732141460, -1352856582448736077739444219917580,
+    -577905746167631031003146169253750, 15454000967587886894313442716371620,
+    19602874199899449470870514079486630, 4821242015032157594245514518102570,
+    9996489843708904891280305589312480],
+  ![-2757671513179788833283309819533240, -1508395755399548446427422160544820,
+    3000110554563088039826100471958630, 8652893926042300937464079024090360,
+    7896413336553239388209914869864040, -6771710982218044504033950802014920,
+    444036453827898070533546229059500, 19602874199899449470870514079486630,
+    38002425120957863687784679021613370, 11774377099748737650832534487006430,
+    24453960687289218362679237777881770],
+  ![-741308143730053003367607869991360, -1636260291464019261947097825044480,
+    2216606245711271776271082674016070, -145763586481911905612336706567460,
+    2254424190791677095114098123233560, -3273080725789734016574447182531880,
+    1383946980798895645909331901037000, 4821242015032157594245514518102570,
+    11774377099748737650832534487006430, 5782852864880184866646845657711270,
+    8234037328967523517523944817400030],
+  ![-1508405502738816320318236884356290, -2189954475750574414620652905897720,
+    1513551748069025757343309633021730, 4156108847837812648900796307593810,
+    5400101469471385118566956290796340, -5448090235664757904472210771106820,
+    -105781514004376252991485052881250, 9996489843708904891280305589312480,
+    24453960687289218362679237777881770, 8234037328967523517523944817400030,
+    19158669014084021699616762774201420]]
+
+/-- Exact integer matrix after 6 fraction-free Schur steps in moment block 5. -/
+def momentBlock5Stage6 : Fin 10 → Fin 10 → ℤ :=
+  ![![116698468136343875412660313821044136732, -14233951353429830531657838647004212566,
+    21119814083599694598774376195236514842, 7217457684001676112186163497615068742,
+    126758009709268426447109075462931666610, 3447793844987239144007156872736286618,
+    775917223771700453977928652212275558, -108747306920362662737617245867144891910,
+    -63894650837585740526857043154267083264, -97921460887782227658632662869036014868],
+  ![-14233951353429830531657838647004212566, 223826784866460536431350758510913106163,
+    -283191277114154432950727187143548736976, 57911890072284257361239349625440476104,
+    -15785425055805574444947305536294629480, 244322220677584187625770749638450388916,
+    3442389849186471418708394747598478091, 55300765923283497229500771974618168965,
+    54578185151553360268745782298265126637, 26659010903854200610478813012969594069],
+  ![21119814083599694598774376195236514842, -283191277114154432950727187143548736976,
+    681677940351707439598024027661249834192, 144201972639320334618738716806050693102,
+    -47561746092777462120377666021412699380, -357776700666927063300398957450435177082,
+    310493854331322568569221113963364907218, 329876945148379341466463704116874274560,
+    19064668653000062671472646751345589906, 164191081697391325458486343951851846672],
+  ![7217457684001676112186163497615068742, 57911890072284257361239349625440476104,
+    144201972639320334618738716806050693102, 291634575012820517160028114877470607262,
+    -41105032210504468192665647894180082660, 53100565178556937124120459215130284108,
+    187734914541331213041086409500190849278, 330374779282640092589020398946150469100,
+    92520259053575573015819093822387540916, 211150197597928801580980029263639248622],
+  ![126758009709268426447109075462931666610, -15785425055805574444947305536294629480,
+    -47561746092777462120377666021412699380, -41105032210504468192665647894180082660,
+    185575357977736282632080520761837455470, 14393260803514385661848676468881998470,
+    -86771990864239396727617013626827217860, -257085742343755765724020101084117212340,
+    -110021219792568223046485273215481841900, -189738980255266459422795125514817172280],
+  ![3447793844987239144007156872736286618, 244322220677584187625770749638450388916,
+    -357776700666927063300398957450435177082, 53100565178556937124120459215130284108,
+    14393260803514385661848676468881998470, 305030391378291799415825161316815299022,
+    -38056413753662302997405748929089422418, -17199856846431794226904278228907755970,
+    30989955884763256420405799946046848124, -19227218822128793774562412413574144532],
+  ![775917223771700453977928652212275558, 3442389849186471418708394747598478091,
+    310493854331322568569221113963364907218, 187734914541331213041086409500190849278,
+    -86771990864239396727617013626827217860, -38056413753662302997405748929089422418,
+    394995772955691224523304685557135052157, 497204523113039430393466929683249104065,
+    121030647997794822855736642679793090619, 251517898560413277692482535834700711303],
+  ![-108747306920362662737617245867144891910, 55300765923283497229500771974618168965,
+    329876945148379341466463704116874274560, 330374779282640092589020398946150469100,
+    -257085742343755765724020101084117212340, -17199856846431794226904278228907755970,
+    497204523113039430393466929683249104065, 995421953821309099632692452808382086915,
+    311482370404568678983118984157375725985, 647757798435482104686936637809368274815],
+  ![-63894650837585740526857043154267083264, 54578185151553360268745782298265126637,
+    19064668653000062671472646751345589906, 92520259053575573015819093822387540916,
+    -110021219792568223046485273215481841900, 30989955884763256420405799946046848124,
+    121030647997794822855736642679793090619, 311482370404568678983118984157375725985,
+    157452241584780133227304640220019986173, 220888932704640400758561366645681277761],
+  ![-97921460887782227658632662869036014868, 26659010903854200610478813012969594069,
+    164191081697391325458486343951851846672, 211150197597928801580980029263639248622,
+    -189738980255266459422795125514817172280, -19227218822128793774562412413574144532,
+    251517898560413277692482535834700711303, 647757798435482104686936637809368274815,
+    220888932704640400758561366645681277761, 517168517560843356338109221534109040697]]
+
+/-- Exact integer matrix after 7 fraction-free Schur steps in moment block 5. -/
+def momentBlock5Stage7 : Fin 9 → Fin 9 → ℤ :=
+  ![![9053684958684183794409184833136244792998952, -11439482823971434483630520003425852178545182,
+    2396707127657573682742026072726714401570670, -13228101135916328074291760269456675584470,
+    9977114725336695161261811283040763052906410, 144189578588406164543942934097887565809028,
+    1713653667984912274043895116528951143433084, 1907217038591733476693678623867054440207082,
+    599881012447755998860464452864987245280214],
+  ![-11439482823971434483630520003425852178545182, 27633276998165600723510332212328289789684946,
+    5825249173926247107538516704132947861085930, -2874069398545466409253367804426308903997886,
+    -14610461676844878784641249152923726030820706, 12651781177589979792118715727976750483681938,
+    14249974590231269160238797699981856620201618, 1248579502832393664611904526838897291502276,
+    7415801335116934610013547429116369931083612],
+  ![2396707127657573682742026072726714401570670, 5825249173926247107538516704132947861085930,
+    11870496598233477873380866472180839110304014, -1995263631771766590478839313783991446648338,
+    2155990076611200710639241162727616650921350, 7651192760763854524833755592702020832563502,
+    13742143952617785026217187263439371269626854, 3932748769664713547883527527626025402797480,
+    8854573434004355488648652921176038738311232],
+  ![-13228101135916328074291760269456675584470, -2874069398545466409253367804426308903997886,
+    -1995263631771766590478839313783991446648338, 1952297364866037776727862957810609233038078,
+    434084119535103769541785860603646791492822, -3571680155506072207018235262683355377348530,
+    -5664979515302657841245796076479810201813086, -1655853701593026766285067441362772381845912,
+    -3398906238409111317795163688270125479642276],
+  ![9977114725336695161261811283040763052906410, -14610461676844878784641249152923726030820706,
+    2155990076611200710639241162727616650921350, 434084119535103769541785860603646791492822,
+    12430631118869609613970770275174964805963566, -1552331638086307045698162099132588811375734,
+    -570189144959308662364733973857568591565842, 1340282684346168930580948174315293887525304,
+    -665874680651590935487717312085456260493100],
+  ![144189578588406164543942934097887565809028, 12651781177589979792118715727976750483681938,
+    7651192760763854524833755592702020832563502, -3571680155506072207018235262683355377348530,
+    -1552331638086307045698162099132588811375734, 16102076926783351174782517043210229569894972,
+    20298376250393033496651361527361883297885632, 4951220038885843034760610645639211857530854,
+    10279849691114811135823208372639607942966018],
+  ![1713653667984912274043895116528951143433084, 14249974590231269160238797699981856620201618,
+    13742143952617785026217187263439371269626854, -5664979515302657841245796076479810201813086,
+    -570189144959308662364733973857568591565842, 20298376250393033496651361527361883297885632,
+    36447980872424677233911827810143719375133416, 10270561780468257926291933924967926515082386,
+    22686455300823924299262663059062025969365290],
+  ![1907217038591733476693678623867054440207082, 1248579502832393664611904526838897291502276,
+    3932748769664713547883527527626025402797480, -1655853701593026766285067441362772381845912,
+    1340282684346168930580948174315293887525304, 4951220038885843034760610645639211857530854,
+    10270561780468257926291933924967926515082386, 4992524539247681426672603852429221701472778,
+    6819088067267859640306106141170251166283730],
+  ![599881012447755998860464452864987245280214, 7415801335116934610013547429116369931083612,
+    8854573434004355488648652921176038738311232, -3398906238409111317795163688270125479642276,
+    -665874680651590935487717312085456260493100, 10279849691114811135823208372639607942966018,
+    22686455300823924299262663059062025969365290, 6819088067267859640306106141170251166283730,
+    17733202819483274798955349336730660117422986]]
+
+/-- Exact integer matrix after 8 fraction-free Schur steps in moment block 5. -/
+def momentBlock5Stage8 : Fin 8 → Fin 8 → ℤ :=
+  ![![1022474578655993334024686563840258801350944067349,
+    686873290863092480776531838661504834151042633275,
+    -224272365674804714556689415832811129960601662791,
+    -155490340872344793044162601925734996759609886431,
+    995683122592599299635725581559330100378000753246,
+    1273522220846298969893310077141199923251859669882,
+    283823965712841739906207923158218110660246881893,
+    634135637977702224523298690906940859183105693371],
+  ![686873290863092480776531838661504834151042633275,
+    871712654607607279210834009193350999396904395629,
+    -154524602895689358972440310772275206198212846993,
+    -37640314548538696530659098523514594332732466625,
+    590632505500030426496266883431731288802757536242,
+    1030946832163462387846561225189753419962001259654,
+    265940317875938489279290195677803747943452632235,
+    674634213062227801182036328458039056320392475237],
+  ![-224272365674804714556689415832811129960601662791,
+    -154524602895689358972440310772275206198212846993,
+    151461373801890196303224127196929261055376654133,
+    34807990296189439606012759595174782923209606917,
+    -277081268187937702818112120567196783998318438450,
+    -439305436169231006849165488728552071756658905006,
+    -128248032138124104075374499676887042175377271087,
+    -263625491330498988311216228231570213923826984921],
+  ![-155490340872344793044162601925734996759609886431,
+    -37640314548538696530659098523514594332732466625,
+    34807990296189439606012759595174782923209606917,
+    111399917693369515909555604553306224062365356501,
+    -132760247994900937648391117893789965173533485514,
+    -190744852831278850263153638386132400192098884582,
+    -59075548553407465861342276678702470345323861391,
+    -102946520680033325466620530163909926433067737545],
+  ![995683122592599299635725581559330100378000753246,
+    590632505500030426496266883431731288802757536242,
+    -277081268187937702818112120567196783998318438450,
+    -132760247994900937648391117893789965173533485514,
+    1249051023280957850156678381659244127708047405580,
+    1572668567759079071875338410988828696916233524316,
+    381768383798093439342643537162170778383135956766,
+    796788727568858290641280393313200232112851636242],
+  ![1273522220846298969893310077141199923251859669882,
+    1030946832163462387846561225189753419962001259654,
+    -439305436169231006849165488728552071756658905006,
+    -190744852831278850263153638386132400192098884582,
+    1572668567759079071875338410988828696916233524316,
+    2802538306871115543788722245979750492323654731668,
+    768802904339879624198690415868481717377855994162,
+    1751248616107136989044086751165510552159871724022],
+  ![283823965712841739906207923158218110660246881893,
+    265940317875938489279290195677803747943452632235,
+    -128248032138124104075374499676887042175377271087,
+    -59075548553407465861342276678702470345323861391,
+    381768383798093439342643537162170778383135956766,
+    768802904339879624198690415868481717377855994162,
+    356159495135734178947423486050845544269111527101,
+    519233651873677332134741322228172925836483820491],
+  ![634135637977702224523298690906940859183105693371,
+    674634213062227801182036328458039056320392475237,
+    -263625491330498988311216228231570213923826984921,
+    -102946520680033325466620530163909926433067737545,
+    796788727568858290641280393313200232112851636242,
+    1751248616107136989044086751165510552159871724022,
+    519233651873677332134741322228172925836483820491,
+    1372691321190251487345052831034193550119487338493]]
+
+/-- Exact integer matrix after 9 fraction-free Schur steps in moment block 5. -/
+def momentBlock5Stage9 : Fin 7 → Fin 7 → ℤ :=
+  ![![46335731079921027031830046106624895425141127726583023,
+    -436372636675539250139937328291149143744417111464541,
+    7545645522863875421091771642991442702888739777493450,
+    -8836338047482530025427742294499406460166297119265746,
+    19811660095489381197795313097578009070944394538969548,
+    8501081434142796576973304439932029614789544533805720,
+    28079782033122109336826469021622408994435097014647694],
+  ![-436372636675539250139937328291149143744417111464541,
+    11549696154942146238004463516874073524264213720698193,
+    79315618801918388239543545157372945301771624677706,
+    -6627615589832913131815078598913422216142083560382157,
+    -18065881493137646959008818393697188926686761605461366,
+    -7452930017577256549477981219051302077717426300769375,
+    -14064026312406173783749470730682056392655014124443334],
+  ![7545645522863875421091771642991442702888739777493450,
+    79315618801918388239543545157372945301771624677706,
+    9910477138391915210063954831768118864407768180769019,
+    2106891236989175692591451027719341366632624086285570,
+    330102186245018953900923322660248343886139913220937,
+    -1797208707155114924637902757704053858881365947270488,
+    -735417001844793507701151206202801350811414168506327],
+  ![-8836338047482530025427742294499406460166297119265746,
+    -6627615589832913131815078598913422216142083560382157,
+    2106891236989175692591451027719341366632624086285570,
+    31560413183938893723393746430047780613001555609114627,
+    37552560221964728871365090720949752235500965598640056,
+    11901202152743984343913931391296044942208147912544028,
+    20245686388072022176903617222672222822212951298081746],
+  ![19811660095489381197795313097578009070944394538969548,
+    -18065881493137646959008818393697188926686761605461366,
+    330102186245018953900923322660248343886139913220937,
+    37552560221964728871365090720949752235500965598640056,
+    137365650911359221481116121678981715826527444422876704,
+    46900825517802555512514496107553206868591182176743731,
+    108576935177978141205482518054356504725341499220821178],
+  ![8501081434142796576973304439932029614789544533805720,
+    -7452930017577256549477981219051302077717426300769375,
+    -1797208707155114924637902757704053858881365947270488,
+    11901202152743984343913931391296044942208147912544028,
+    46900825517802555512514496107553206868591182176743731,
+    31325144126894258611271300294973506618037085773219025,
+    38759943542797797692353061200642436751593809311053228],
+  ![28079782033122109336826469021622408994435097014647694,
+    -14064026312406173783749470730682056392655014124443334,
+    -735417001844793507701151206202801350811414168506327,
+    20245686388072022176903617222672222822212951298081746,
+    108576935177978141205482518054356504725341499220821178,
+    38759943542797797692353061200642436751593809311053228,
+    110608440372647356406811094567153773029786498584628033]]
+
+/-- Exact integer matrix after 10 fraction-free Schur steps in moment block 5. -/
+def momentBlock5Stage10 : Fin 6 → Fin 6 → ℤ :=
+  ![![523214175862798823971454394623599203403817242218080306942,
+    6814702840468964798109069869985341444213690357885391512,
+    -304116460492016271580637070665618503135774404340386391353,
+    -810240740971701075008643425068897413285234668930672350550,
+    -334118156933522509691795552173162265309051357133018994645,
+    -625359012279801235102687718936656250278289728594562513972],
+  ![6814702840468964798109069869985341444213690357885391512,
+    393430257924153291302688896301402060415615250636697973613,
+    160688807162558217920265031750208407133522389085490879690,
+    -131246527757866950536698318930672889835466774292602564301,
+    -144180725359502441889625949113758030123426424864027464376,
+    -240549908178259210535551529907166324442922075253004217329],
+  ![-304116460492016271580637070665618503135774404340386391353,
+    160688807162558217920265031750208407133522389085490879690,
+    1353866371712052531008281846062437388426798022918701319845,
+    1872993126352712445175674415394083937974306938444795302304,
+    612796977918208037861247055958189285007521902830250600836,
+    1160147304502828652177869426421369424099625903714378664418],
+  ![-810240740971701075008643425068897413285234668930672350550,
+    -131246527757866950536698318930672889835466774292602564301,
+    1872993126352712445175674415394083937974306938444795302304,
+    5841158410371824749214926308655489125949092130595825591312,
+    1960697649262904213271327228343023560854603766289515178697,
+    4376328435055062255146906556601273659303368724058160448518],
+  ![-334118156933522509691795552173162265309051357133018994645,
+    -144180725359502441889625949113758030123426424864027464376,
+    612796977918208037861247055958189285007521902830250600836,
+    1960697649262904213271327228343023560854603766289515178697,
+    1348889348981691899545874440656248121870796509340015607075,
+    1523032297783300357572895186487987257145510749983461386036],
+  ![-625359012279801235102687718936656250278289728594562513972,
+    -240549908178259210535551529907166324442922075253004217329,
+    1160147304502828652177869426421369424099625903714378664418,
+    4376328435055062255146906556601273659303368724058160448518,
+    1523032297783300357572895186487987257145510749983461386036,
+    4241326757433120764385198150654513012157852506133078307327]]
+
+/-- Exact integer matrix after 11 fraction-free Schur steps in moment block 5. -/
+def momentBlock5Stage11 : Fin 5 → Fin 5 → ℤ :=
+  ![![4441536654067207312744541410775295634779174124319286438449274,
+    1859194256986982664664035953171611088757636099056216391607292,
+    -1362846608976616239147901145333646731194610678105415563954954,
+    -1578921530664455197607913696955116197388210270699205164158824,
+    -2624270369541152006467643218037039857497800202071457348872098],
+  ![1859194256986982664664035953171611088757636099056216391607292,
+    13291583881545110131313818502232486630036767201567831155043147,
+    15831605364018126484680920690785617971118008185161161374600966,
+    4726659737432232512396053498168613399422612318851190099270949,
+    8995726121912932528670829676928627113171947457131641121950680],
+  ![-1362846608976616239147901145333646731194610678105415563954954,
+    15831605364018126484680920690785617971118008185161161374600966,
+    51789121904591066615987676405955952412821330660594165936126148,
+    16297329167566208154116986112483760011035374684022595189030688,
+    38481441522825503972906030272608585765809244921043372079323972],
+  ![-1578921530664455197607913696955116197388210270699205164158824,
+    4726659737432232512396053498168613399422612318851190099270949,
+    16297329167566208154116986112483760011035374684022595189030688,
+    12822136878344507769116920897258748700128599053415924971935375,
+    12688443112688685896436934659058430585646946200997654714659564],
+  ![-2624270369541152006467643218037039857497800202071457348872098,
+    8995726121912932528670829676928627113171947457131641121950680,
+    38481441522825503972906030272608585765809244921043372079323972,
+    12688443112688685896436934659058430585646946200997654714659564,
+    39452240141902045184077140976948458238212777336704860071960750]]
+
+/-- Exact integer matrix after 12 fraction-free Schur steps in moment block 5. -/
+def momentBlock5Stage12 : Fin 4 → Fin 4 → ℤ :=
+  ![![106225053294145294974465711642438576461932375035290680497149327017,
+    139236388206500785427422012803240807054998893772191903038135984806,
+    45734912051443112102300759669373460670261296594116725029809312127,
+    85689336735430569264513363729262425837232874667270338269207765708],
+  ![139236388206500785427422012803240807054998893772191903038135984806,
+    436085149958605965731216725424884963711533196626648964262814072958,
+    134234430654369008871151518151385441594419393677189057602590124648,
+    319831271342861214426805080909031448628100661845809081996233703158],
+  ![45734912051443112102300759669373460670261296594116725029809312127,
+    134234430654369008871151518151385441594419393677189057602590124648,
+    104081655736557013498277335227301228514711116001561460552008966797,
+    99792151260427080563271797507101467390463236346005295009769153452],
+  ![85689336735430569264513363729262425837232874667270338269207765708,
+    319831271342861214426805080909031448628100661845809081996233703158,
+    99792151260427080563271797507101467390463236346005295009769153452,
+    321745440909100621092871884785405228773806515212193450512486576588]]
+
+/-- Exact integer matrix after 13 fraction-free Schur steps in moment block 5. -/
+def momentBlock5Stage13 : Fin 3 → Fin 3 → ℤ :=
+  ![![6064657030282673262377005217824827367722792214017459952890997666013225,
+    1776658889881873302473752004110878021677626637595729306768381908408371,
+    4962926528703179073707443205585342856417541491186736418246160385507387],
+  ![1776658889881873302473752004110878021677626637595729306768381908408371,
+    2018309865572432249802512898586295888129377370350729704785643211845330,
+    1504306465762595569907126354569822236561240459403940472122338096917532],
+  ![4962926528703179073707443205585342856417541491186736418246160385507387,
+    1504306465762595569907126354569822236561240459403940472122338096917532,
+    6041774788233781169079328957485057385885978179987736861803617778167718]]
+
+/-- Exact integer matrix after 14 fraction-free Schur steps in moment block 5. -/
+def momentBlock5Stage14 : Fin 2 → Fin 2 → ℤ :=
+  ![![85515045865711073411531054772627787802830934486134692747902326566489360977,
+    2877619137448483727317247820204600502072907251827294721231424271713012419],
+  ![2877619137448483727317247820204600502072907251827294721231424271713012419,
+    113067980133485168793241219710718462563851970392321178078854433237250640693]]
+
+/-- Exact integer matrix after 15 fraction-free Schur steps in moment block 5. -/
+def momentBlock5Stage15 : Fin 1 → Fin 1 → ℤ :=
+  ![![1592956166675066997824970032930007841490817345747039235160160057222186565737180]]
+
+/-- Exact integer matrix after 16 fraction-free Schur steps in moment block 5. -/
+def momentBlock5Stage16 : Fin 0 → Fin 0 → ℤ := fun i => Fin.elim0 i
+
+theorem momentBlock5Stage15_psd : IsPSD (fun i j => (momentBlock5Stage15 i j : ℝ)) := by
+  apply integer_schur_step momentBlock5Stage15 momentBlock5Stage16
+    (85515045865711073411531054772627787802830934486134692747902326566489360977)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact quadraticForm_zero _
+
+theorem momentBlock5Stage14_psd : IsPSD (fun i j => (momentBlock5Stage14 i j : ℝ)) := by
+  apply integer_schur_step momentBlock5Stage14 momentBlock5Stage15
+    (6064657030282673262377005217824827367722792214017459952890997666013225)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock5Stage15_psd
+
+theorem momentBlock5Stage13_psd : IsPSD (fun i j => (momentBlock5Stage13 i j : ℝ)) := by
+  apply integer_schur_step momentBlock5Stage13 momentBlock5Stage14
+    (106225053294145294974465711642438576461932375035290680497149327017)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock5Stage14_psd
+
+theorem momentBlock5Stage12_psd : IsPSD (fun i j => (momentBlock5Stage12 i j : ℝ)) := by
+  apply integer_schur_step momentBlock5Stage12 momentBlock5Stage13
+    (4441536654067207312744541410775295634779174124319286438449274)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock5Stage13_psd
+
+theorem momentBlock5Stage11_psd : IsPSD (fun i j => (momentBlock5Stage11 i j : ℝ)) := by
+  apply integer_schur_step momentBlock5Stage11 momentBlock5Stage12
+    (523214175862798823971454394623599203403817242218080306942)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock5Stage12_psd
+
+theorem momentBlock5Stage10_psd : IsPSD (fun i j => (momentBlock5Stage10 i j : ℝ)) := by
+  apply integer_schur_step momentBlock5Stage10 momentBlock5Stage11
+    (46335731079921027031830046106624895425141127726583023)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock5Stage11_psd
+
+theorem momentBlock5Stage9_psd : IsPSD (fun i j => (momentBlock5Stage9 i j : ℝ)) := by
+  apply integer_schur_step momentBlock5Stage9 momentBlock5Stage10
+    (1022474578655993334024686563840258801350944067349)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock5Stage10_psd
+
+theorem momentBlock5Stage8_psd : IsPSD (fun i j => (momentBlock5Stage8 i j : ℝ)) := by
+  apply integer_schur_step momentBlock5Stage8 momentBlock5Stage9
+    (9053684958684183794409184833136244792998952)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock5Stage9_psd
+
+theorem momentBlock5Stage7_psd : IsPSD (fun i j => (momentBlock5Stage7 i j : ℝ)) := by
+  apply integer_schur_step momentBlock5Stage7 momentBlock5Stage8
+    (116698468136343875412660313821044136732)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock5Stage8_psd
+
+theorem momentBlock5Stage6_psd : IsPSD (fun i j => (momentBlock5Stage6 i j : ℝ)) := by
+  apply integer_schur_step momentBlock5Stage6 momentBlock5Stage7
+    (2862661741483201582491309929483230)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock5Stage7_psd
+
+theorem momentBlock5Stage5_psd : IsPSD (fun i j => (momentBlock5Stage5 i j : ℝ)) := by
+  apply integer_schur_step momentBlock5Stage5 momentBlock5Stage6 (101648688693585509423120042500)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock5Stage6_psd
+
+theorem momentBlock5Stage4_psd : IsPSD (fun i j => (momentBlock5Stage4 i j : ℝ)) := by
+  apply integer_schur_step momentBlock5Stage4 momentBlock5Stage5 (2044842456426383762347120)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock5Stage5_psd
+
+theorem momentBlock5Stage3_psd : IsPSD (fun i j => (momentBlock5Stage3 i j : ℝ)) := by
+  apply integer_schur_step momentBlock5Stage3 momentBlock5Stage4 (118636920772367302208)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock5Stage4_psd
+
+theorem momentBlock5Stage2_psd : IsPSD (fun i j => (momentBlock5Stage2 i j : ℝ)) := by
+  apply integer_schur_step momentBlock5Stage2 momentBlock5Stage3 (26790268834952)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock5Stage3_psd
+
+theorem momentBlock5Stage1_psd : IsPSD (fun i j => (momentBlock5Stage1 i j : ℝ)) := by
+  apply integer_schur_step momentBlock5Stage1 momentBlock5Stage2 (21035497)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock5Stage2_psd
+
+theorem momentBlock5Stage0_psd : IsPSD (fun i j => (momentBlock5Stage0 i j : ℝ)) := by
+  apply integer_schur_step momentBlock5Stage0 momentBlock5Stage1 (1)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock5Stage1_psd
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/MomentBlock6.lean b/LeanPool/PersistentSOS/MomentBlock6.lean
new file mode 100644
index 0000000000..b015d8dd35
--- /dev/null
+++ b/LeanPool/PersistentSOS/MomentBlock6.lean
@@ -0,0 +1,866 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.PSD
+
+/-!
+# Exact moment block certificate
+
+Generated by `scripts/generate_moments.py`; all identities below are checked
+by the Lean kernel with integer arithmetic. No external verifier is trusted.
+-/
+
+@[expose] public section
+
+
+namespace PersistentSOS
+
+
+/-- Exact integer matrix after 0 fraction-free Schur steps in moment block 6. -/
+def momentBlock6Stage0 : Fin 16 → Fin 16 → ℤ :=
+  ![![5373335, 6700445, -1192529, -868051, 4143478, 3462345, 412026, 549857, 487649, 555248,
+    487668, 555251, 2833858, 1418658, 1418815, 752865],
+  ![6700445, 13951051, -868051, -2410969, 7594848, 5800689, 549857, 2599146, 555248, 390599,
+    555251, 390534, 3953065, 2037393, 2037568, 1065899],
+  ![-1192529, -868051, 1188822, 1563499, 2022744, 1400984, -70012, -71505, -110636, -92651,
+    -110643, -92653, -906164, -442446, -442523, -233311],
+  ![-868051, -2410969, 1563499, 3215208, 3598238, 2688879, -71505, -742651, -92651, 72861, -92653,
+    72892, -1199593, -607622, -607709, -315518],
+  ![4143478, 7594848, 2022744, 3598238, 12788775, 9655915, 331233, 900626, 297189, 454472, 297189,
+    454472, 1220643, 651390, 651390, 344016],
+  ![3462345, 5800689, 1400984, 2688879, 9655915, 7390663, 299603, 451763, 297238, 449043, 297238,
+    449043, 1201302, 630690, 630691, 338068],
+  ![412026, 549857, -70012, -71505, 331233, 299603, 194717, 89718, 153598, -9261, 153615, -9266,
+    312527, 124516, 124519, 78020],
+  ![549857, 2599146, -71505, -742651, 900626, 451763, 89718, 1340107, -9261, -257922, -9266,
+    -257943, 399703, 197247, 197239, 105630],
+  ![487649, 555248, -110636, -92651, 297189, 297238, 153598, -9261, 200318, 77972, 195058, 78186,
+    231540, 82775, 79784, 54692],
+  ![555248, 390599, -92651, 72861, 454472, 449043, -9261, -257922, 77972, 215330, 78186, 210862,
+    278253, 129317, 130616, 68507],
+  ![487668, 555251, -110643, -92653, 297189, 297238, 153615, -9266, 195058, 78186, 200325, 77940,
+    231538, 79776, 82777, 54684],
+  ![555251, 390534, -92653, 72892, 454472, 449043, -9266, -257943, 78186, 210862, 77940, 215328,
+    278254, 130613, 129312, 68496],
+  ![2833858, 3953065, -906164, -1199593, 1220643, 1201302, 312527, 399703, 231540, 278253, 231538,
+    278254, 2595168, 1338800, 1338790, 725460],
+  ![1418658, 2037393, -442446, -607622, 651390, 630690, 124516, 197247, 82775, 129317, 79776,
+    130613, 1338800, 741344, 725460, 395345],
+  ![1418815, 2037568, -442523, -607709, 651390, 630691, 124519, 197239, 79784, 130616, 82777,
+    129312, 1338790, 725460, 741348, 395329],
+  ![752865, 1065899, -233311, -315518, 344016, 338068, 78020, 105630, 54692, 68507, 54684, 68496,
+    725460, 395345, 395329, 236319]]
+
+/-- Exact integer matrix after 1 fraction-free Schur steps in moment block 6. -/
+def momentBlock6Stage1 : Fin 15 → Fin 15 → ℤ :=
+  ![![30067707427060, 3326146155320, -7138616128920, 13046516130370, 7969792984290, 193808311525,
+    10281795585545, -283931791725, -1621589407695, -284042980175, -1621958775805, 2253032854965,
+    1441955212845, 1441843576605, 682901878240],
+  ![3326146155320, 4965813445529, 7366027908186, 15810098807102, 11656903182145, 115155023734,
+    271500099178, -12948716739, 164304481107, -12963672033, 164297312024, -1489664890058,
+    -685619771328, -685846291070, -355844816600],
+  ![-7138616128920, 7366027908186, 16522877140079, 22931288405108, 17453739681060, -26560737849,
+    -3513208692378, -74540658986, 873490143083, -74534912687, 873659320621, -3985881781897,
+    -2033489063812, -2033820259950, -1041858696415],
+  ![13046516130370, 15810098807102, 22931288405108, 51549962378141, 37538315690615, 72605205627,
+    2561044825064, -423666847907, 141372431576, -423745573989, 141360001142, -5183104523719,
+    -2378041526874, -2378692052920, -1270966351110],
+  ![7969792984290, 11656903182145, 17453739681060, 37538315690615, 27724675272080, 183291125035,
+    523679304940, -91249728175, 490398331845, -91315512730, 490387944810, -3356795994840,
+    -1522974781860, -1523512996690, -790125751645],
+  ![193808311525, 115155023734, -26560737849, 72605205627, 183291125035, 876514246519,
+    255529489248, 624409442456, -278539067883, 624492960657, -278567170636, 511689091237,
+    84542199752, 84493631675, 109027642210],
+  ![10281795585545, 271500099178, -3513208692378, 2561044825064, 523679304940, 255529489248,
+    6898501126396, -317899671628, -1691208309406, -317936985586, -1691322799012, 589521461199,
+    279815176839, 279685862610, 153617285745],
+  ![-283931791725, -12948716739, -74540658986, -423666847907, -91249728175, 624409442456,
+    -317899671628, 838574173329, 148203544668, 810301165898, 149351975411, -137786033942,
+    -247029350417, -263177556295, -73255426565],
+  ![-1621589407695, 164304481107, 873490143083, 141372431576, 490398331845, -278539067883,
+    -1691208309406, 148203544668, 848739884046, 149342888646, 824730157522, -78347403029,
+    -92843454989, -85950666760, -49915724675],
+  ![-284042980175, -12963672033, -74534912687, -423745573989, -91315512730, 624492960657,
+    -317936985586, 810301165898, 149342888646, 838593255651, 148019585232, -137850623914,
+    -263170936584, -247122122125, -73312717680],
+  ![-1621958775805, 164297312024, 873659320621, 141360001142, 490387944810, -278567170636,
+    -1691322799012, 149351975411, 824730157522, 148019585232, 848725805879, -78350531268,
+    -85883868803, -92961752045, -49977089955],
+  ![2253032854965, -1489664890058, -3985881781897, -5183104523719, -3356795994840, 511689091237,
+    589521461199, -137786033942, -78347403029, -137850623914, -78350531268, 5913955881116,
+    3173545575436, 3173046926380, 1764627105930],
+  ![1441955212845, -685619771328, -2033489063812, -2378041526874, -1522974781860, 84542199752,
+    279815176839, -247029350417, -92843454989, -263170936584, -85883868803, 3173545575436,
+    1970899141276, 1885326358830, 1056263170405],
+  ![1441843576605, -685846291070, -2033820259950, -2378692052920, -1523512996690, 84493631675,
+    279685862610, -263177556295, -85950666760, -247122122125, -92961752045, 3173046926380,
+    1885326358830, 1970475151355, 1056058997240],
+  ![682901878240, -355844816600, -1041858696415, -1270966351110, -790125751645, 109027642210,
+    153617285745, -73255426565, -49915724675, -73312717680, -49977089955, 1764627105930,
+    1056263170405, 1056058997240, 703015445640]]
+
+/-- Exact integer matrix after 2 fraction-free Schur steps in moment block 6. -/
+def momentBlock6Stage2 : Fin 14 → Fin 14 → ℤ :=
+  ![![25728412163205291404, 45637142042029396536, 80393053077372379032, 60295451166344192540,
+    524406684515691424, -4845290551983967632, 103299051883997796, 1923182239855237692,
+    103284192886932812, 1923370766055225224, -9730404794597567968, -4729124180391900648,
+    -4730322618769265680, -2413932742278939680],
+  ![45637142042029396536, 82973645876364766804, 145649832211242161728, 108254413875179130240,
+    108852815594141436, -5999316865856260368, -794319876525944896, 2733487073183239948,
+    -794435438579194732, 2733943029040870196, -19310687046217619012, -9463171286962337192,
+    -9465172881287238240, -4922702214112933460],
+  ![80393053077372379032, 145649832211242161728, 256782352770093271136, 190703364068084052760,
+    -64289902274196578, -10633408385736137886, -1681333869700537102, 4728318125560602226,
+    -1681504432469100554, 4729145398074312222, -34473618314809797914, -16807950522924751854,
+    -16811319634066885430, -8770071987830951240],
+  ![60295451166344192540, 108254413875179130240, 190703364068084052760, 143318781423214528420,
+    738188071289062910, -12319713212937286990, -89477489837849150, 5149294702355302350,
+    -89680686144093830, 5149784430437077230, -22125433330706322150, -10660873498255641990,
+    -10663719620509140110, -5434214790107697980],
+  ![524406684515691424, 108852815594141436, -64289902274196578, 738188071289062910,
+    4897742697666731109, 1059023582154334853, 3504264813491649991, -1500139800518645463,
+    3504736168819069177, -1500283733242990521, 2782008081666452957, 421065729623602297,
+    420797982554351725, 585457483569051960],
+  ![-4845290551983967632, -5999316865856260368, -10633408385736137886, -12319713212937286990,
+    1059023582154334853, 18928057359309653241, -1235580077347711133, -6360650477185470551,
+    -1235576118587968071, -6360584349273067597, -1012344185680317591, -1193390672857213311,
+    -1193900665516168875, -447122301797428660],
+  ![103299051883997796, -794319876525944896, -1681333869700537102, -89477489837849150,
+    3504264813491649991, -1235580077347711133, 4677427637992588269, 743620123212403323,
+    4519213775381336803, 750026908613180821, -651960560950975537, -1306114230187537837,
+    -1396481055797569445, -373832113490010940],
+  ![1923182239855237692, 2733487073183239948, 4728318125560602226, 5149294702355302350,
+    -1500139800518645463, -6360650477185470551, 743620123212403323, 4259944765778299041,
+    749962024355084481, 4125481458364547507, 241519916560970561, -84366699937120039,
+    -45830239492730075, -73225464872109220],
+  ![103284192886932812, -794435438579194732, -1681504432469100554, -89680686144093830,
+    3504736168819069177, -1235576118587968071, 4519213775381336803, 749962024355084481,
+    4677522664533907261, 742537656377259227, -652275367518940379, -1396408276903953099,
+    -1306609418613137975, -374138567802397280],
+  ![1923370766055225224, 2733943029040870196, 4729145398074312222, 5149784430437077230,
+    -1500283733242990521, -6360584349273067597, 750026908613180821, 4125481458364547507,
+    742537656377259227, 4259643023663076629, 241657287395357847, -45323645013924373,
+    -84963234189457405, -73521904812879460],
+  ![-9730404794597567968, -19310687046217619012, -34473618314809797914, -22125433330706322150,
+    2782008081666452957, -1012344185680317591, -651960560950975537, 241519916560970561,
+    -652275367518940379, 241657287395357847, 32148179505723164641, 17153679679142019641,
+    17150936184867409385, 9588028881610922520],
+  ![-4729124180391900648, -9463171286962337192, -16807950522924751854, -10660873498255641990,
+    421065729623602297, -1193390672857213311, -1306114230187537837, -84366699937120039,
+    -1396408276903953099, -45323645013924373, 17153679679142019641, 10641656236262896721,
+    10162844397461189145, 5727299349570899900],
+  ![-4730322618769265680, -9465172881287238240, -16811319634066885430, -10663719620509140110,
+    420797982554351725, -1193900665516168875, -1396481055797569445, -45830239492730075,
+    -1306609418613137975, -84963234189457405, 17150936184867409385, 10162844397461189145,
+    10639343618783644165, 5726171040542763520],
+  ![-2413932742278939680, -4922702214112933460, -8770071987830951240, -5434214790107697980,
+    585457483569051960, -447122301797428660, -373832113490010940, -73225464872109220,
+    -374138567802397280, -73521904812879460, 9588028881610922520, 5727299349570899900,
+    5726171040542763520, 3847090821790192480]]
+
+/-- Exact integer matrix after 3 fraction-free Schur steps in moment block 6. -/
+def momentBlock6Stage3 : Fin 13 → Fin 13 → ℤ :=
+  ![![1730475333139569419414492, 2608437385468790571892016, 1114222272562442921007192,
+    -702807565078369872091452, 2220731869742868697965168, -836474238594187754760344,
+    -580032881909511264367732, -836550569853641069831516, -579928875866701052280548,
+    -1754887693724726928091900, -919546638336413844828904, -919440362901560951039808,
+    -548373038487541331246956],
+  ![2608437385468790571892016, 4774531798062139466913232, 1967537626769512452257696,
+    -1457135753775875775887518, 3856196457754758945122238, -1714882222718453234927978,
+    -1096138586319456753555514, -1714988441294555975430430, -1095934772596151946554958,
+    -3481958572931514658097638, -1737849403902756506328738, -1737527987977832693770666,
+    -1050183284018522710038520],
+  ![1114222272562442921007192, 1967537626769512452257696, 1723551686057603456058568,
+    -419949898610158495182622, -825393138843145680029378, -283712241678964417384174,
+    549560875730874187758462, -283856316128128864260830, 549601871661603711668666,
+    580253055269026053020102, 361095993827340743207166, 361063872198216634702846,
+    190751020561029527605788],
+  ![-702807565078369872091452, -1457135753775875775887518, -419949898610158495182622,
+    4181766791803197857325371, 990694020765073817458843, 2996736580459310177791481,
+    -1317185382635830339902441, 2997140170135243645791687, -1317311831413623779668391,
+    2550222362972844042246851, 442778585761996427311079, 442570381066900032779187,
+    543066808366790892289736],
+  ![2220731869742868697965168, 3856196457754758945122238, -825393138843145680029378,
+    990694020765073817458843, 15415608981176211340512999, -1040618066622712471519411,
+    -5132784424651847815826521, -1040617073648961276592425, -5132697459910430806472627,
+    -2434260977695280895537609, -1783242967342183191239553, -1783872482695913314399221,
+    -771590332704081475204940],
+  ![-836474238594187754760344, -1714882222718453234927978, -283712241678964417384174,
+    2996736580459310177791481, -1040618066622712471519411, 4002038257543567039406751,
+    629695568470426971494361, 3866657469295930300247201, 635177095163292346053923,
+    -524441993950639159966607, -1101372004591652582692139, -1178693201868401186668075,
+    -311588429375643125958308],
+  ![-580032881909511264367732, -1096138586319456753555514, 549560875730874187758462,
+    -1317185382635830339902441, -5132784424651847815826521, 629695568470426971494361,
+    3522150302135410200033195, 635123172934530207487707, 3407080339698082921907797,
+    829037787697845375061375, 230291797995090050539711, 263343428400834074076971,
+    91741535126201369418628],
+  ![-836550569853641069831516, -1714988441294555975430430, -283856316128128864260830,
+    2997140170135243645791687, -1040617073648961276592425, 3866657469295930300247201,
+    635123172934530207487707, 4002119672185746360663535, 628769623312410769203597,
+    -524716177049186546755685, -1178637380592855805247997, -1101793949039690439001529,
+    -311851849907355226362816],
+  ![-579928875866701052280548, -1095934772596151946554958, 549601871661603711668666,
+    -1317311831413623779668391, -5132697459910430806472627, 635177095163292346053923,
+    3407080339698082921907797, 628769623312410769203597, 3521867988575279735587899,
+    829216343701811068990217, 263729910143301348139141, 229887667617270539950845,
+    91503012138433065673508],
+  ![-1754887693724726928091900, -3481958572931514658097638, 580253055269026053020102,
+    2550222362972844042246851, -2434260977695280895537609, -524441993950639159966607,
+    829037787697845375061375, -524716177049186546755685, 829216343701811068990217,
+    24359716713687777506350399, 13147681753270489331904295, 13144946358754720921520055,
+    7423120525930932613938664],
+  ![-919546638336413844828904, -1737849403902756506328738, 361095993827340743207166,
+    442778585761996427311079, -1783242967342183191239553, -1101372004591652582692139,
+    230291797995090050539711, -1178637380592855805247997, 263729910143301348139141,
+    13147681753270489331904295, 8362070930817650193127423, 7952171508617945910394599,
+    4521080660247684488406916],
+  ![-919440362901560951039808, -1737527987977832693770666, 361063872198216634702846,
+    442570381066900032779187, -1783872482695913314399221, -1178693201868401186668075,
+    263343428400834074076971, -1101793949039690439001529, 229887667617270539950845,
+    13144946358754720921520055, 7952171508617945910394599, 8359715029892159295962971,
+    4520018971409600538745728],
+  ![-548373038487541331246956, -1050183284018522710038520, 190751020561029527605788,
+    543066808366790892289736, -771590332704081475204940, -311588429375643125958308,
+    91741535126201369418628, -311851849907355226362816, 91503012138433065673508,
+    7423120525930932613938664, 4521080660247684488406916, 4520018971409600538745728,
+    3098090109930416182002592]]
+
+/-- Exact integer matrix after 4 fraction-free Schur steps in moment block 6. -/
+def momentBlock6Stage4 : Fin 12 → Fin 12 → ℤ :=
+  ![![56679125811396949140140088272, 19371436352667867181555643840,
+    -26752834455463947756942098806, 34219477368470585393461432902, -30537085022558188336731939618,
+    -14919744324653385541957667394, -30536490478096061731785764726,
+    -14916580453916353005634111942, -56277423755356015888481218974,
+    -23659668275865248411161004858, -23648824640799006557896539586,
+    -15038609108139312242300434536],
+  ![19371436352667867181555643840, 67671195346035577590480233848, 2190998079429596123603924690,
+    -151688777092462545474552263258, 17142961964902960006867447610, 62082614551601768098223153262,
+    17136577299965337393659191378, 62080867712262885145941674522, 115026474799253877302344804646,
+    64109943701344768710601148310, 64103180744412365335995891142, 36578214894796557448624812612],
+  ![-26752834455463947756942098806, 2190998079429596123603924690, 262064590922125788984144807107,
+    127295796682414531630916138623, 178708980575965710902105538941,
+    -104437393733386565458168264809, 178734040645286233805610214143,
+    -104443057520807722742798993567, 123588992820946865829045090923, 4662280986383218362053609315,
+    4651180343727936529097570247, 21546724013707867878885183500],
+  ![34219477368470585393461432902, -151688777092462545474552263258,
+    127295796682414531630916138623, 845162185370152046458974940971, 2208496350049965555222685145,
+    -295162378566375724397837077189, 2215151621895826493231263947,
+    -295165506594391171781005052855, -12254683462461750355633235157,
+    -40569602037253261626732928701, -40621115905586988408034839297,
+    -4564158651200703505805226668],
+  ![-30537085022558188336731939618, 17142961964902960006867447610, 178708980575965710902105538941,
+    2208496350049965555222685145, 241979151128176977028401333139, 23495040484271119207067157101,
+    232871050624765859350402787397, 23867105617738956996106525551, -92327978366966404841463599211,
+    -103973542702192415109553370991, -109170658136467384306543429663,
+    -38785759674194325665028293100],
+  ![-14919744324653385541957667394, 62082614551601768098223153262,
+    -104437393733386565458168264809, -295162378566375724397837077189,
+    23495040484271119207067157101, 223820888628120641846276799379, 23858376586921760761590965483,
+    216083706737703331026569017797, 16197535735571552397422470175, -5241404326632533507851515829,
+    -3015978442565594526017602081, -6192295478809175004951270304],
+  ![-30536490478096061731785764726, 17136577299965337393659191378, 178734040645286233805610214143,
+    2215151621895826493231263947, 232871050624765859350402787397, 23858376586921760761590965483,
+    241979663477685318921828988391, 23434422923734800986925135589, -92351626148757279353010652605,
+    -109173086948462778986885941297, -104001195004721399320497132149,
+    -38805104075780058434274106492],
+  ![-14916580453916353005634111942, 62080867712262885145941674522,
+    -104443057520807722742798993567, -295165506594391171781005052855,
+    23867105617738956996106525551, 216083706737703331026569017797, 23434422923734800986925135589,
+    223806589509409179596436187651, 16216639350747236062030529041, -2988662637848644771918305255,
+    -5262473137496228050655485911, -6206121595817344965287512688],
+  ![-56277423755356015888481218974, 115026474799253877302344804646,
+    123588992820946865829045090923, -12254683462461750355633235157,
+    -92327978366966404841463599211, 16197535735571552397422470175, -92351626148757279353010652605,
+    16216639350747236062030529041, 1518720153807189410314903891127,
+    821583459892297485353457081635, 821406727987727148019623782715,
+    461870471945706524121519515372],
+  ![-23659668275865248411161004858, 64109943701344768710601148310, 4662280986383218362053609315,
+    -40569602037253261626732928701, -103973542702192415109553370991,
+    -5241404326632533507851515829, -109173086948462778986885941297, -2988662637848644771918305255,
+    821583459892297485353457081635, 529562079977584683493304239475,
+    501996324676907111947733005419, 284485646885935667613099838412],
+  ![-23648824640799006557896539586, 64103180744412365335995891142, 4651180343727936529097570247,
+    -40621115905586988408034839297, -109170658136467384306543429663,
+    -3015978442565594526017602081, -104001195004721399320497132149, -5262473137496228050655485911,
+    821406727987727148019623782715, 501996324676907111947733005419,
+    529411219937290858190529098767, 284416503568759214444478215232],
+  ![-15038609108139312242300434536, 36578214894796557448624812612, 21546724013707867878885183500,
+    -4564158651200703505805226668, -38785759674194325665028293100, -6192295478809175004951270304,
+    -38805104075780058434274106492, -6206121595817344965287512688, 461870471945706524121519515372,
+    284485646885935667613099838412, 284416503568759214444478215232,
+    196687440081329260708571858132]]
+
+/-- Exact integer matrix after 5 fraction-free Schur steps in moment block 6. -/
+def momentBlock6Stage5 : Fin 11 → Fin 11 → ℤ :=
+  ![![1999619169481118721904681517406368, 371241746935773832425236688791160,
+    -5351401162167635840882247862487768, 903332897593601826325591839332120,
+    2200438876840486185453431533118472, 903117121962294443830844683266168,
+    2200346244461277108436365371717592, 4397505369435758143108142664775016,
+    2364678215619047792748229664918120, 2364335318345690268650675392068392,
+    1366411099810083604167144891684912],
+  ![371241746935773832425236688791160, 8169938916457071392479773397924629,
+    4698409929868681877278084482906379, 5381247010574793244364884268912207,
+    -3651346833936464953482839451860361, 5382077007133499516478009083679845,
+    -3651483429937124269692173745757003, 3177933465088985306599928439440561,
+    -213068150119871725914578789821829, -213264094402537844990095839782921,
+    473236483411846126548259959038252],
+  ![-5351401162167635840882247862487768, 4698409929868681877278084482906379,
+    27005343739557163119367866052963749, 676194979436097408560595396735953,
+    -9372569158133048019148581876140935, 676401206004404999866771409369883,
+    -9372734176316805473659214193758453, 711480400342244029798927432662207,
+    -860935759294137795288736890270843, -862837447510108936885074749317911,
+    147890476514540032820788140255028],
+  ![903332897593601826325591839332120, 5381247010574793244364884268912207,
+    676194979436097408560595396735953, 7386787285585111337367242042882077,
+    506261394090867649021692992998565, 7088475597001647555772593012655023,
+    518503661573016310159843558214223, -4017172300993667431220728266386397,
+    -3823011332740136394652099582016463, -3993043705299775261692570960307627,
+    -1535750430142762906895930054208444],
+  ![2200438876840486185453431533118472, -3651346833936464953482839451860361,
+    -9372569158133048019148581876140935, 506261394090867649021692992998565,
+    7202283266555911756279947734411581, 518167049566432437840122060407271,
+    6948890748758730177939428476486983, 45315521469294960192870784149707,
+    -375662342184450537876251150527495, -302678361707497296997519815566323,
+    -332478646981215365868730890673516],
+  ![903117121962294443830844683266168, 5382077007133499516478009083679845,
+    676401206004404999866771409369883, 7088475597001647555772593012655023,
+    518167049566432437840122060407271, 7386825050051953137684350159971653,
+    504336913391119088005618724956773, -4017927513242938790583630502247727,
+    -3993306482360605392679358541082101, -3823717563581404980815060441705817,
+    -1536378860163483054145573335971380],
+  ![2200346244461277108436365371717592, -3651483429937124269692173745757003,
+    -9372734176316805473659214193758453, 518503661573016310159843558214223,
+    6948890748758730177939428476486983, 504336913391119088005618724956773,
+    7201869470843335828855740511105349, 46044125152932989993623382075857,
+    -301833907138527478529244425850613, -376215690548520068945795500939337,
+    -332904005260533225647992247914244],
+  ![4397505369435758143108142664775016, 3177933465088985306599928439440561,
+    711480400342244029798927432662207, -4017172300993667431220728266386397,
+    45315521469294960192870784149707, -4017927513242938790583630502247727,
+    46044125152932989993623382075857, 47913183538406836718482608989458829,
+    26140290037106192824537706155174559, 26134854098304746801486964105333723,
+    14638798904200816936036550460204860],
+  ![2364678215619047792748229664918120, -213068150119871725914578789821829,
+    -860935759294137795288736890270843, -3823011332740136394652099582016463,
+    -375662342184450537876251150527495, -3993306482360605392679358541082101,
+    -301833907138527478529244425850613, 26140290037106192824537706155174559,
+    17021528876479458137812951741548933, 16118802136578149446505435597700665,
+    9112287801263802136653872992022228],
+  ![2364335318345690268650675392068392, -213264094402537844990095839782921,
+    -862837447510108936885074749317911, -3993043705299775261692570960307627,
+    -302678361707497296997519815566323, -3823717563581404980815060441705817,
+    -376215690548520068945795500939337, 26134854098304746801486964105333723,
+    16118802136578149446505435597700665, 17016884130023337645920834617808909,
+    9110117351612043904486896261935124],
+  ![1366411099810083604167144891684912, 473236483411846126548259959038252,
+    147890476514540032820788140255028, -1535750430142762906895930054208444,
+    -332478646981215365868730890673516, -1536378860163483054145573335971380,
+    -332904005260533225647992247914244, 14638798904200816936036550460204860,
+    9112287801263802136653872992022228, 9110117351612043904486896261935124,
+    6311510016249943090671490529719424]]
+
+/-- Exact integer matrix after 6 fraction-free Schur steps in moment block 6. -/
+def momentBlock6Stage6 : Fin 10 → Fin 10 → ℤ :=
+  ![![285800915315320132474203561322721341926, 200809273518373236562537917107844476266,
+    183931732288553701325850148885614811658, -143230824046951093410598400982982540494,
+    183962427574107228899181937736122016390, -143235036373300425032564657706999035242,
+    83313195696275153246217871181480057654, -23005337686961455096643904827421407126,
+    -23010004593114327505222658064657012734, 7745777548918287629121564185858346128],
+  ![200809273518373236562537917107844476266, 447482353662137221462125635084976143014,
+    109144752545743266321609934013034797062, -122904820661270475924437582364482100322,
+    109131655530673348834468472788217830794, -122919388397337113423168814557318644934,
+    440294461754972466385451872283632422362, 192889321187123422223838604422980848838,
+    192789855413834304096662596627261788014, 134228227242961782011013179146711479760],
+  ![183931732288553701325850148885614811658, 109144752545743266321609934013034797062,
+    246206181437867829940224707517267850838, -17209136948358885178110853379530383010,
+    235685291335755299889587870848253531082, -16775757811699679028448380492585913158,
+    -211810359384853919718003603619061443478, -172561912881791119835609728846671712922,
+    -178555128838322084132344267145874875058, -75958124549658361410658293013151597856],
+  ![-143230824046951093410598400982982540494, -122904820661270475924437582364482100322,
+    -17209136948358885178110853379530383010, 168666899784911338003120452262450252342,
+    -16780732705096928255316413263799898094, 159730899152381808156958169649544659810,
+    -169124485485425189172175146789290055358, -105056516174298891287171216184745067650,
+    -102468355386393570750086228126274204154, -64777547803621758487389704797283856016],
+  ![183962427574107228899181937736122016390, 109131655530673348834468472788217830794,
+    235685291335755299889587870848253531082, -16780732705096928255316413263799898094,
+    246214390852507803845513285486759448390, -17267178943112741685531312848167717386,
+    -211820261838100463976850586914272194442, -178560862245395477551090434019404717174,
+    -172572362520636872251154729329611302046, -75975093451077604784808284366974144048],
+  ![-143235036373300425032564657706999035242, -122919388397337113423168814557318644934,
+    -16775757811699679028448380492585913158, 159730899152381808156958169649544659810,
+    -17267178943112741685531312848167717386, 168659493554893982542316663004180056294,
+    -169091593635894619671869994550535426618, -102448010880272866416238649197712463142,
+    -105058861790916055330614614011347017390, -64790321124446738818213576230287309168],
+  ![83313195696275153246217871181480057654, 440294461754972466385451872283632422362,
+    -211810359384853919718003603619061443478, -169124485485425189172175146789290055358,
+    -211820261838100463976850586914272194442, -169091593635894619671869994550535426618,
+    1349175127621193551112884463080425085878, 738754158685379260105974374711619585786,
+    738588984740003048740163267460926776786, 410437218741823890115586009948580511904],
+  ![-23005337686961455096643904827421407126, 192889321187123422223838604422980848838,
+    -172561912881791119835609728846671712922, -105056516174298891287171216184745067650,
+    -178560862245395477551090434019404717174, -102448010880272866416238649197712463142,
+    738754158685379260105974374711619585786, 501857993832039661226539009997395057702,
+    470024425011637292019214364485604750190, 264470959799470341328772958577224748112],
+  ![-23010004593114327505222658064657012734, 192789855413834304096662596627261788014,
+    -178555128838322084132344267145874875058, -102468355386393570750086228126274204154,
+    -172572362520636872251154729329611302046, -105058861790916055330614614011347017390,
+    738588984740003048740163267460926776786, 470024425011637292019214364485604750190,
+    501722738425488750898368932640146297334, 264402653627943952609963734181787431824],
+  ![7745777548918287629121564185858346128, 134228227242961782011013179146711479760,
+    -75958124549658361410658293013151597856, -64777547803621758487389704797283856016,
+    -75975093451077604784808284366974144048, -64790321124446738818213576230287309168,
+    410437218741823890115586009948580511904, 264470959799470341328772958577224748112,
+    264402653627943952609963734181787431824, 189726587508852629583814088092802637104]]
+
+/-- Exact integer matrix after 7 fraction-free Schur steps in moment block 6. -/
+def momentBlock6Stage7 : Fin 9 → Fin 9 → ℤ :=
+  ![![43791589553444026504852905105581378581835506, -2871310420520077769153450242569626610929662,
+    -3182722298567298520821872275213622264716926, -2876264882368878021417773880086885525216572,
+    -3184381413542049587040931001488615241958784, 54563638687203784932592723710966993844835036,
+    29879504362472252525727265530128917201758928, 29865756619184928073225462412516539382112256,
+    18407068109028552160895525904549899900742434],
+  ![-2871310420520077769153450242569626610929662, 18271014014155858534646724227467690334978443,
+    10715193582588527204192339755956894890636244, 16764464215004690359452712173276393287424634,
+    10777522918254229557662508373307007122734546, -37936991278221301694914514413924014495775595,
+    -22547763957089927831126412317100557786392948, -23403931091339823343056644152458162390380752,
+    -11569000816502831689443884303536024431298535],
+  ![-3182722298567298520821872275213622264716926, 10715193582588527204192339755956894890636244,
+    13847679501863182688897858987145417934896942, 10778623078479154698783771523642015531800912,
+    12570175998197401468198468231140883461003534, -18204924035535675568105866903942697054935474,
+    -16663333931471320234853728068386114025754908, -16293748418073633590582854053589670496173400,
+    -8703681490239584895138845856361753978496988],
+  ![-2876264882368878021417773880086885525216572, 16764464215004690359452712173276393287424634,
+    10778623078479154698783771523642015531800912, 18266539983196016586768915061322216577982030,
+    10709483978191607886683244900506042477517508, -37939685517512577139763606951054876109903914,
+    -23404826686731362422035001224895806372743788, -22548475005260415193507856140295195095206952,
+    -11571545044168209338837342295131992604687876],
+  ![-3184381413542049587040931001488615241958784, 10777522918254229557662508373307007122734546,
+    12570175998197401468198468231140883461003534, 10709483978191607886683244900506042477517508,
+    13846017487885345820089758785541673583302510, -18200047375409307908126013265469109936851750,
+    -16290554801312845994593892443836977890200538, -16664051943111110820470103449027411755245676,
+    -8705490834286566142854797777968511588208344],
+  ![54563638687203784932592723710966993844835036, -37936991278221301694914514413924014495775595,
+    -18204924035535675568105866903942697054935474, -37939685517512577139763606951054876109903914,
+    -18200047375409307908126013265469109936851750, 189363256562464430737122303946797896716022509,
+    106546919632371080123340417844400643273413930, 106523506149132018004104754798102990122876554,
+    58340112505225824127626498182465974256394319],
+  ![29879504362472252525727265530128917201758928, -22547763957089927831126412317100557786392948,
+    -16663333931471320234853728068386114025754908, -23404826686731362422035001224895806372743788,
+    -16290554801312845994593892443836977890200538, 106546919632371080123340417844400643273413930,
+    71464722190324769665566305663467323580209082, 66914770574919363333824892985354869540835792,
+    37889333013761252096450275122145531014043130],
+  ![29865756619184928073225462412516539382112256, -23403931091339823343056644152458162390380752,
+    -16293748418073633590582854053589670496173400, -22548475005260415193507856140295195095206952,
+    -16664051943111110820470103449027411755245676, 106523506149132018004104754798102990122876554,
+    66914770574919363333824892985354869540835792, 71445283054677907499461363758036158056659496,
+    37879588249445914140584270711424146020528682],
+  ![18407068109028552160895525904549899900742434, -11569000816502831689443884303536024431298535,
+    -8703681490239584895138845856361753978496988, -11571545044168209338837342295131992604687876,
+    -8705490834286566142854797777968511588208344, 58340112505225824127626498182465974256394319,
+    37889333013761252096450275122145531014043130, 37879588249445914140584270711424146020528682,
+    27087175461465478184084483310874801793199565]]
+
+/-- Exact integer matrix after 8 fraction-free Schur steps in moment block 6. -/
+def momentBlock6Stage8 : Fin 8 → Fin 8 → ℤ :=
+  ![![2770713039979204806122917869763712593732481275339,
+    1609850602281304862043870419028143930384506244102,
+    2539823519659152969443728399077447451656509957890,
+    1619384290609382012709971009732363126996635592118,
+    -5264685751423612513512455520847791659997118808213,
+    -3154675314199559819871297405593582996191410274252,
+    -3285998874620527684417503501963748679481993341040,
+    -1587722447727060215458389657231981009219007904427],
+  ![1609850602281304862043870419028143930384506244102,
+    2086355024880047990268338540290518167444354081876,
+    1619514356403202862419084807802300109074628431300,
+    1890592217311301612229417007090474481208987732970,
+    -2181804249951776919738798084122488718837997598858,
+    -2220481745533344208274354265134444520639055879620,
+    -2164005432850137029171078210241781195987359483144,
+    -1128629909903360663962007071971195850782499039594],
+  ![2539823519659152969443728399077447451656509957890,
+    1619514356403202862419084807802300109074628431300,
+    2769927874299254162385034955980384985779155364946,
+    1608903882491043950521478299304866669970249553100,
+    -5264152693491180447899812871456025454179813205542,
+    -3285480012191313222260928041192515857245066363812,
+    -3154404647524207436332698437793773837432783292280,
+    -1587793191576624092577265215270292887423502943608],
+  ![1619384290609382012709971009732363126996635592118,
+    1890592217311301612229417007090474481208987732970,
+    1608903882491043950521478299304866669970249553100,
+    2086063402332331100570498993440333999562892514954,
+    -2180740278381451842941768177848259846058352354226,
+    -2163189542052993825486184015948959957695108546126,
+    -2220571484210606295249153848985868842327587725252,
+    -1128800289377029227985455701353879609600389766408],
+  ![-5264685751423612513512455520847791659997118808213,
+    -2181804249951776919738798084122488718837997598858,
+    -5264152693491180447899812871456025454179813205542,
+    -2180740278381451842941768177848259846058352354226,
+    18598006711192337656437621331928656279633718795983,
+    10621115363430046695952769022418717516475793409822,
+    10620152501746332921980012409221443982298372260958,
+    5424928909091217520896182714345888745730903792665],
+  ![-3154675314199559819871297405593582996191410274252,
+    -2220481745533344208274354265134444520639055879620,
+    -3285480012191313222260928041192515857245066363812,
+    -2163189542052993825486184015948959957695108546126,
+    10621115363430046695952769022418717516475793409822,
+    7826318534686327105658501516665895374786343682158,
+    7130593548449109109139542903245027984983122479984,
+    3881163385024633905222726812694621909236721362878],
+  ![-3285998874620527684417503501963748679481993341040,
+    -2164005432850137029171078210241781195987359483144,
+    -3154404647524207436332698437793773837432783292280,
+    -2220571484210606295249153848985868842327587725252,
+    10620152501746332921980012409221443982298372260958,
+    7130593548449109109139542903245027984983122479984,
+    7826213887929412109922653882045002196110283608440,
+    3880555678530882881416765496736733228457513003838],
+  ![-1587722447727060215458389657231981009219007904427,
+    -1128629909903360663962007071971195850782499039594,
+    -1587793191576624092577265215270292887423502943608,
+    -1128800289377029227985455701353879609600389766408,
+    5424928909091217520896182714345888745730903792665,
+    3881163385024633905222726812694621909236721362878,
+    3880555678530882881416765496736733228457513003838,
+    2964897130106491427795826250602926347363574648209]]
+
+/-- Exact integer matrix after 9 fraction-free Schur steps in moment block 6. -/
+def momentBlock6Stage9 : Fin 7 → Fin 7 → ℤ :=
+  ![![72823849152673654694121963583888972873805321517023260,
+    9099307126590346644300296808696064350318973213414320,
+    60087376618606485649229349507354504614575783496641549,
+    55494766609506289855738093695309398536608165951939144,
+    -24519817247292643104629800378325605894871150488907746,
+    -16118866914358395119825406211939521299491649436016956,
+    -13041629129580779823832263161267953893777437416085302],
+  ![9099307126590346644300296808696064350318973213414320,
+    27949927887757047634059269497315033324408122046795849,
+    7875043179557810537564376595893295282378926315299980,
+    -27724132181497235239583042039601076978088223603864028,
+    -24908978267301805524585970026034783786119844343967498,
+    -8999281984287110874064096863985930034563626544161220,
+    -8375683299094092736031618995106606020451427088410097],
+  ![60087376618606485649229349507354504614575783496641549,
+    7875043179557810537564376595893295282378926315299980,
+    72102374510513793300436279362113227423322788100949997,
+    56708237815856436897708231677343927850275879498220420,
+    -20208122960343503143681604726087462469603029423404913,
+    -18982444333819274687039370163680476007029412999108118,
+    -12706752535964872812702327857402871156637712793072571],
+  ![55494766609506289855738093695309398536608165951939144,
+    -27724132181497235239583042039601076978088223603864028,
+    56708237815856436897708231677343927850275879498220420,
+    543776188393823388927519234826929650312115490959173478,
+    292743168043706137448084936836628797523869873209013247,
+    276894346434930675535082240276484222055388785312479957,
+    152359427681254224504544052279436778356228733450755414],
+  ![-24519817247292643104629800378325605894871150488907746,
+    -24908978267301805524585970026034783786119844343967498,
+    -20208122960343503143681604726087462469603029423404913,
+    292743168043706137448084936836628797523869873209013247,
+    267916889994315008119505955970770481858581063194140093,
+    214437728590925148129668779524150822068797531081057416,
+    131185947989428910288426267593611125113534029096230923],
+  ![-16118866914358395119825406211939521299491649436016956,
+    -8999281984287110874064096863985930034563626544161220,
+    -18982444333819274687039370163680476007029412999108118,
+    276894346434930675535082240276484222055388785312479957,
+    214437728590925148129668779524150822068797531081057416,
+    248595777864127067944408165559939747236805487444958260,
+    126386187413348221198726434411838932660659622332968917],
+  ![-13041629129580779823832263161267953893777437416085302,
+    -8375683299094092736031618995106606020451427088410097,
+    -12706752535964872812702327857402871156637712793072571,
+    152359427681254224504544052279436778356228733450755414,
+    131185947989428910288426267593611125113534029096230923,
+    126386187413348221198726434411838932660659622332968917,
+    130025345680076109085531063817831445498564221367159337]]
+
+/-- Exact integer matrix after 10 fraction-free Schur steps in moment block 6. -/
+def momentBlock6Stage10 : Fin 6 → Fin 6 → ℤ :=
+  ![![704736980685940358538302473262364204456102735698690035060,
+    9650029400123665812086323716323834185897860794413634080,
+    -910935888615672562273219672466402938889160639175615768240,
+    -574167842396327754633055705466710670266656541515500364840,
+    -183596000661090989093343161785596062338292128294216869520,
+    -177311652687909104795565265905024970993472650820603463220],
+  ![9650029400123665812086323716323834185897860794413634080,
+    592006314738855789014656859659427642625609068519657193321,
+    286993710036016150417021940465152412660867871934580913496,
+    612909171839932584820163065779413927570256191318298266,
+    -149360193493707048742664058520869725232514982402611090324,
+    -51148331359213422117757879938000669115876539087672521058],
+  ![-910935888615672562273219672466402938889160639175615768240,
+    286993710036016150417021940465152412660867871934580913496,
+    13180796953133106855447779114662789476045997294486818567096,
+    8185404088511136386680651376998811354897992557138791723996,
+    7600579551026193296183798695724852643441928885998507383556,
+    4265740252657084748690734457757440952821949532310726436552],
+  ![-574167842396327754633055705466710670266656541515500364840,
+    612909171839932584820163065779413927570256191318298266,
+    8185404088511136386680651376998811354897992557138791723996,
+    6824783899201900278312313635428665577436000729932736877176,
+    5493513369644460343577555662792213965504636781558199824056,
+    3332603265380985058024986068005410198697041317864155421592],
+  ![-183596000661090989093343161785596062338292128294216869520,
+    -149360193493707048742664058520869725232514982402611090324,
+    7600579551026193296183798695724852643441928885998507383556,
+    5493513369644460343577555662792213965504636781558199824056,
+    6440177419708496795110920531421275113735956660635274558176,
+    3245992000294834324087581520864848971388140107652151953772],
+  ![-177311652687909104795565265905024970993472650820603463220,
+    -51148331359213422117757879938000669115876539087672521058,
+    4265740252657084748690734457757440952821949532310726436552,
+    3332603265380985058024986068005410198697041317864155421592,
+    3245992000294834324087581520864848971388140107652151953772,
+    3356125999084470677066403336643336169443009573111891817544]]
+
+/-- Exact integer matrix after 11 fraction-free Schur steps in moment block 6. -/
+def momentBlock6Stage11 : Fin 5 → Fin 5 → ℤ :=
+  ![![5727733765543955840299661389508292077093372067450334431748211,
+    2898029165568474614299757091917757349535978648327834603210696,
+    82015389030120329161304716807975374455254780654078969394366,
+    -1421072165196019866213508355656489187431629680534507687651484,
+    -471480955034531438056574652118318304159852819492958770797238],
+  ![2898029165568474614299757091917757349535978648327834603210696,
+    116159622885120074998696771817896744800031337256796769616136616,
+    72030343497865814813918304628397092958654716791261774753492116,
+    71256399635866955434849795125392363104393419928283358233930156,
+    39062826137918030998426353435245303156878355906936088413418632],
+  ![82015389030120329161304716807975374455254780654078969394366,
+    72030343497865814813918304628397092958654716791261774753492116,
+    61518430292297080809771232475828276827353383100796312493818296,
+    51714749353792464663087513820934597649779246263346460507912456,
+    30852559156860608609437821708791959687883724149832030132270672],
+  ![-1421072165196019866213508355656489187431629680534507687651484,
+    71256399635866955434849795125392363104393419928283358233930156,
+    51714749353792464663087513820934597649779246263346460507912456,
+    61860554623306327044063965475303452384468341248567456292814816,
+    30965362550210632265895448850614557700136557229899852705690292],
+  ![-471480955034531438056574652118318304159852819492958770797238,
+    39062826137918030998426353435245303156878355906936088413418632,
+    30852559156860608609437821708791959687883724149832030132270672,
+    30965362550210632265895448850614557700136557229899852705690292,
+    32046461542080902552327730684663189729021232963397899925644124]]
+
+/-- Exact integer matrix after 12 fraction-free Schur steps in moment block 6. -/
+def momentBlock6Stage12 : Fin 4 → Fin 4 → ℤ :=
+  ![![932167374710573499987367421770086084450819519297600064050325156326,
+    585087712022271841855730770394276404693765139834437919506535891679,
+    584978518347801803709956978954548602081256600528878142039127542813,
+    319421060588196264636832542788022726587800440315841231551748336250],
+  ![585087712022271841855730770394276404693765139834437919506535891679,
+    499980096860331963457068301895797465749493446769815939633803102525,
+    420475828511804016613183149765216908781748422426515527567687163256,
+    250808341798809472067583590910377400680814560890785898952020992565],
+  ![584978518347801803709956978954548602081256600528878142039127542813,
+    420475828511804016613183149765216908781748422426515527567687163256,
+    499904717685721827821840853605793488001452448439161615788654604532,
+    250719557823620187828492998990315124561253362047178020849581037857],
+  ![319421060588196264636832542788022726587800440315841231551748336250,
+    250808341798809472067583590910377400680814560890785898952020992565,
+    250719557823620187828492998990315124561253362047178020849581037857,
+    260141457840598651584528201401595712397153407976701201042702166892]]
+
+/-- Exact integer matrix after 13 fraction-free Schur steps in moment block 6. -/
+def momentBlock6Stage13 : Fin 3 → Fin 3 → ℤ :=
+  ![![21603221903004388993871617043925855814512118649515841070832975772677119,
+    8675351953284917446100220227858187636087963532388357285566180040362239,
+    8189280078100591395962043584006234244376119569193524367305905520084040],
+  ![8675351953284917446100220227858187636087963532388357285566180040362239,
+    21613260397480008869661193988863928265585492667110750595514681723120533,
+    8180920268144362646487778356436617868297653232112958316911976340987612],
+  ![8189280078100591395962043584006234244376119569193524367305905520084040,
+    8180920268144362646487778356436617868297653232112958316911976340987612,
+    24523759589936909462376167671515309103764349839267102272067328688364172]]
+
+/-- Exact integer matrix after 14 fraction-free Schur steps in moment block 6. -/
+def momentBlock6Stage14 : Fin 2 → Fin 2 → ℤ :=
+  ![![420154512511679452042481743615683038481271574411451746971674212786787730231,
+    113380227488413065142343366830880242204566135292774811775361694100652690418],
+  ![113380227488413065142343366830880242204566135292774811775361694100652690418,
+    496400029300998729213289489577047492884001131389503486626029409738433307518]]
+
+/-- Exact integer matrix after 15 fraction-free Schur steps in moment block 6. -/
+def momentBlock6Stage15 : Fin 1 → Fin 1 → ℤ :=
+  ![![9059280009950859153457221477598227105006560541472811809786935847679127895326386]]
+
+/-- Exact integer matrix after 16 fraction-free Schur steps in moment block 6. -/
+def momentBlock6Stage16 : Fin 0 → Fin 0 → ℤ := fun i => Fin.elim0 i
+
+theorem momentBlock6Stage15_psd : IsPSD (fun i j => (momentBlock6Stage15 i j : ℝ)) := by
+  apply integer_schur_step momentBlock6Stage15 momentBlock6Stage16
+    (420154512511679452042481743615683038481271574411451746971674212786787730231)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact quadraticForm_zero _
+
+theorem momentBlock6Stage14_psd : IsPSD (fun i j => (momentBlock6Stage14 i j : ℝ)) := by
+  apply integer_schur_step momentBlock6Stage14 momentBlock6Stage15
+    (21603221903004388993871617043925855814512118649515841070832975772677119)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock6Stage15_psd
+
+theorem momentBlock6Stage13_psd : IsPSD (fun i j => (momentBlock6Stage13 i j : ℝ)) := by
+  apply integer_schur_step momentBlock6Stage13 momentBlock6Stage14
+    (932167374710573499987367421770086084450819519297600064050325156326)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock6Stage14_psd
+
+theorem momentBlock6Stage12_psd : IsPSD (fun i j => (momentBlock6Stage12 i j : ℝ)) := by
+  apply integer_schur_step momentBlock6Stage12 momentBlock6Stage13
+    (5727733765543955840299661389508292077093372067450334431748211)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock6Stage13_psd
+
+theorem momentBlock6Stage11_psd : IsPSD (fun i j => (momentBlock6Stage11 i j : ℝ)) := by
+  apply integer_schur_step momentBlock6Stage11 momentBlock6Stage12
+    (704736980685940358538302473262364204456102735698690035060)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock6Stage12_psd
+
+theorem momentBlock6Stage10_psd : IsPSD (fun i j => (momentBlock6Stage10 i j : ℝ)) := by
+  apply integer_schur_step momentBlock6Stage10 momentBlock6Stage11
+    (72823849152673654694121963583888972873805321517023260)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock6Stage11_psd
+
+theorem momentBlock6Stage9_psd : IsPSD (fun i j => (momentBlock6Stage9 i j : ℝ)) := by
+  apply integer_schur_step momentBlock6Stage9 momentBlock6Stage10
+    (2770713039979204806122917869763712593732481275339)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock6Stage10_psd
+
+theorem momentBlock6Stage8_psd : IsPSD (fun i j => (momentBlock6Stage8 i j : ℝ)) := by
+  apply integer_schur_step momentBlock6Stage8 momentBlock6Stage9
+    (43791589553444026504852905105581378581835506)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock6Stage9_psd
+
+theorem momentBlock6Stage7_psd : IsPSD (fun i j => (momentBlock6Stage7 i j : ℝ)) := by
+  apply integer_schur_step momentBlock6Stage7 momentBlock6Stage8
+    (285800915315320132474203561322721341926)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock6Stage8_psd
+
+theorem momentBlock6Stage6_psd : IsPSD (fun i j => (momentBlock6Stage6 i j : ℝ)) := by
+  apply integer_schur_step momentBlock6Stage6 momentBlock6Stage7
+    (1999619169481118721904681517406368)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock6Stage7_psd
+
+theorem momentBlock6Stage5_psd : IsPSD (fun i j => (momentBlock6Stage5 i j : ℝ)) := by
+  apply integer_schur_step momentBlock6Stage5 momentBlock6Stage6 (56679125811396949140140088272)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock6Stage6_psd
+
+theorem momentBlock6Stage4_psd : IsPSD (fun i j => (momentBlock6Stage4 i j : ℝ)) := by
+  apply integer_schur_step momentBlock6Stage4 momentBlock6Stage5 (1730475333139569419414492)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock6Stage5_psd
+
+theorem momentBlock6Stage3_psd : IsPSD (fun i j => (momentBlock6Stage3 i j : ℝ)) := by
+  apply integer_schur_step momentBlock6Stage3 momentBlock6Stage4 (25728412163205291404)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock6Stage4_psd
+
+theorem momentBlock6Stage2_psd : IsPSD (fun i j => (momentBlock6Stage2 i j : ℝ)) := by
+  apply integer_schur_step momentBlock6Stage2 momentBlock6Stage3 (30067707427060)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock6Stage3_psd
+
+theorem momentBlock6Stage1_psd : IsPSD (fun i j => (momentBlock6Stage1 i j : ℝ)) := by
+  apply integer_schur_step momentBlock6Stage1 momentBlock6Stage2 (5373335)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock6Stage2_psd
+
+theorem momentBlock6Stage0_psd : IsPSD (fun i j => (momentBlock6Stage0 i j : ℝ)) := by
+  apply integer_schur_step momentBlock6Stage0 momentBlock6Stage1 (1)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock6Stage1_psd
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/MomentBlock7.lean b/LeanPool/PersistentSOS/MomentBlock7.lean
new file mode 100644
index 0000000000..b3dd9d8aff
--- /dev/null
+++ b/LeanPool/PersistentSOS/MomentBlock7.lean
@@ -0,0 +1,344 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.PSD
+
+/-!
+# Exact moment block certificate
+
+Generated by `scripts/generate_moments.py`; all identities below are checked
+by the Lean kernel with integer arithmetic. No external verifier is trusted.
+-/
+
+@[expose] public section
+
+
+namespace PersistentSOS
+
+
+/-- Exact integer matrix after 0 fraction-free Schur steps in moment block 7. -/
+def momentBlock7Stage0 : Fin 11 → Fin 11 → ℤ :=
+  ![![76574425, 39889758, 4143478, 7594848, 10073399, 5911137, 10073398, 5911137, 5506403,
+    5975451, 5975450],
+  ![39889758, 22979581, 2022744, 3598238, 4832959, 2789333, 4832959, 2789334, 2769171, 2933691,
+    2933688],
+  ![4143478, 2022744, 291310, 474628, 583593, 301842, 583593, 301842, 331233, 297189, 297189],
+  ![7594848, 3598238, 474628, 1305861, 883142, 470215, 883143, 470216, 900626, 454472, 454472],
+  ![10073399, 4832959, 583593, 883142, 1779888, 1136477, 1201302, 630691, 615867, 1128524, 615337],
+  ![5911137, 2789333, 301842, 470215, 1136477, 784189, 630690, 338068, 326209, 777072, 326753],
+  ![10073398, 4832959, 583593, 883143, 1201302, 630690, 1779896, 1136476, 615867, 615337, 1128523],
+  ![5911137, 2789334, 301842, 470216, 630691, 338068, 1136476, 784192, 326209, 326753, 777071],
+  ![5506403, 2769171, 331233, 900626, 615867, 326209, 615867, 326209, 635359, 323085, 323085],
+  ![5975451, 2933691, 297189, 454472, 1128524, 777072, 615337, 326753, 323085, 780189, 321057],
+  ![5975450, 2933688, 297189, 454472, 615337, 326753, 1128523, 777071, 323085, 321057, 780185]]
+
+/-- Exact integer matrix after 1 fraction-free Schur steps in moment block 7. -/
+def momentBlock7Stage1 : Fin 10 → Fin 10 → ℤ :=
+  ![![168455408517361, -10391875976124, -27423642903634, -31744391873867, -22202253826321,
+    -31744351984109, -22202177251896, -7601406068799, -13713592878183, -13713782711700],
+  ![-10391875976124, 5138485810266, 4875280587556, 2949391267303, -1379288523636, 2949395410781,
+    -1379288523636, 2548316826391, -2002072967253, -2002068823775],
+  ![-27423642903634, 4875280587556, 42313839061821, -8879843405002, -8887743770801,
+    -8879759235729, -8887667196376, 27144624278306, -10581709997848, -10581702403000],
+  ![-31744391873867, 2949391267303, -8879843405002, 34820532751199, 27479831256062,
+    -9484347438452, -11250440866988, -8308533072322, 26222974270751, -13074015098325],
+  ![-22202253826321, -1379288523636, -8887743770801, 27479831256062, 25107281133556,
+    -11250511530276, -9054177921869, -7569835905386, 24182132085813, -10300780494625],
+  ![-31744351984109, 2949395410781, -8879759235729, -9484347438452, -11250511530276,
+    34821165493396, 27479760592774, -8308527565919, -13074019196273, 26222913745175],
+  ![-22202177251896, -1379288523636, -8887667196376, -11250440866988, -9054177921869,
+    27479760592774, 25107510856831, -7569835905386, -10300786405762, 24182061422525],
+  ![-7601406068799, 2548316826391, 27144624278306, -8308533072322, -7569835905386, -8308527565919,
+    -7569835905386, 18331776095166, -8163193211628, -8163187705225],
+  ![-13713592878183, -2002072967253, -10581709997848, 26222974270751, 24182132085813,
+    -13074019196273, -10300786405762, -8163193211628, 24036509412924, -11121253510725],
+  ![-13713782711700, -2002068823775, -10581702403000, -13074015098325, -10300780494625,
+    26222913745175, 24182061422525, -8163187705225, -11121253510725, 24036215066125]]
+
+/-- Exact integer matrix after 2 fraction-free Schur steps in moment block 7. -/
+def momentBlock7Stage2 : Fin 9 → Fin 9 → ℤ :=
+  ![![9893833875029145018, 7003438643456064652, 2180324925983571355, -6047341261341008688,
+    2180339454603238121, -6047330869465032564, 4574436999171006619, -6265407490259369553,
+    -6265424137267631159],
+  ![7003438643456064652, 83264599832005116881, -30903327257132592048, -27503375811137748171,
+    -30903127808142322403, -27503179932086327176, 56992925852933960948, -28189868281960158598,
+    -28189919559307117216],
+  ![2180324925983571355, -30903327257132592048, 63441555766873110118, 51248561830954301019,
+    -34024346528629389531, -33953793677015775860, -21429078258417915247, 52002638961975797714,
+    -34446543305075431497],
+  ![-6047341261341008688, -27503375811137748171, 51248561830954301019, 48795890078770047051,
+    -33953969307183024905, -26355583022149733309, -18856793855488933409, 49221894508305678270,
+    -26636818636952146669],
+  ![2180339454603238121, -30903127808142322403, -34024346528629389531, -33953969307183024905,
+    63442980803964933219, 51248449689530909950, -21429062185145208722, -34446466479686912540,
+    52002434259547909595],
+  ![-6047330869465032564, -27503179932086327176, -33953793677015775860, -26355583022149733309,
+    51248449689530909950, 48796439849426677351, -18856786254082864610, -26636762886230931706,
+    49221697729551535829],
+  ![4574436999171006619, 56992925852933960948, -21429078258417915247, -18856793855488933409,
+    -21429062185145208722, -18856786254082864610, 39573336094096783653, -19319461235264931981,
+    -19319467966210431853],
+  ![-6265407490259369553, -28189868281960158598, 52002638961975797714, 49221894508305678270,
+    -34446466479686912540, -26636762886230931706, -19319461235264931981, 50421761349914856579,
+    -26921528125120539369],
+  ![-6265424137267631159, -28189919559307117216, -34446543305075431497, -26636818636952146669,
+    52002434259547909595, 49221697729551535829, -19319467966210431853, -26921528125120539369,
+    50421045824523165685]]
+
+/-- Exact integer matrix after 3 fraction-free Schur steps in moment block 7. -/
+def momentBlock7Stage3 : Fin 8 → Fin 8 → ℤ :=
+  ![![4599187241270072192852714, -1905680326533233653882084, -1363931558032288793597982,
+    -1905669216383097589928186, -1363920485571362873267040, 3157166375776657593195716,
+    -1395185104918514435482128, -1395187424483406074231020],
+  ![-1905680326533233653882084, 3697871159083478034463859, 3088235222343942773237262,
+    -2026560522605467427981633, -1915925708041497382323660, -1317793838436131548050031,
+    3135346616199209318255247, -1942043413686858048697741],
+  ![-1363931558032288793597982, 3088235222343942773237262, 2648820229754926728842334,
+    -1915935367206050940160122, -1765025155354050432527154, -943292979477174592158090,
+    2666012293681509327233436, -1789372149647067899922594],
+  ![-1905669216383097589928186, -2026560522605467427981633, -1915935367206050940160122,
+    3697954479209210453050541, 3088229023036252098287904, -1317793288937392085964695,
+    -1942038576623602020281487, 3135335349312733854291709],
+  ![-1363920485571362873267040, -1915925708041497382323660, -1765025155354050432527154,
+    3088229023036252098287904, 2648853265357213416878502, -943292815219658915503224,
+    -1789367891144132644368600, 2666000525244090577343286],
+  ![3157166375776657593195716, -1317793838436131548050031, -943292979477174592158090,
+    -1317793288937392085964695, -943292815219658915503224, 2200027547931825465589913,
+    -964545036627336960549591, -964544979901144528428853],
+  ![-1395185104918514435482128, 3135346616199209318255247, 2666012293681509327233436,
+    -1942038576623602020281487, -1789367891144132644368600, -964545036627336960549591,
+    2728373066253063538448733, -1814204512285870117416129],
+  ![-1395187424483406074231020, -1942043413686858048697741, -1789372149647067899922594,
+    3135335349312733854291709, 2666000525244090577343286, -964544979901144528428853,
+    -1814204512285870117416129, 2728329803230044411039809]]
+
+/-- Exact integer matrix after 4 fraction-free Schur steps in moment block 7. -/
+def momentBlock7Stage4 : Fin 7 → Fin 7 → ℤ :=
+  ![![1351911151605230695767042622515, 1172867327503107959798254545810,
+    -1309111088519443567579695336477, -1153334253646054024711090534700,
+    -4470537812606448185170567055, 1188747405346204363886085893367,
+    -1171497587617583630527542826653],
+  ![1172867327503107959798254545810, 1043287267654888419762554874564,
+    -1153339344836544999366198077320, -1008504437609954083858115134402,
+    -3256794334516494450583302286, 1046970553893971938679467647756,
+    -1024132590677206710895170279542],
+  ![-1309111088519443567579695336477, -1153339344836544999366198077320,
+    1351954163195098442903185887371, 1172868110026403106893006930112,
+    -4473827674277759871619647003, -1171493325606991141583114352807,
+    1188743287819220636729829797417],
+  ![-1153334253646054024711090534700, -1008504437609954083858115134402,
+    1172868110026403106893006930112, 1043305677197438836281156829046,
+    -3260251250277770359800206072, -1024128729937966041956888335640,
+    1046966324914865438526850827078],
+  ![-4470537812606448185170567055, -3256794334516494450583302286, -4473827674277759871619647003,
+    -3260251250277770359800206072, 15225554265289807332461836457, -3162750178435600547099153407,
+    -3161983625574637821083913429],
+  ![1188747405346204363886085893367, 1046970553893971938679467647756,
+    -1171493325606991141583114352807, -1024128729937966041956888335640,
+    -3162750178435600547099153407, 1071551963845590510848740303221,
+    -1040083256819220382737591520537],
+  ![-1171497587617583630527542826653, -1024132590677206710895170279542,
+    1188743287819220636729829797417, 1046966324914865438526850827078,
+    -3161983625574637821083913429, -1040083256819220382737591520537,
+    1071531198670407949687779621457]]
+
+/-- Exact integer matrix after 5 fraction-free Schur steps in moment block 7. -/
+def momentBlock7Stage5 : Fin 6 → Fin 6 → ℤ :=
+  ![![7569581693416363876930222540246740, -5174544288946890700295012087857995,
+    -2326570173225783598465831944088395, 182739060917997807361209607584090,
+    4602590352695387686511780760903255, -2288453316066993030805831250700300],
+  ![-5174544288946890700295012087857995, 24776131438071576460927018468625124,
+    16474827641193189584677657661095770, -2587554609335360682307791005932770,
+    -5990728293146513931999896556415089, 15971262142923539975974403963486541],
+  ![-2326570173225783598465831944088395, 16474827641193189584677657661095770,
+    17454535919436846022698798508500085, -2079409667857604810149355215446470,
+    -2937029621794626588700807799626050, 13975763710529654978785677680190255],
+  ![182739060917997807361209607584090, -2587554609335360682307791005932770,
+    -2079409667857604810149355215446470, 4471140184891289773888429390855345,
+    225818809886653683822075708985470, -2068179590966685021676989050964525],
+  ![4602590352695387686511780760903255, -5990728293146513931999896556415089,
+    -2937029621794626588700807799626050, 225818809886653683822075708985470,
+    7723681134625007859232039044001059, -2932134556523701541778935102262336],
+  ![-2288453316066993030805831250700300, 15971262142923539975974403963486541,
+    13975763710529654978785677680190255, -2068179590966685021676989050964525,
+    -2932134556523701541778935102262336, 16569966601442685500125108339393689]]
+
+/-- Exact integer matrix after 6 fraction-free Schur steps in moment block 7. -/
+def momentBlock7Stage6 : Fin 5 → Fin 5 → ℤ :=
+  ![![118919828553923542045657866871874361549, 83340249970189150008472059665458527285,
+    -13788712827292880004674803840797166350, -15926342177565356266252272197608128909,
+    80666595856660628886820430817375857856],
+  ![83340249970189150008472059665458527285, 93727022401916105718616829219260715625,
+    -11328485668697969434292588996118033150, -8524107675506045215056302491437612585,
+    74314379156844150137579732671808146680],
+  ![-13788712827292880004674803840797166350, -11328485668697969434292588996118033150,
+    25009977384770728769526813169475526480, 642261800617824702506127280167591990,
+    -11270758838296314076536287610210428100],
+  ![-15926342177565356266252272197608128909, -8524107675506045215056302491437612585,
+    642261800617824702506127280167591990, 27576662359394869706003978806578540009,
+    -8626468457430902091870858574192299876],
+  ![80666595856660628886820430817375857856, 74314379156844150137579732671808146680,
+    -11270758838296314076536287610210428100, -8626468457430902091870858574192299876,
+    88904287182091225160992129928550702924]]
+
+/-- Exact integer matrix after 7 fraction-free Schur steps in moment block 7. -/
+def momentBlock7Stage7 : Fin 4 → Fin 4 → ℤ :=
+  ![![554905718695829534725527603952408164455435, -26160864328293574657837594103920562163040,
+    41431604485551872251751836462180786799835, 279365366691807318251466831034699541894814],
+  ![-26160864328293574657837594103920562163040, 367794910479969691613788459340577684618023,
+    -18921269531183719366623483494234533810086, -30124278055993018156976820471005183804745],
+  ![41431604485551872251751836462180786799835, -18921269531183719366623483494234533810086,
+    399726656935802968526549109009978602494959, 34198145738249839003557025865289435728607],
+  ![279365366691807318251466831034699541894814, -30124278055993018156976820471005183804745,
+    34198145738249839003557025865289435728607, 537068370084058385638680585514775226114171]]
+
+/-- Exact integer matrix after 8 fraction-free Schur steps in moment block 7. -/
+def momentBlock7Stage8 : Fin 3 → Fin 3 → ℤ :=
+  ![![1710455781711110105489034302522637020408021345,
+    -79176317343238464616295111900358867098740490, -79109554926238300805467841257092545054874735],
+  ![-79176317343238464616295111900358867098740490, 1850776549840007637972874226273920889205468060,
+    62245223098817672905271272081157383747663895],
+  ![-79109554926238300805467841257092545054874735, 62245223098817672905271272081157383747663895,
+    1849794979175375364458536820010498274561964761]]
+
+/-- Exact integer matrix after 9 fraction-free Schur steps in moment block 7. -/
+def momentBlock7Stage9 : Fin 2 → Fin 2 → ℤ :=
+  ![![5693584431832039955382298029046993389648193182760,
+    180578601249692850469674007294113615470253140675],
+  ![180578601249692850469674007294113615470253140675,
+    5690577856814233892476020259897020320265497075272]]
+
+/-- Exact integer matrix after 10 fraction-free Schur steps in moment block 7. -/
+def momentBlock7Stage10 : Fin 1 → Fin 1 → ℤ :=
+  ![![18923129851434570969679744770567303891184915294505751]]
+
+/-- Exact integer matrix after 11 fraction-free Schur steps in moment block 7. -/
+def momentBlock7Stage11 : Fin 0 → Fin 0 → ℤ := fun i => Fin.elim0 i
+
+theorem momentBlock7Stage10_psd : IsPSD (fun i j => (momentBlock7Stage10 i j : ℝ)) := by
+  apply integer_schur_step momentBlock7Stage10 momentBlock7Stage11
+    (5693584431832039955382298029046993389648193182760)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact quadraticForm_zero _
+
+theorem momentBlock7Stage9_psd : IsPSD (fun i j => (momentBlock7Stage9 i j : ℝ)) := by
+  apply integer_schur_step momentBlock7Stage9 momentBlock7Stage10
+    (1710455781711110105489034302522637020408021345)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock7Stage10_psd
+
+theorem momentBlock7Stage8_psd : IsPSD (fun i j => (momentBlock7Stage8 i j : ℝ)) := by
+  apply integer_schur_step momentBlock7Stage8 momentBlock7Stage9
+    (554905718695829534725527603952408164455435)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock7Stage9_psd
+
+theorem momentBlock7Stage7_psd : IsPSD (fun i j => (momentBlock7Stage7 i j : ℝ)) := by
+  apply integer_schur_step momentBlock7Stage7 momentBlock7Stage8
+    (118919828553923542045657866871874361549)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock7Stage8_psd
+
+theorem momentBlock7Stage6_psd : IsPSD (fun i j => (momentBlock7Stage6 i j : ℝ)) := by
+  apply integer_schur_step momentBlock7Stage6 momentBlock7Stage7
+    (7569581693416363876930222540246740)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock7Stage7_psd
+
+theorem momentBlock7Stage5_psd : IsPSD (fun i j => (momentBlock7Stage5 i j : ℝ)) := by
+  apply integer_schur_step momentBlock7Stage5 momentBlock7Stage6 (1351911151605230695767042622515)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock7Stage6_psd
+
+theorem momentBlock7Stage4_psd : IsPSD (fun i j => (momentBlock7Stage4 i j : ℝ)) := by
+  apply integer_schur_step momentBlock7Stage4 momentBlock7Stage5 (4599187241270072192852714)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock7Stage5_psd
+
+theorem momentBlock7Stage3_psd : IsPSD (fun i j => (momentBlock7Stage3 i j : ℝ)) := by
+  apply integer_schur_step momentBlock7Stage3 momentBlock7Stage4 (9893833875029145018)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock7Stage4_psd
+
+theorem momentBlock7Stage2_psd : IsPSD (fun i j => (momentBlock7Stage2 i j : ℝ)) := by
+  apply integer_schur_step momentBlock7Stage2 momentBlock7Stage3 (168455408517361)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock7Stage3_psd
+
+theorem momentBlock7Stage1_psd : IsPSD (fun i j => (momentBlock7Stage1 i j : ℝ)) := by
+  apply integer_schur_step momentBlock7Stage1 momentBlock7Stage2 (76574425)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock7Stage2_psd
+
+theorem momentBlock7Stage0_psd : IsPSD (fun i j => (momentBlock7Stage0 i j : ℝ)) := by
+  apply integer_schur_step momentBlock7Stage0 momentBlock7Stage1 (1)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlock7Stage1_psd
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/MomentBlockFull0.lean b/LeanPool/PersistentSOS/MomentBlockFull0.lean
new file mode 100644
index 0000000000..603d366b90
--- /dev/null
+++ b/LeanPool/PersistentSOS/MomentBlockFull0.lean
@@ -0,0 +1,7361 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.PSD
+
+/-!
+# Exact moment block certificate
+
+Generated by `scripts/generate_moments.py`; all identities below are checked
+by the Lean kernel with integer arithmetic. No external verifier is trusted.
+-/
+
+@[expose] public section
+
+
+namespace PersistentSOS
+
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger0 : ℤ := Int.ofNat (181355688403183751340640073158732082 * 10 ^ 60 +
+  150306678330376594572253802493709192464704682258716141755016)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger1 : ℤ := Int.ofNat (94353158036457576410171530657379369 * 10 ^ 60 +
+  721941356954919870268065016395429943807580456119752309555222)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger2 : ℤ := Int.ofNat (83355574141259580777961072865016599 * 10 ^ 60 +
+  43795880563393368375055477538852588249585872321946119369163)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger3 : ℤ := Int.ofNat (53588648925373159441088575844936516 * 10 ^ 60 +
+  676918229567509702495165670405410321022618435083364571634768)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger4 : ℤ := Int.ofNat (55722116089257953863020702891822085 * 10 ^ 60 +
+  331377341314507836064106007752835074098072417965937108012110)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger5 : ℤ := Int.ofNat (53411055873977991097042500580422328 * 10 ^ 60 +
+  715300727844299309186703955147407773716256133194575921301924)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger6 : ℤ := Int.ofNat (1277540979817846465782226392934510 * 10 ^ 60 +
+  925997034375820374927659220928515962016249163559305543239859)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger7 : ℤ := Int.ofNat (18571477337002863093090802470203599 * 10 ^ 60 +
+  894865097490924570229920729741178121698636405440829498847105)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger8 : ℤ := Int.ofNat (37104540634320479205280292071239648 * 10 ^ 60 +
+  336360894653256094108512852601860584918331509245026951067641)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger9 : ℤ := Int.ofNat (20820886267387004914547629549922843 * 10 ^ 60 +
+  201031015453911525318219285025079412739389178445293802992486)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger10 : ℤ := Int.ofNat (15772833310343474736617628872753760 * 10 ^ 60 +
+  372143032272584796533272149827333985964188234489391976059634)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger11 : ℤ := Int.ofNat (10794253535614276429342207475969779 * 10 ^ 60 +
+  18980416019609274867488027654664373724391152360715588036026)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger12 : ℤ := Int.ofNat (15093999109860459998616985432514850 * 10 ^ 60 +
+  584303652356686212530693292594113360245598845616813933892687)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger13 : ℤ := Int.ofNat (3351895751375130471232363555496095 * 10 ^ 60 +
+  38537446492317066548487997000778123136074348129292802299549)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger14 : ℤ := Int.ofNat (83251032693425950311280054782274428 * 10 ^ 60 +
+  786316444549080230130264331030056531612104960243044169678758)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger15 : ℤ := Int.ofNat (41608816494757001909793743275950811 * 10 ^ 60 +
+  738277425075496552291097298925085035089492797650625747800834)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger16 : ℤ := Int.ofNat (41095756611551676802424763741106662 * 10 ^ 60 +
+  944308242811983472448689095141312330284198738824833745146372)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger17 : ℤ := Int.ofNat (32118749764848380578038228102443829 * 10 ^ 60 +
+  883455047556994050788059107960088500551322268042250456908610)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger18 : ℤ := Int.ofNat (30902194650016455148172087437641909 * 10 ^ 60 +
+  31554893557346870296823835756054153871258587479936802520713)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger19 : ℤ := Int.ofNat (9350585156974748475101212789860292 * 10 ^ 60 +
+  915913043444274900195543236975972676259514527882506887692966)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger20 : ℤ := Int.ofNat (11720479407219885323620588096628365 * 10 ^ 60 +
+  925859507810217238447550682111567823989902830927967054538587)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger21 : ℤ := Int.ofNat (15792204200890400559784873273347828 * 10 ^ 60 +
+  49209840438891576374380807748446964975080615993275618388749)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger22 : ℤ := Int.ofNat (11779912097202474607128375009990054 * 10 ^ 60 +
+  450044339954417775050339545752606552216165375392725755327807)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger23 : ℤ := Int.ofNat (12684218893533233775868564552173131 * 10 ^ 60 +
+  726040998151113192402038793534323831312279741589752796425612)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger24 : ℤ := Int.ofNat (17253793520661376049866846273375003 * 10 ^ 60 +
+  14451804070186120559106628373135945547300283816615092998117)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger25 : ℤ := Int.ofNat (16905249444988101346622237766742157 * 10 ^ 60 +
+  185367663340328305178852872584090296118916851767627140187944)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger26 : ℤ := Int.ofNat (4142470543081585942876767376671185 * 10 ^ 60 +
+  194893093753464006050568660955851807608253731945963854704120)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger27 : ℤ := Int.ofNat (128588641136858771057336097353332629 * 10 ^ 60
+  + 301436131461483107490091560496180248170328608265283187298436)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger28 : ℤ := Int.ofNat (26393061377717783448333722884786090 * 10 ^ 60 +
+  988463261954937989141919538318257786218849590731492105045764)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger29 : ℤ := Int.ofNat (31263360909780268954313365349560274 * 10 ^ 60 +
+  296665351607625796092890006397890090066002989412843904075621)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger30 : ℤ := Int.ofNat (30931076240249347885828671890208589 * 10 ^ 60 +
+  574792695582599007455200015059064681346832610795564246802243)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger31 : ℤ := Int.ofNat (5073972157739184413149596740828942 * 10 ^ 60 +
+  651234006286558616862849738167822012163028570329054339488414)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger32 : ℤ := Int.ofNat (14923990043650759406482862284436719 * 10 ^ 60 +
+  550203165788823785645852886792172817174036019576029706498041)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger33 : ℤ := Int.ofNat (19134506688726273759548712095983681 * 10 ^ 60 +
+  854879703515769256985103004158086321028091996389739316536451)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger34 : ℤ := Int.ofNat (11315923482965386846312811813813634 * 10 ^ 60 +
+  408242479466470936785136936862507485357766199715790927021529)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger35 : ℤ := Int.ofNat (4621278001948057118106753335060423 * 10 ^ 60 +
+  723859996820863582386140841768997393051793911434946526479449)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger36 : ℤ := Int.ofNat (9080113026914863301798591614593211 * 10 ^ 60 +
+  746480927443376003277828188624194982492426249324444155529453)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger37 : ℤ := Int.ofNat (2805981671281837526522144042126582 * 10 ^ 60 +
+  955068126424696725656482956423549165991045578298153694589835)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger38 : ℤ := Int.ofNat (334217908068992489284535365834609 * 10 ^ 60 +
+  275652687060040897586254589369150108880709596841681349812345)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger39 : ℤ := Int.ofNat (49996453488478404321363113060955169 * 10 ^ 60 +
+  341971307813455858247207459637417122208819861911847040530326)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger40 : ℤ := Int.ofNat (6443567015217770180943072693713044 * 10 ^ 60 +
+  140429886050022647809444932387399464788653997404713653291226)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger41 : ℤ := Int.ofNat (13731880090346459187708551620078330 * 10 ^ 60 +
+  258899237238821902529706295847241955601096250563428069941431)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger42 : ℤ := Int.ofNat (3502867794645953462999766364439439 * 10 ^ 60 +
+  405672870973124143829063500061988922170235225744580953131984)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger43 : ℤ := Int.ofNat (2378597139110949964413458575094080 * 10 ^ 60 +
+  4228988885906453326424132670632788303433634901207729085438)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger44 : ℤ := Int.ofNat (14472148792462571089417384810388861 * 10 ^ 60 +
+  652090369409440930267533615367518413731273320959228489287255)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger45 : ℤ := Int.ofNat (5198736568503684657393277550626734 * 10 ^ 60 +
+  392892957367269747573090536162241754532539888345562415017865)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger46 : ℤ := Int.ofNat (186640103281238613670211054035811 * 10 ^ 60 +
+  875481605838392354878513933890519648342525415042867204633618)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger47 : ℤ := Int.ofNat (12239564687288790540511752195933079 * 10 ^ 60 +
+  486503149811282230740556134840383461365194682508424940286037)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger48 : ℤ := Int.ofNat (16088855179781632465238198665720787 * 10 ^ 60 +
+  176492453309581443088334501108417402564184242623706003368672)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger49 : ℤ := Int.ofNat (1405177900810053685860928362556769 * 10 ^ 60 +
+  45800620005621526737658481612550510353281548946065773972194)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger50 : ℤ := Int.ofNat (42872243609405267423658111480364412 * 10 ^ 60 +
+  809358639999334403979655085901536012210346021024870133279436)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger51 : ℤ := Int.ofNat (18846017286384482482443461463433920 * 10 ^ 60 +
+  693475148610640484023639326360971383227566280104797918507770)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger52 : ℤ := Int.ofNat (17674353038677596474356373892466596 * 10 ^ 60 +
+  414018970160543067301112236062645538834517569110605178122214)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger53 : ℤ := Int.ofNat (8430649052924752813824133552199588 * 10 ^ 60 +
+  536166047217541157676909212118587200223273549557758136900045)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger54 : ℤ := Int.ofNat (3512431270780799711157226281042933 * 10 ^ 60 +
+  925402207029136929483914264939192248250983792358724272255097)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger55 : ℤ := Int.ofNat (11986013204895620981624324488891819 * 10 ^ 60 +
+  926807645174817296989581820650715216860164437487672535972791)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger56 : ℤ := Int.ofNat (17401186876678960909749610742127864 * 10 ^ 60 +
+  747467614482179565508925560511062807296672268411336364008957)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger57 : ℤ := Int.ofNat (11745040401157971123038727719696509 * 10 ^ 60 +
+  276707659978603125808806198733033714272398606881643785247720)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger58 : ℤ := Int.ofNat (2489284403263345485175593774855300 * 10 ^ 60 +
+  612613725147031205049900763095574621388419475396605864583637)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger59 : ℤ := Int.ofNat (276529053428823728201828553622385 * 10 ^ 60 +
+  81838757984044757549393640887370875926278823550371778311145)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger60 : ℤ := Int.ofNat (20325313151936507116352037655565210 * 10 ^ 60 +
+  819250831810695886120538974554444405298946998585128940309570)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger61 : ℤ := Int.ofNat (2342856839598661794209997169483123 * 10 ^ 60 +
+  826107957401741534679715001847408706431401852132544619386968)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger62 : ℤ := Int.ofNat (7606454514383429583792389199328960 * 10 ^ 60 +
+  873776347471858711602529277072105633127329709451855711918505)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger63 : ℤ := Int.ofNat (9169370951330358626393034156306859 * 10 ^ 60 +
+  340213365926354077110543803465305012851417798285251283525284)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger64 : ℤ := Int.ofNat (4553408286307385939919604959200993 * 10 ^ 60 +
+  615232406006140695514148683470317034365521593567177853518178)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger65 : ℤ := Int.ofNat (4528284768834545796709879939021070 * 10 ^ 60 +
+  841035879779394332361123359067194243777024565725865985905469)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger66 : ℤ := Int.ofNat (4446528454854447996020258994371955 * 10 ^ 60 +
+  282981543357431082016860976614862640502852139102494676829766)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger67 : ℤ := Int.ofNat (3509707191876428690465206477057279 * 10 ^ 60 +
+  448269757950888380007164222173960659852474085213494735400043)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger68 : ℤ := Int.ofNat (1559347879160683819048283919246998 * 10 ^ 60 +
+  586961821859645395822880410539444858335965491127551433734082)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger69 : ℤ := Int.ofNat (25756291124809538680885693480323994 * 10 ^ 60 +
+  361619360473068567706878917644521261569055638596263853673622)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger70 : ℤ := Int.ofNat (2311290685033130537632021548765397 * 10 ^ 60 +
+  48306576397413013774514475170069156017863991206400974792161)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger71 : ℤ := Int.ofNat (8148574034121854058671205861220021 * 10 ^ 60 +
+  380863810642856344644476244118977625827948581702366335039145)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger72 : ℤ := Int.ofNat (5439074913649049080826465444740667 * 10 ^ 60 +
+  164054365761290291428625099593134276839142132894358609965220)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger73 : ℤ := Int.ofNat (22360334888385646278434224517283785 * 10 ^ 60 +
+  923045263436472608876863827266957614038775270343846401130348)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger74 : ℤ := Int.ofNat (7038102190302287778362128825831719 * 10 ^ 60 +
+  884973079463994032426186343963071075426067610627195580977809)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger75 : ℤ := Int.ofNat (8543237462198106246089808297638342 * 10 ^ 60 +
+  309368276202777761009268578706663781387888946114200529573161)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger76 : ℤ := Int.ofNat (784090705102246972926132438957031 * 10 ^ 60 +
+  717529607755824533315541910851490356949040208696905014328713)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger77 : ℤ := Int.ofNat (6496095148746106252364565622317287 * 10 ^ 60 +
+  961329055410338065797142077383626581482992808853472260313315)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger78 : ℤ := Int.ofNat (2042294376253905582479842559091346 * 10 ^ 60 +
+  127504295171644381505531904207034915504598868366510003491840)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger79 : ℤ := Int.ofNat (555078857178626586543396876118905 * 10 ^ 60 +
+  826830087871128040283710848858016715154023381729171647239381)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger80 : ℤ := Int.ofNat (1495047086755459961517470037542240 * 10 ^ 60 +
+  73575338461511221404205504084606070559329220726861091507360)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger81 : ℤ := Int.ofNat (2045557990607204768243658976253782 * 10 ^ 60 +
+  895165063319059196808016215049742107231165373290710236871173)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger82 : ℤ := Int.ofNat (276875609099720401317598495454175 * 10 ^ 60 +
+  62699389653819284922853724428246898820141702211939135435410)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger83 : ℤ := Int.ofNat (915872201156981995639407422918014 * 10 ^ 60 +
+  223552525684729685656191752896202732801624973981020227181186)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger84 : ℤ := Int.ofNat (20089335056365715692195595553350091 * 10 ^ 60 +
+  860530851616027652066619467156863439831265135767433627841788)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger85 : ℤ := Int.ofNat (4985243499421685171919750482695491 * 10 ^ 60 +
+  675536833000397366482592025568739510690600929195061954829876)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger86 : ℤ := Int.ofNat (10602381928485534353060984874291087 * 10 ^ 60 +
+  630157505497983914058141665210942813309280554483771854417002)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger87 : ℤ := Int.ofNat (4231099609236402588730488742223890 * 10 ^ 60 +
+  724188309609348045066018152263921595863622376246189167885966)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger88 : ℤ := Int.ofNat (9537712040817558997512570688484930 * 10 ^ 60 +
+  507089841130126757597055496822990154016875635370450361795751)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger89 : ℤ := Int.ofNat (1674339649595103570773019291486236 * 10 ^ 60 +
+  851676270021738996612813324419722805462258654044711435628611)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger90 : ℤ := Int.ofNat (13914545263894584530289227405533071 * 10 ^ 60 +
+  622722051369617727804986656022766922308418968876908661048252)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger91 : ℤ := Int.ofNat (6698485123535062305188559050588588 * 10 ^ 60 +
+  733433015398088100644249145601702988622402467032322061484069)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger92 : ℤ := Int.ofNat (1461613343752947897528635939753166 * 10 ^ 60 +
+  423814145442567217942238042952318405103262448965390822399445)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger93 : ℤ := Int.ofNat (1510673425344664665208548606069363 * 10 ^ 60 +
+  555358699414145170267475627302507603097259152124650772852801)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger94 : ℤ := Int.ofNat (790755951519150596712704392698716 * 10 ^ 60 +
+  243714666077947953860645676166768605303325609733256260232520)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger95 : ℤ := Int.ofNat (49456923810312278856868438505046679 * 10 ^ 60 +
+  261318893237088147674453645941926741936651957004114223877834)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger96 : ℤ := Int.ofNat (5186075732462513678556784009016675 * 10 ^ 60 +
+  997958901439367770905803452087858130317564344107005066093534)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger97 : ℤ := Int.ofNat (7451526972952763143766732438816727 * 10 ^ 60 +
+  286274189888238528960524603047420398208438445231948763467829)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger98 : ℤ := Int.ofNat (766955968074581024251218678959975 * 10 ^ 60 +
+  605677791164662478426674211555562147151827673442772157909104)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger99 : ℤ := Int.ofNat (17742547222578322189231444011093840 * 10 ^ 60 +
+  673207889673925840759749049012618093116075199884243156926721)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger100 : ℤ := Int.ofNat (3184409357839926498848025134570929 * 10 ^ 60 +
+  705716720849729529299560199777433853661244008061894709713689)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger101 : ℤ := Int.ofNat (1744200229876833388163951675229390 * 10 ^ 60 +
+  607529675470522768883532099895768468392412543482515131907151)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger102 : ℤ := Int.ofNat (18401002761339050191686303434484578 * 10 ^ 60
+  + 894552703477537493916400946694519448735802803003735546171381)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger103 : ℤ := Int.ofNat (1281492204966407226442998876730433 * 10 ^ 60 +
+  37163120005363907830622139863604542935080574148611707153700)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger104 : ℤ := Int.ofNat (9988286211928826034590750789048685 * 10 ^ 60 +
+  767075837863828503454668765156055468622220764271628981474240)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger105 : ℤ := Int.ofNat (25607959669304851316835131443676007144328 * 10
+  ^ 60 + 567389713490387291703358135791188393689548995967413900204764)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger106 : ℤ := Int.ofNat (1317968014386389709361921629728096381125 * 10
+  ^ 60 + 578193823929956548651012624077258304112399693396440172833402)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger107 : ℤ := Int.ofNat (9906233454581196458236735776716851133584 * 10
+  ^ 60 + 787721621117849148422453036583481559167950858238322762793536)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger108 : ℤ := Int.ofNat (2345068320728427353491828863089484553522 * 10
+  ^ 60 + 735300528830603657387458638647172018803855474876106130650540)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger109 : ℤ := Int.ofNat (2334431859351207567596277017837018415198 * 10
+  ^ 60 + 637746539433066238202766068880718983921341988921389053309680)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger110 : ℤ := Int.ofNat (7507395965681965697864450391397842403713 * 10
+  ^ 60 + 239505594738728660984503340390927652478819140360849995920874)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger111 : ℤ := Int.ofNat (1542951480782576556032891832817991516947 * 10
+  ^ 60 + 837280038316150571648865500911959716653832631123039110650842)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger112 : ℤ := Int.ofNat (2632597647516116959502574187272783871060 * 10
+  ^ 60 + 546995404608858332981892596571969996715763368066181945827558)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger113 : ℤ := Int.ofNat (710256076882571546486915832598433139340 * 10 ^
+  60 + 296074776688528825922371601220614972638867922074937851971620)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger114 : ℤ := Int.ofNat (3356809376795372118190289974656739422440 * 10
+  ^ 60 + 521689020117666166610736505587691020939785557135828783320964)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger115 : ℤ := Int.ofNat (8723741755817863884688990842341111413121 * 10
+  ^ 60 + 607276741513806895944027653815139675009625811253059726055100)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger116 : ℤ := Int.ofNat (6785618443689050260860155040779439319819 * 10
+  ^ 60 + 247157492966353990574425329259429755351704660802236104241790)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger117 : ℤ := Int.ofNat (1797978216130586353378088052103977853309 * 10
+  ^ 60 + 96296792624134230685916342565656065241295747740947903504602)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger118 : ℤ := Int.ofNat (67670860338236638640122910071470703151701 * 10
+  ^ 60 + 388653077382473127422304412456115356370700353621319088868667)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger119 : ℤ := Int.ofNat (1321080863639390077422868239097311230224 * 10
+  ^ 60 + 633168823527457633220882155815745437793021392749221872960240)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger120 : ℤ := Int.ofNat (4236791198600282001591670726044168082554 * 10
+  ^ 60 + 528253556044380740406412004076501203427521659935903192260086)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger121 : ℤ := Int.ofNat (4783948819979291505429092729039949491215 * 10
+  ^ 60 + 851615279937688275940690001601215191876645618489630148348956)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger122 : ℤ := Int.ofNat (4243588465480053827707678424313186046695 * 10
+  ^ 60 + 524021833715290524019771793101904472403937002798985588511021)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger123 : ℤ := Int.ofNat (4788482778284391169819060646462532347997 * 10
+  ^ 60 + 378446571637337390556955023782060504212238920557661864480921)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger124 : ℤ := Int.ofNat (1559415514359543679632940797428287628293 * 10
+  ^ 60 + 549726474334490387678124929942039868832450495787510272384673)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger125 : ℤ := Int.ofNat (15655867620539009609380201357532320497578 * 10
+  ^ 60 + 919482847822783408550886939098929524144572448573861754977442)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger126 : ℤ := Int.ofNat (1970170817733039850497939071728644481405 * 10
+  ^ 60 + 447275895336274462547145207189502256317075345459662659582598)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger127 : ℤ := Int.ofNat (3087443844274565270243593911730224295358 * 10
+  ^ 60 + 527746015745205497903118010961246030273540905531918577251810)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger128 : ℤ := Int.ofNat (3097030100226785890817408472215965054402 * 10
+  ^ 60 + 580135971080961817130906316272896808299827521378267606223401)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger129 : ℤ := Int.ofNat (1405368265512180924892256766079640281140 * 10
+  ^ 60 + 158753680720153281038784112705724454013985480723191711122267)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger130 : ℤ := Int.ofNat (25607414212826262886108526057096931856026 * 10
+  ^ 60 + 520304131791296207331692071444082162967261942142074170547952)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger131 : ℤ := Int.ofNat (7512246597753272435450490203529833977953 * 10
+  ^ 60 + 767654181503049321397540617542242797414407912276480547138384)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger132 : ℤ := Int.ofNat (1537056077657685617090029383573656488162 * 10
+  ^ 60 + 560755138579649042709532914804232387481397311479078454426216)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger133 : ℤ := Int.ofNat (2342765894874672618826718197257857793698 * 10
+  ^ 60 + 359153950129722256041547537842163985961492640757426427155792)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger134 : ℤ := Int.ofNat (2330551807359891709576914398202845451687 * 10
+  ^ 60 + 565890037172033744083195742568007521427769626265905798439392)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger135 : ℤ := Int.ofNat (2629703444375969690673011019547158487304 * 10
+  ^ 60 + 286632321119222251322912910824492598420214933350620032257352)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger136 : ℤ := Int.ofNat (714823451825405730590603115591534698147 * 10 ^
+  60 + 229766079566398945191083590873069166181421041831613584929848)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger137 : ℤ := Int.ofNat (3353742335232401977390406837858177136533 * 10
+  ^ 60 + 344780882515283497218934923891246377396016818331784242203344)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger138 : ℤ := Int.ofNat (6783835129688279093644204992396718239876 * 10
+  ^ 60 + 309683799127433173120406767638910846684119079071243475203944)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger139 : ℤ := Int.ofNat (8716866827025602887902995969273466786468 * 10
+  ^ 60 + 376677891076007728559286099437436763756583615631972042969616)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger140 : ℤ := Int.ofNat (1795754183346073499789954999063801873544 * 10
+  ^ 60 + 41355267354744288367182376558980761679643315748168726765216)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger141 : ℤ := Int.ofNat (19303199743892698968084813203141360674303 * 10
+  ^ 60 + 451366055283981877822818804553185750909469098642804432184556)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger142 : ℤ := Int.ofNat (1825492474196281947146685300993053996398 * 10
+  ^ 60 + 143865195965673638378110251603725316216868464695444126457080)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger143 : ℤ := Int.ofNat (13542875923071948897171915904497092928947 * 10
+  ^ 60 + 844231714609815755181277826475257985580248088357078170824434)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger144 : ℤ := Int.ofNat (2042278745366097241817205557404964170501 * 10
+  ^ 60 + 508463015772514366691083795352902961984751152180882735794770)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger145 : ℤ := Int.ofNat (5912862481546519447981943307848767642805 * 10
+  ^ 60 + 591301752923845375931863735750147763450735389409475895642398)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger146 : ℤ := Int.ofNat (4189293317709281151733896164411483104807 * 10
+  ^ 60 + 84980665256475172669996009779857072050481166006954849867476)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger147 : ℤ := Int.ofNat (16676609280983535155736931709856174592369 * 10
+  ^ 60 + 126047887097226994546444990073308462802993788506462445811412)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger148 : ℤ := Int.ofNat (6317954883971270117023379165424007896058 * 10
+  ^ 60 + 527366621313125270880013941438091163458022214556840017827460)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger149 : ℤ := Int.ofNat (5342349107495013996661486916582175572070 * 10
+  ^ 60 + 412586177926743091712823408143744560458278189220009491415922)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger150 : ℤ := Int.ofNat (564709957579648254874555557005544654082 * 10 ^
+  60 + 317944126146894673011678770934032497002894996973459865807670)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger151 : ℤ := Int.ofNat (3444566088900140226526394155580160283049 * 10
+  ^ 60 + 250308937484951317303025452997461043770889299985469251915264)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger152 : ℤ := Int.ofNat (2038232583574299659342730865955503829507 * 10
+  ^ 60 + 858329854322099895484385328657688056232721594269258010508924)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger153 : ℤ := Int.ofNat (1601865441193750580300877383346213321820 * 10
+  ^ 60 + 964523800389663058333063048916332572498365160180665622811860)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger154 : ℤ := Int.ofNat (1318005258582600507338333512999272511600 * 10
+  ^ 60 + 565706004948492196239236123053670172523502595296504091249940)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger155 : ℤ := Int.ofNat (1183275981291866599766233170550851005051 * 10
+  ^ 60 + 978253504191969580162889288274723297315149985743736364669096)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger156 : ℤ := Int.ofNat (87681593024872011826564664021251158978 * 10 ^
+  60 + 639751513230810087665659995697631201803232276142700059005472)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger157 : ℤ := Int.ofNat (950123876997745217358856034531727501505 * 10 ^
+  60 + 335066516432404762205420707284184004477925055186691163109992)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger158 : ℤ := Int.ofNat (701342089272607445858575863532299017121 * 10 ^
+  60 + 770035245154796621947268301285575723024864005088409676602100)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger159 : ℤ := Int.ofNat (428905179950935745902553283548122243460 * 10 ^
+  60 + 375453897594461022628916284637258755735667982557062178237516)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger160 : ℤ := Int.ofNat (19300086400556571350043651619737117423939 * 10
+  ^ 60 + 65052940707103239035430146844384596012166842035192747373851)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger161 : ℤ := Int.ofNat (1830601864161924493677880509623467680813 * 10
+  ^ 60 + 451084491388990424662217132962303365608595355027617740559551)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger162 : ℤ := Int.ofNat (5912215838455859559587340281704869239138 * 10
+  ^ 60 + 479363891678799163200110149016766923600066010157291852927881)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger163 : ℤ := Int.ofNat (4187056693528880416364613537601643809857 * 10
+  ^ 60 + 869271812681738870028006947227713784767289719717618602403914)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger164 : ℤ := Int.ofNat (16677946864620783287053574789396574642976 * 10
+  ^ 60 + 455380791797455996218598945590239382491232849408469848393122)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger165 : ℤ := Int.ofNat (5332737176074540018773202885287227193915 * 10
+  ^ 60 + 198024895939861046981618034329278348974921285004300088764318)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger166 : ℤ := Int.ofNat (6324279943293263334148519623292565689651 * 10
+  ^ 60 + 435189031315167901051399389784252863626657746948290291823183)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger167 : ℤ := Int.ofNat (570052317539154850136441919307011868070 * 10 ^
+  60 + 701394283074782296139150874399547271659357278070226119068877)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger168 : ℤ := Int.ofNat (3443879003020471426866110060389433906884 * 10
+  ^ 60 + 930113031842304198527421869002550504482434984737774238164715)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger169 : ℤ := Int.ofNat (1317299792014964163698011122079630276410 * 10
+  ^ 60 + 211556689419035877900188199168193510813683910333971289230565)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger170 : ℤ := Int.ofNat (1182155377593791811329769591368353084590 * 10
+  ^ 60 + 361422845785640328997640040322189018804927429560891939238054)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger171 : ℤ := Int.ofNat (90062549552258785703168412219882608003 * 10 ^
+  60 + 901424370294041855745923488696792599940520007233748934897610)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger172 : ℤ := Int.ofNat (704761468862920866999293927332916156818 * 10 ^
+  60 + 309808214544449784985613919168735865011389209072562390569878)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger173 : ℤ := Int.ofNat (951091669587473164188114303674113458375 * 10 ^
+  60 + 829411536579067058801938913280858715473809335911222346153075)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger174 : ℤ := Int.ofNat (429238574602135183307285685139687064108 * 10 ^
+  60 + 272710000325202346012048437142954580100290392064006815125911)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger175 : ℤ := Int.ofNat (9368397736242216276866058997736728838884 * 10
+  ^ 60 + 153160321777203660497777443342074542989038601062878093975587)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger176 : ℤ := Int.ofNat (543746866819163488993304071882798092949 * 10 ^
+  60 + 555294713015707492818946235872888208723248865973187768030690)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger177 : ℤ := Int.ofNat (5528525501463785738073111637002904634936 * 10
+  ^ 60 + 149147296869565699124480267266414815453534614063898659427478)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger178 : ℤ := Int.ofNat (4827069037006282726168451450970341873903 * 10
+  ^ 60 + 768384619583226748429512834100524170955949982994339574648082)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger179 : ℤ := Int.ofNat (4834561166843832863851743437112684231658 * 10
+  ^ 60 + 6157140485484988952981137642218929023708244657838267399469)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger180 : ℤ := Int.ofNat (741019259038607306166450855384492621965 * 10 ^
+  60 + 466509183713490178817971581703368719470668857496767362985927)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger181 : ℤ := Int.ofNat (8638475735887402114780855153582562403550 * 10
+  ^ 60 + 654048859350611182496098969332811501342091991466246834370316)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger182 : ℤ := Int.ofNat (6378555248818608454621174247280579138334 * 10
+  ^ 60 + 773620694997903065973066619028488389788391894876740255755268)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger183 : ℤ := Int.ofNat (166679170381959693097917326071723255003 * 10 ^
+  60 + 992087897162449282411908975155573289548759057761682511144604)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger184 : ℤ := Int.ofNat (166576874822558770761705088901387347478 * 10 ^
+  60 + 113993671706452574134369088108852843351687113214628980319946)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger185 : ℤ := Int.ofNat (304287678312106116453109980313328756589 * 10 ^
+  60 + 6585355199226143753743153251916013414605010008217499880586)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger186 : ℤ := Int.ofNat (36044459098644809530276596877344356994830 * 10
+  ^ 60 + 967320080431067476971502085906355788087192545942318487795228)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger187 : ℤ := Int.ofNat (4591183874306840168172000278176850258242 * 10
+  ^ 60 + 587280791503922207583167155727209436511489958963164479790068)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger188 : ℤ := Int.ofNat (4601605466216281160475659542640567846069 * 10
+  ^ 60 + 967771805001742827807031959448505994328912181660001282628786)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger189 : ℤ := Int.ofNat (356384919927947417520058250608795330112 * 10 ^
+  60 + 74673201460465841357494431326828840155968940880959728942238)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger190 : ℤ := Int.ofNat (12818161172420606123259033097273724880198 * 10
+  ^ 60 + 45500974424077468677965960593268564270758367175193901264660)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger191 : ℤ := Int.ofNat (1713591398271466326951307093778323038098 * 10
+  ^ 60 + 596969913937867867532413825226539782719026054922203579267322)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger192 : ℤ := Int.ofNat (1157899177533471893559478629935068309709 * 10
+  ^ 60 + 839628657540292465261195367402273362999835520842491371398702)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger193 : ℤ := Int.ofNat (12851648136301329184544240702129477529702 * 10
+  ^ 60 + 146489831737102005298112516375807195638508260050586450800987)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger194 : ℤ := Int.ofNat (1169720369950586450449684102498324310942 * 10
+  ^ 60 + 792879771183234721840387485205564062544629160791982042251703)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger195 : ℤ := Int.ofNat (7440748561190181190834595864689426161512 * 10
+  ^ 60 + 181334880177107012765988367442593900442355936783083662840459)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger196 : ℤ := Int.ofNat (9545747574198440209340581944733611071645914277
+  * 10 ^ 60 + 824991268529697780085688875695314665617564289649094807997874)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger197 : ℤ := Int.ofNat (258532195626058046724603054195923720588353903
+  * 10 ^ 60 + 193520920220610163548649133474741732819872766159522653894552)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger198 : ℤ := Int.ofNat (615289788601600451010707885290723875828886207
+  * 10 ^ 60 + 73098773126926998838314613276876601800892243392810972122924)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger199 : ℤ := Int.ofNat (692472764820279048409149978482806047075479792
+  * 10 ^ 60 + 521173228130485854429213470116950978526022980442739362586734)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger200 : ℤ := Int.ofNat (653765818294350815118469868181238345506365656
+  * 10 ^ 60 + 178953849684821008023449198723382787962839987245955395695462)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger201 : ℤ := Int.ofNat (687361039846493719912511483543369404258328377
+  * 10 ^ 60 + 44877428959732768734579663439929240139012988379431534174508)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger202 : ℤ := Int.ofNat (201062180217735290284457697163761203371000463
+  * 10 ^ 60 + 899622603412606571492792467559728512662483572144477509350616)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger203 : ℤ := Int.ofNat (2205493168398252096819332693845382333784344364
+  * 10 ^ 60 + 600180359708249476977578640209058319833255560809713418655778)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger204 : ℤ := Int.ofNat (253798972937715693805984777736118774264533336
+  * 10 ^ 60 + 247476908561490388740712558592214501487641344460060005008584)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger205 : ℤ := Int.ofNat (499354339765896652884963198875541824803947072
+  * 10 ^ 60 + 933884601879123791563094258448563335341695476526806157257690)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger206 : ℤ := Int.ofNat (387996618436275573982064041712770997290215159
+  * 10 ^ 60 + 124003303762374169874698879836515007871053138022339777615174)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger207 : ℤ := Int.ofNat (185375691164386101896311092179693142193909734
+  * 10 ^ 60 + 240586125416763248739114781037979765220731465644605572480874)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger208 : ℤ := Int.ofNat (3074732168868577314821281387372159963414208336
+  * 10 ^ 60 + 872243574254746990976354486455034168484094548101332609543752)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger209 : ℤ := Int.ofNat (1188846647445065124299581484219406050085387325
+  * 10 ^ 60 + 68532893323989061515782291087252125540113375423921441693176)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger210 : ℤ := Int.ofNat (344551072970733861851265828969771312307343360
+  * 10 ^ 60 + 945736141919872472055828403790962634158090883484941053668844)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger211 : ℤ := Int.ofNat (740883689977718463039164617287453059957116937
+  * 10 ^ 60 + 706877032871790038126864841508623823772728030450704065306472)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger212 : ℤ := Int.ofNat (413361802587415012546544763917646062711174888
+  * 10 ^ 60 + 263860195323955031124290884409527087740310483787366476888800)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger213 : ℤ := Int.ofNat (515122891686742241328685025010311930083160589
+  * 10 ^ 60 + 138929999896568168587575734255681747593260417336598931256876)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger214 : ℤ := Int.ofNat (139731666860178414823329904371982320888076819
+  * 10 ^ 60 + 507932192294976311150874765132200761936704768003255463799012)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger215 : ℤ := Int.ofNat (656918108606966246930401615201027718328543834
+  * 10 ^ 60 + 496195723630605553111039068433657402242147513204437668713720)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger216 : ℤ := Int.ofNat (481378636326956682376638311537335373582339009
+  * 10 ^ 60 + 216020312142111025388099907770052498810168505481661327198476)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger217 : ℤ := Int.ofNat (860194985257152138510823296920698867641597106
+  * 10 ^ 60 + 26327521959693667067939058955026731369050456691919327578824)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger218 : ℤ := Int.ofNat (351777180082280695357633631037324699019257747
+  * 10 ^ 60 + 272015134349376811314931702354793301894727162895928502953856)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger219 : ℤ := Int.ofNat (2695345370223714551225912611420475176119928172
+  * 10 ^ 60 + 319060870286338319685831372923687270013062463871845598750824)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger220 : ℤ := Int.ofNat (227578940693705219767746401177058107915614925
+  * 10 ^ 60 + 84495007591417967379878696348585786951615218782940823762620)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger221 : ℤ := Int.ofNat (1815217746367429619820263728783219801958167673
+  * 10 ^ 60 + 61222348215578628541044798218659018795840343881174943821976)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger222 : ℤ := Int.ofNat (268424252558237908274365466788358830011470956
+  * 10 ^ 60 + 144444614892359625381094142671302041218393609267944093345600)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger223 : ℤ := Int.ofNat (800872163933872306103364969062459639477884048
+  * 10 ^ 60 + 550519298372184348231742528417694694955300000616466057877672)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger224 : ℤ := Int.ofNat (582356452269028115035783593694986023552776025
+  * 10 ^ 60 + 880486834149903493542676064478897991659491285390307282666304)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger225 : ℤ := Int.ofNat (2398192684474919707530897045157416794271420909
+  * 10 ^ 60 + 872068447893160986967536562495928251322552587305558931271708)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger226 : ℤ := Int.ofNat (779309238523772212368096246864811980876918353
+  * 10 ^ 60 + 783148696788166184318271131416265712984772104783393799410340)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger227 : ℤ := Int.ofNat (842098754539225023554142629390766559554910597
+  * 10 ^ 60 + 286603320114034591189186153292005118506520291079879799311188)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger228 : ℤ := Int.ofNat (102987955542034409396823903633753232767342707
+  * 10 ^ 60 + 920449158754750472467842561268589775410244449776732628764060)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger229 : ℤ := Int.ofNat (456333838246471845308834545861123043149633676
+  * 10 ^ 60 + 320778857240974672458524820481533615115071571599327124383456)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger230 : ℤ := Int.ofNat (191168381753237342478990684509600159744219048
+  * 10 ^ 60 + 887825314110533193305682977281061160600374962229888439182726)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger231 : ℤ := Int.ofNat (206327084907218843708200429247250519675166506
+  * 10 ^ 60 + 646163137128530278618451045447955260600646650745521775237530)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger232 : ℤ := Int.ofNat (152219133171759137409830594355254626709435647
+  * 10 ^ 60 + 275864446225555401582900954304983408037463610246150829825170)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger233 : ℤ := Int.ofNat (176224568979059728059655554827640866476479693
+  * 10 ^ 60 + 301735423155702878399425598548398184057235781275785908039684)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger234 : ℤ := Int.ofNat (55590147414997365409636192105952900693257347 *
+  10 ^ 60 + 946074748257273010025090975781658585961372392162487905660008)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger235 : ℤ := Int.ofNat (21867266863180116983793235424412176761188879 *
+  10 ^ 60 + 967522160455966175936761045460500976104039409028032710480868)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger236 : ℤ := Int.ofNat (186376860381041312112647321399381154575856944
+  * 10 ^ 60 + 209617680323442248882682233082469015061949163220987819573850)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger237 : ℤ := Int.ofNat (37418892011250956700774897857604649968376911 *
+  10 ^ 60 + 820765963029047344631900030180960855695998056637469396613054)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger238 : ℤ := Int.ofNat (2414453297988346098287589786278912335413211214
+  * 10 ^ 60 + 925952687099452448894547997432822533035011889356166847107018)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger239 : ℤ := Int.ofNat (194614413789311866686281507217906925290502133
+  * 10 ^ 60 + 513564096360819965517998947996263283477934183467147191740316)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger240 : ℤ := Int.ofNat (725843412733370775580814556110517321223608622
+  * 10 ^ 60 + 176249511084080182572741400566295417532190136609000022713712)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger241 : ℤ := Int.ofNat (561823046367717188023673265631799396867488162
+  * 10 ^ 60 + 901022962028869899970698441448174677861463550369461951457526)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger242 : ℤ := Int.ofNat (2493933837043047062099813465227146383906799214
+  * 10 ^ 60 + 606470290543288497317205843524581468742195077600226255263484)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger243 : ℤ := Int.ofNat (391870448037148567253367927715849156572310362
+  * 10 ^ 60 + 154420302698783863458304066402059283774127981231488406440222)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger244 : ℤ := Int.ofNat (1173904343054057491055202970594020232995674029
+  * 10 ^ 60 + 218077544761671578791946761082394486680855203349362908728642)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger245 : ℤ := Int.ofNat (154922138977174910241119090348180625163086966
+  * 10 ^ 60 + 477579375523577282314012683700117906393136077214560177903886)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger246 : ℤ := Int.ofNat (473158664604415393046889246367618510452079450
+  * 10 ^ 60 + 336276875454295560737226021609567949027735241996004806897706)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger247 : ℤ := Int.ofNat (163608816293640233837710293357205458197193197
+  * 10 ^ 60 + 50013095980719835299002231085103948916340850986275476583614)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger248 : ℤ := Int.ofNat (172966605977625200520687059800066795593056240
+  * 10 ^ 60 + 437334818451230144456139051593015340368058534165686689997706)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger249 : ℤ := Int.ofNat (41276412122449070281262870820584228135501862 *
+  10 ^ 60 + 874701252086005297928194145200416656245097029918405251876608)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger250 : ℤ := Int.ofNat (25293902007747705964755748797511767878994009 *
+  10 ^ 60 + 537296808931624568383960589230132028576762007063931940487162)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger251 : ℤ := Int.ofNat (192028148931842608800438024850719959924314835
+  * 10 ^ 60 + 45131408409649542514582875044041264680215258372950219339780)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger252 : ℤ := Int.ofNat (45312783008264388794644141022990805150819309 *
+  10 ^ 60 + 12967857517335013752933172131447763629716135421287126922820)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger253 : ℤ := Int.ofNat (1284630126980346795315061400346714987024613060
+  * 10 ^ 60 + 506074902317388631141850012028134436637673710259907636367694)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger254 : ℤ := Int.ofNat (87088893941050650074080824344215145174523539 *
+  10 ^ 60 + 997777207767928303538981856283280158904443813594387567547570)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger255 : ℤ := Int.ofNat (829372311754181668130641719240868460552495281
+  * 10 ^ 60 + 219452703250608128950571026470868314135423121627944413856944)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger256 : ℤ := Int.ofNat (554960740867150047481407002132071373852007379
+  * 10 ^ 60 + 799243959413203947389467608538219870028924653743932080064178)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger257 : ℤ := Int.ofNat (781155814733380245824287695283046357053915864
+  * 10 ^ 60 + 188068122362135516211484961931502968178771368684183729571196)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger258 : ℤ := Int.ofNat (130733944606135674234219483853393826184526616
+  * 10 ^ 60 + 887148926851137400807234609815851649188784286092714562209884)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger259 : ℤ := Int.ofNat (1216996701330102330118252656026109074095342132
+  * 10 ^ 60 + 202356097770770666773151805844937225666833262768939935665064)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger260 : ℤ := Int.ofNat (913817378865716570284603389393060643220341399
+  * 10 ^ 60 + 585823619020528960711197371637030161742973859802378765561152)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger261 : ℤ := Int.ofNat (10629813375821379710441640687493309473246336 *
+  10 ^ 60 + 853713354360277333778974638722774023205972223161587357134284)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger262 : ℤ := Int.ofNat (50096143701506523101612418242197412487740784 *
+  10 ^ 60 + 519490198811216831946929947791740910877170464549428892297034)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger263 : ℤ := Int.ofNat (35924771355885475513728036337176791877172017 *
+  10 ^ 60 + 975800067355599680055634796194405300734365847028094097946654)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger264 : ℤ := Int.ofNat (5027451268475663025126246307491423890862183942
+  * 10 ^ 60 + 996909572608304515344700022126351934546141029070651929181056)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger265 : ℤ := Int.ofNat (809761143459699760244686567050063219681683102
+  * 10 ^ 60 + 334815903787721696564112657442315792654813471146524034858772)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger266 : ℤ := Int.ofNat (524161664907112179736944796244165205953801833
+  * 10 ^ 60 + 985146454109840566631458826469189896141820522868446916933184)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger267 : ℤ := Int.ofNat (17042865036639719583876174040807040561590360 *
+  10 ^ 60 + 877315234811796387806080994887177813099543276652544388132844)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger268 : ℤ := Int.ofNat (1390324650612777114215134569436861135686056863
+  * 10 ^ 60 + 62585546029583626785177590434753285947235863334371394383140)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger269 : ℤ := Int.ofNat (84444020887881512319192774013534580531249832 *
+  10 ^ 60 + 451400819825279920761930336295407652374146455823810948431062)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger270 : ℤ := Int.ofNat (77010751205330877299504422250391051015414692 *
+  10 ^ 60 + 895968998600320223557077870045879365378202545064230764559758)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger271 : ℤ := Int.ofNat (1560799509447309337059170563132943002830027339
+  * 10 ^ 60 + 46638447601224050623760167445369131609959721517277893712998)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger272 : ℤ := Int.ofNat (232441268172792407192498135043508507352175620
+  * 10 ^ 60 + 816764256258196518892470512859090838128830293788028649045042)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger273 : ℤ := Int.ofNat (1032830373549109254137922492125744900940213991
+  * 10 ^ 60 + 392610615525562321547488945157145023294381538179650897303642)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger274 : ℤ := Int.ofNat
+  (1143542032410067135723137509916790422516761985117949 * 10 ^ 60 +
+  984583302732254426996802987019707457269628174726091525044396)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger275 : ℤ := Int.ofNat
+  (449372084677628046553253232165819568880607390197616 * 10 ^ 60 +
+  737871798037601623403032747781805538303121083114159847140348)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger276 : ℤ := Int.ofNat
+  (135427582598665834940920485914059215256034679928723 * 10 ^ 60 +
+  245154971711739042146349166875816890383207302579173399330166)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger277 : ℤ := Int.ofNat
+  (282775679605460399102752585073282291668630101060582 * 10 ^ 60 +
+  557770858397429647836251221980861972174964929404478349368968)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger278 : ℤ := Int.ofNat
+  (161026197962860698519630203238302195248195799704107 * 10 ^ 60 +
+  273040597270067726198824179747004781191484720363668371625544)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger279 : ℤ := Int.ofNat
+  (189989835568802405812907743396978320903583426354114 * 10 ^ 60 +
+  327246413862903196331644076352512157509953166830809341431578)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger280 : ℤ := Int.ofNat
+  (29820893135048862817032016869307030437236086491492 * 10 ^ 60 +
+  251125496595708551764616418791943086649924391943949790544538)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger281 : ℤ := Int.ofNat
+  (242313691371460733627956981533880962787717578284144 * 10 ^ 60 +
+  354661042790383627814396466937315952915651030065938907166708)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger282 : ℤ := Int.ofNat
+  (174399672359963371933852638455894547378738872855706 * 10 ^ 60 +
+  259283862182307629330865250166055829980264270740993240769046)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger283 : ℤ := Int.ofNat
+  (324567592219328186580842239322553713829681167749374 * 10 ^ 60 +
+  241998743509895304924736103683659794630774125925839587109016)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger284 : ℤ := Int.ofNat
+  (129258661046080365273256568613488444727165784115159 * 10 ^ 60 +
+  989748070971524007205349327484815801016447820495551426276764)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger285 : ℤ := Int.ofNat
+  (989946303135941232559993595485177303475098897978538 * 10 ^ 60 +
+  211491859512950638769442339726463658062528284086941091595600)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger286 : ℤ := Int.ofNat
+  (68195190969478663158073431632052143234388274290623 * 10 ^ 60 +
+  167340173238274956423180107695744857256999902982812939858476)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger287 : ℤ := Int.ofNat
+  (660941175535482235381570763084614360151992217392451 * 10 ^ 60 +
+  954897497885127688368963582539921064096372864121605722987974)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger288 : ℤ := Int.ofNat
+  (83543708926490155070383356739381678437812594367945 * 10 ^ 60 +
+  965683073594635775826811086691862514994049873226889123297572)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger289 : ℤ := Int.ofNat
+  (303367981002746174415774378939912492059605425177232 * 10 ^ 60 +
+  232940667507667347821190042972399391718892589294778378059108)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger290 : ℤ := Int.ofNat
+  (270074039721402802054671642073942649993381347362026 * 10 ^ 60 +
+  139534679884397169853887176202839906795552968126168105262362)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger291 : ℤ := Int.ofNat
+  (887863866449847353844838504583338950325391420501880 * 10 ^ 60 +
+  268981698657499118652424671224339161975081410935051161689834)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger292 : ℤ := Int.ofNat
+  (278500971539154313749348301017722541329903873337138 * 10 ^ 60 +
+  906946749655708993859629278086348564352102974883294853771900)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger293 : ℤ := Int.ofNat
+  (304582320761452260546065782140474467789144839294276 * 10 ^ 60 +
+  44457322871003604842757909059769087334588323093471845110824)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger294 : ℤ := Int.ofNat
+  (33936216246087667663832917602348627361649017217310 * 10 ^ 60 +
+  441072455683932334201751359086521761912899945477347484929776)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger295 : ℤ := Int.ofNat
+  (151379850230501086261401244200073073663615172406321 * 10 ^ 60 +
+  194390829584348365754673613699431354388144254869340895968217)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger296 : ℤ := Int.ofNat
+  (53582171729590708957279642861929292615846217174509 * 10 ^ 60 +
+  22540829454456654869626590723876280793574822232609643467994)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger297 : ℤ := Int.ofNat
+  (58324344845893787376347908173650436015646130344705 * 10 ^ 60 +
+  436021023237332361133416537252607575761369367377023023927757)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger298 : ℤ := Int.ofNat
+  (62178928958782645592336728445753198804281701139781 * 10 ^ 60 +
+  334257131147529795974185447928699888549734160038786709023891)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger299 : ℤ := Int.ofNat
+  (6050903771095186763634535791962986925495180355617 * 10 ^ 60 +
+  218885261255001097185560042872348174345548577743095284039501)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger300 : ℤ := Int.ofNat
+  (13858997082173696261245864783343501616077263028049 * 10 ^ 60 +
+  881037569435788308395838967788256124843069165233652857706024)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger301 : ℤ := Int.ofNat
+  (5351846552360032799520779553102558442020997910555 * 10 ^ 60 +
+  522447474942459064841105383207581871444118363834598745043327)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger302 : ℤ := Int.ofNat
+  (58982808129381972888194479832067249344977333303769 * 10 ^ 60 +
+  925570573645200436400838921836972377162269669438191023762656)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger303 : ℤ := Int.ofNat
+  (18961249600009453583150248036632773120552085745074 * 10 ^ 60 +
+  5177506010007314834929526945142494344118888162209243405158)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger304 : ℤ := Int.ofNat
+  (883332848818550330277564435588018608918188939934494 * 10 ^ 60 +
+  157731087228297762559042200046729505978426197104403138482092)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger305 : ℤ := Int.ofNat
+  (54997232651167621658013937908974236340793071511946 * 10 ^ 60 +
+  906276831063721737730376528478385513982786631427865107929892)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger306 : ℤ := Int.ofNat
+  (275701995328753153039073573897068937434691180274557 * 10 ^ 60 +
+  968297221001833575510636183737354539030818361117094195768420)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger307 : ℤ := Int.ofNat
+  (265733667025828391381474670045933700020052668630812 * 10 ^ 60 +
+  385131015389154885495761004674251119675334266127402748103690)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger308 : ℤ := Int.ofNat
+  (923171470403285140487913366022547630724631492296101 * 10 ^ 60 +
+  676104214059092411842657519642117718172382709487018490616622)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger309 : ℤ := Int.ofNat
+  (133327122671443285450733052270143175789926582588528 * 10 ^ 60 +
+  688072866473767582626250659539161551833920222949963827695232)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger310 : ℤ := Int.ofNat
+  (427684819475473451741360251154256584166583869066268 * 10 ^ 60 +
+  816996841407750834122717373545623078815522152096467910820480)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger311 : ℤ := Int.ofNat
+  (53016927527123441915449518049472224155100292590022 * 10 ^ 60 +
+  341981025777218550010765191616240788108827408405174478737184)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger312 : ℤ := Int.ofNat
+  (157926989419907237134594454192123709141867856609445 * 10 ^ 60 +
+  704157365452447131398234059152371766852189180094079089241695)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger313 : ℤ := Int.ofNat
+  (66384467660593876007161609694966630203872840821491 * 10 ^ 60 +
+  533923382844201021940507351947495268233354815393762671884201)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger314 : ℤ := Int.ofNat
+  (5276698478468067356057907611063268638859392563774 * 10 ^ 60 +
+  318962247350007167991225375859120189043969622085903088051505)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger315 : ℤ := Int.ofNat
+  (8574001512593101135813793182563997715813576625962 * 10 ^ 60 +
+  761598295949336210440223463020192431898920637197169620987480)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger316 : ℤ := Int.ofNat
+  (3974838910062936541794907502818024910757647189488 * 10 ^ 60 +
+  247970289352078555015881451591510758642255621187496039255263)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger317 : ℤ := Int.ofNat
+  (61166859756351366032772977771951877830554731160318 * 10 ^ 60 +
+  680205708855521579997932082694898940242805486483518880047952)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger318 : ℤ := Int.ofNat
+  (21866811083490576410863162346677500901327953599516 * 10 ^ 60 +
+  60991025220288426123403306752842097480763902808343930294048)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger319 : ℤ := Int.ofNat
+  (477286323310690981466239884487259364475215680146503 * 10 ^ 60 +
+  273068250647894848808773201188163892501876082040968447756025)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger320 : ℤ := Int.ofNat
+  (49780219878231614874077156823228404525212966767686 * 10 ^ 60 +
+  766214895446099942124410045152787610281820806035298299921227)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger321 : ℤ := Int.ofNat
+  (311153571419499555474611306711474851005282449591358 * 10 ^ 60 +
+  249481682492177786595505993276414165228568621578551107598200)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger322 : ℤ := Int.ofNat
+  (210790570114523164104907983666506596301085949902675 * 10 ^ 60 +
+  684426421529019142816340369083532254012557721099806724517883)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger323 : ℤ := Int.ofNat
+  (294233815067024948388503771942760985587658660028463 * 10 ^ 60 +
+  144272356764696333216965010156693493541299798341263407422142)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger324 : ℤ := Int.ofNat
+  (50188507472340235140157031606520040171901799721682 * 10 ^ 60 +
+  68879264508599313180143979028765752959207724602410440613750)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger325 : ℤ := Int.ofNat
+  (263704851182362131141562242730011606179629600397630 * 10 ^ 60 +
+  775483844054931733391660390745850273215875621950267895935493)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger326 : ℤ := Int.ofNat
+  (362497522192497479635720935401432589836651577811747 * 10 ^ 60 +
+  136977391115386075290646830004390772032868434419059928590300)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger327 : ℤ := Int.ofNat
+  (39044620603481973883349513087040612784667098011267 * 10 ^ 60 +
+  476187513886694213103482896454635354506305675423975759432561)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger328 : ℤ := Int.ofNat
+  (52090406684649079210761225937278171140759926179216 * 10 ^ 60 +
+  117768811181807768216999994724834323642656828972334224547792)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger329 : ℤ := Int.ofNat
+  (2574044253322183015205464001589541288906360731428 * 10 ^ 60 +
+  776391587047855504849491995748499879357311097458952850329634)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger330 : ℤ := Int.ofNat
+  (1871541796015691395931615442535350840704700955811880 * 10 ^ 60 +
+  233981790633782639461681427531194596035749884252022203126992)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger331 : ℤ := Int.ofNat
+  (296901430277143164131903705459888697072932595397232 * 10 ^ 60 +
+  665595294451388288765229535587509572030270420589533273737162)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger332 : ℤ := Int.ofNat
+  (191543639608738870603984481457730538516835803636909 * 10 ^ 60 +
+  957297919738938264518114096796919905347406790068408875712300)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger333 : ℤ := Int.ofNat
+  (4515733742519352767816529398272318548553585827461 * 10 ^ 60 +
+  692353633175043752159959591164562924878256677156595314494910)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger334 : ℤ := Int.ofNat
+  (508526785126949484761583565315923097250465347983606 * 10 ^ 60 +
+  212817515874133807187343331611096440205529300209095700431215)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger335 : ℤ := Int.ofNat
+  (23911843045011822035138161137317539745379295636697 * 10 ^ 60 +
+  412900318629152469882275167332999018354992885722805096437652)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger336 : ℤ := Int.ofNat
+  (32321721764020335689783456502862473269121960333486 * 10 ^ 60 +
+  752583229113871217201762477656506830411947416847375423851968)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger337 : ℤ := Int.ofNat
+  (575932520421653041481224247436823256764959055608784 * 10 ^ 60 +
+  517719928831745490163806549247108212186991985561206159573534)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger338 : ℤ := Int.ofNat
+  (89454639990781260025259324116933011313467954242758 * 10 ^ 60 +
+  124190389666280757306491624298601270828755513747056555479056)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger339 : ℤ := Int.ofNat
+  (383660940303913952939922287093352502449853222392958 * 10 ^ 60 +
+  26100802546382426946304368006889280359829152418320495393588)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger340 : ℤ := Int.ofNat
+  (97437097487410880174382323349241979676611915925700224410 * 10 ^ 60 +
+  161988218205652118446438839723347673122850228620643781732504)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger341 : ℤ := Int.ofNat
+  (1794169815773102647599302047599934872275904909945367574 * 10 ^ 60 +
+  456625072143388374823361585866356718807959245747079849346772)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger342 : ℤ := Int.ofNat
+  (65866241868196610113772492582518052253143420415945549131 * 10 ^ 60 +
+  906894208542014835593368544135675921900470382673770447924660)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger343 : ℤ := Int.ofNat
+  (2427789364264275933779526435121673500268777590562887229 * 10 ^ 60 +
+  404816822161206973120216749851874143726589282099535625517800)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger344 : ℤ := Int.ofNat
+  (27398368441443720426271607952170541511496251704422169226 * 10 ^ 60 +
+  657690156599698833726862276571544379524285619003166662088876)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger345 : ℤ := Int.ofNat
+  (30949942586762013457819221356447328982147401679301434644 * 10 ^ 60 +
+  140027017452662068291989018301909412030641056732789978517872)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger346 : ℤ := Int.ofNat
+  (117769577525775177537316350367076229523765493680163785439 * 10 ^ 60 +
+  134991697164837615394677727351146725631414031035310207184852)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger347 : ℤ := Int.ofNat
+  (41573266868087939587054487355514429661654226710596597876 * 10 ^ 60 +
+  783370535768806729270345379491080729001677931146994876464092)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger348 : ℤ := Int.ofNat
+  (21208508711516834467681581922241952812470395247670575049 * 10 ^ 60 +
+  470855078151574927958833311143251512676228265495561651599264)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger349 : ℤ := Int.ofNat
+  (10150354691671259122374004239097961443361472407636984403 * 10 ^ 60 +
+  337355272262146515142813242445089007238286002619714156497832)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger350 : ℤ := Int.ofNat
+  (16213354718108214599735229018500185813619740385449308739 * 10 ^ 60 +
+  157210003146531381272663276893481263488553878060644304487124)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger351 : ℤ := Int.ofNat
+  (2407128271026850884446462614084650697361106335936238873 * 10 ^ 60 +
+  868110122623459060443671827128387915170803961983719564178564)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger352 : ℤ := Int.ofNat
+  (4702507663226566423256461118168742359631180980553359863 * 10 ^ 60 +
+  672722640632792034021433499378433999470330040769565702873782)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger353 : ℤ := Int.ofNat
+  (4753357900207900548299051905647277431544166549241726944 * 10 ^ 60 +
+  37338960506746266606840905227189795480900957389056918916612)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger354 : ℤ := Int.ofNat
+  (1147949301964324815886823865823017674403579142593064801 * 10 ^ 60 +
+  509257694392315975349399453320735349357817141693327809188796)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger355 : ℤ := Int.ofNat
+  (5098008591285903227115409237021589468910474549056337777 * 10 ^ 60 +
+  434959956382097498515573937547355493852901584959173296675468)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger356 : ℤ := Int.ofNat
+  (1833116203216378062120148902046006202660531762605460624 * 10 ^ 60 +
+  764649617364752092551282675273614585175783577005188935634856)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger357 : ℤ := Int.ofNat
+  (2461191823770400214721299628878911203863567470303461099 * 10 ^ 60 +
+  204469623841662606927750385024305250583521109571302480005880)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger358 : ℤ := Int.ofNat
+  (437660631264827423612041200614643874253395986841926109 * 10 ^ 60 +
+  42005042314918496120732679623340900152542106415808379874256)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger359 : ℤ := Int.ofNat
+  (97442986945348384943840839113246287612881063512192547469 * 10 ^ 60 +
+  444798904384066551639856550523013333658619863223605533295592)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger360 : ℤ := Int.ofNat
+  (1818333714012094354970734459077339431300911917524739912 * 10 ^ 60 +
+  570824318477474973284324731422230450055600689056181875218360)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger361 : ℤ := Int.ofNat
+  (27399877607660087655322535794098822617918430367927883218 * 10 ^ 60 +
+  756920002290444843080073461420289325952226286822500531931184)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger362 : ℤ := Int.ofNat
+  (30950430236219525059743891030742138050673174776572850883 * 10 ^ 60 +
+  21424463629582175914510180894724654088345545584259793457044)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger363 : ℤ := Int.ofNat
+  (117770325429712128286106220946631284713801334757474182728 * 10 ^ 60 +
+  929728005912603324455272318213239572622329851558905822863844)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger364 : ℤ := Int.ofNat
+  (21138329202738267379753924847351872023327573415512809176 * 10 ^ 60 +
+  541178553745339992307151005968870795825507203180845228840600)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger365 : ℤ := Int.ofNat
+  (41620181461748758762402079616740934405022248406319516220 * 10 ^ 60 +
+  661958080391396108496350193411330738525847347138124127893408)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger366 : ℤ := Int.ofNat
+  (10180270327005928284673642079139071341791757716759471693 * 10 ^ 60 +
+  975748475167186805054525038485537474537632130842001333553584)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger367 : ℤ := Int.ofNat
+  (16202682170364944619221038318313352180216845209576890438 * 10 ^ 60 +
+  760473511006294904739097029017229890549388931010637554389466)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger368 : ℤ := Int.ofNat
+  (4747673018121695990550600101354282710066641295415218222 * 10 ^ 60 +
+  410190641131386077473993596583774038479371004511759753483086)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger369 : ℤ := Int.ofNat
+  (1135172647259749392146790877739188094992988885381352957 * 10 ^ 60 +
+  725974839305099910994052464318807033832706464088244257259598)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger370 : ℤ := Int.ofNat
+  (5114694597985931409983682883778042388649105175093913942 * 10 ^ 60 +
+  657372736030119541588247991313792443743789833487074601516768)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger371 : ℤ := Int.ofNat
+  (2465759817910749081134502959102370069608648572064030672 * 10 ^ 60 +
+  713257763575006516354314688303340668304534483665180016625374)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger372 : ℤ := Int.ofNat
+  (1852446822779707282054078373407401124214667694089285295 * 10 ^ 60 +
+  874467633023071007236377920915250054008222519696727573539712)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger373 : ℤ := Int.ofNat
+  (439105142278321493871403220734517940836090637744384546 * 10 ^ 60 +
+  859266350858129041300405522674504533794985861181504937462608)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger374 : ℤ := Int.ofNat
+  (53395591138243056973481277662243132315841826969991010602 * 10 ^ 60 +
+  319123831009730548396980506030397854184314429249981289005684)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger375 : ℤ := Int.ofNat
+  (6556997229404695720720964647179987962463291228642359244 * 10 ^ 60 +
+  326252492247338691281944380474480770128559962702159137716644)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger376 : ℤ := Int.ofNat
+  (42097732284334232300718216201672795137972746146083594890 * 10 ^ 60 +
+  15855684604430523589600375214072046972429169417829562021076)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger377 : ℤ := Int.ofNat
+  (28722951230939520705143360804644899175644544281368729750 * 10 ^ 60 +
+  115278805750564783075020936950806858706025373092255329525744)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger378 : ℤ := Int.ofNat
+  (28788126783446468313690667410199034865894015829027103503 * 10 ^ 60 +
+  431954272890700788693133214963055233067108407909307589019516)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger379 : ℤ := Int.ofNat
+  (8585026888626643735523176991995767265745202785861634904 * 10 ^ 60 +
+  170645226654178129846161716894297420915263384656256002459408)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger380 : ℤ := Int.ofNat
+  (31497616448897969676225631917422677199178345104237025301 * 10 ^ 60 +
+  376889240935769056324421546963681270508821289320010856214716)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger381 : ℤ := Int.ofNat
+  (44182727511793084861745013400365953204654266578730801790 * 10 ^ 60 +
+  158436895886460079883608487110870501203792108342916233258796)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger382 : ℤ := Int.ofNat
+  (5222212132087064570824073361551883087762260680978180605 * 10 ^ 60 +
+  847650229183234905190458860295692783511808819574911135484596)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger383 : ℤ := Int.ofNat
+  (5226272081759612426250533356987254117773424154409992904 * 10 ^ 60 +
+  364319940027312385512207580331960544215505724032953375631976)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger384 : ℤ := Int.ofNat
+  (712163867937080938022527621104388660167333813112950982 * 10 ^ 60 +
+  464791923737898182338279890983629467059319987664109889882904)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger385 : ℤ := Int.ofNat
+  (218052150232444140276577739546210159227349780327408012693 * 10 ^ 60 +
+  181553067151806840795202119059588955457413220599402231577432)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger386 : ℤ := Int.ofNat
+  (31140550733243657344617181599253411898106813090755541059 * 10 ^ 60 +
+  725200628133859420850220126425439691998546656253617807192416)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger387 : ℤ := Int.ofNat
+  (31185129502925059374686971778339451362585205959596399630 * 10 ^ 60 +
+  426005222542337913607268877794139040304406259434051873786872)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger388 : ℤ := Int.ofNat
+  (2740195228791318871741105408422713112502224794038390325 * 10 ^ 60 +
+  252183530146132711813140702500709342534193084275026320486948)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger389 : ℤ := Int.ofNat
+  (57733195163192166191980630115187073714630485401201812425 * 10 ^ 60 +
+  128994810506561059903111007083417512305323693583869136829976)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger390 : ℤ := Int.ofNat
+  (8794353578234607817014568902861105849444494522904527419 * 10 ^ 60 +
+  853396965489638496207534670592725900054647943280384170155072)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger391 : ℤ := Int.ofNat
+  (6233552172904703681660607609790390601555448607383744101 * 10 ^ 60 +
+  267764508865347472308348481690824720825307785697775679347028)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger392 : ℤ := Int.ofNat
+  (57958679371577123961070760757596022208052325294019623632 * 10 ^ 60 +
+  394468603319721666200652121357351657553951854366168760502292)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger393 : ℤ := Int.ofNat
+  (6321345496024729608997972489614657336695366293503355909 * 10 ^ 60 +
+  109103359918026250867138950226579113643822036537611435932048)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger394 : ℤ := Int.ofNat
+  (44210744805024583304970508818060561101651472605183581337 * 10 ^ 60 +
+  112800373013017885032128132243037079694504424628384928276848)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger395 : ℤ := Int.ofNat ((1 * 10 ^ 60 +
+  378666576527819410258279082118088862266702632052782853471949) * 10 ^ 60 +
+  867874629822963585044343081689610788042459563045788650384572)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger396 : ℤ := Int.ofNat
+  (101761339480600880240184586493303786886796832728116099534736 * 10 ^ 60 +
+  735827847111627696807118489822268009308449396565550023505916)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger397 : ℤ := Int.ofNat
+  (396874638935825757510685615805957336005377354923015963206947 * 10 ^ 60 +
+  744235607298174140537448846338131590460344055068284019047668)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger398 : ℤ := Int.ofNat
+  (362029606015904425310306262625151909025465229823360148693241 * 10 ^ 60 +
+  418108766065378318398992312938657353652946190755916866509556)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger399 : ℤ := Int.ofNat
+  (146371795781232665644531355571238788748447465628377967930676 * 10 ^ 60 +
+  457567208033428283184847200147118549124502213529383016475208)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger400 : ℤ := Int.ofNat
+  (249607387221365200811030426242562564883030437902590768563249 * 10 ^ 60 +
+  571418130490420595740583426990469781700478676435032348196268)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger401 : ℤ := Int.ofNat
+  (90966504678020421571457042078570319230167019110537346674081 * 10 ^ 60 +
+  247860608247519786116378297103184942826384197987548415577900)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger402 : ℤ := Int.ofNat
+  (176434023220775560004530514922612488148163008559076968941895 * 10 ^ 60 +
+  182272721332721939664712045965534291910081778108211750432272)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger403 : ℤ := Int.ofNat
+  (53216969623655876836527134125289676349098403020728835951247 * 10 ^ 60 +
+  847614846893656306315562967298263653475549065209325624190968)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger404 : ℤ := Int.ofNat ((4 * 10 ^ 60 +
+  508972870679456282764513078633053617977682814678127936839204) * 10 ^ 60 +
+  948136927569896581923525341713921287444715568738876410347108)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger405 : ℤ := Int.ofNat
+  (15096775978397581701108415422227820334973998639532658237804 * 10 ^ 60 +
+  490306078175208517725834163194980565205012142697952183647640)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger406 : ℤ := Int.ofNat
+  (756541481225040345535278102919799703219417302355871178703390 * 10 ^ 60 +
+  367147309937392353298240221835007487521565069908164540630956)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger407 : ℤ := Int.ofNat
+  (854506136445154217839222077961475546593057864498481124513960 * 10 ^ 60 +
+  531982690893151962619332243008525183386919713454864877630936)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger408 : ℤ := Int.ofNat ((3 * 10 ^ 60 +
+  251440783645473168743579654707805417640296373097182638327106) * 10 ^ 60 +
+  830767734000552144376874171988445822989947991470596100795836)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger409 : ℤ := Int.ofNat
+  (593434599081727423171404840560047292588642157241560012656873 * 10 ^ 60 +
+  154500098779024815873655291856341824588625254911406945550420)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger410 : ℤ := Int.ofNat ((2 * 10 ^ 60 +
+  324728640251963557117266495280188318417657657519238253516205) * 10 ^ 60 +
+  165910990079493051016546688430985758221698694990474789136352)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger411 : ℤ := Int.ofNat
+  (282779527088787325610349872124906877727788243659138236356156 * 10 ^ 60 +
+  473105612206268555701999994985839018343259207097377006596296)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger412 : ℤ := Int.ofNat ((1 * 10 ^ 60 +
+  375417882698460185175795416341916958213339876220104384763923) * 10 ^ 60 +
+  605900179578478707447301944891695030000598923364699366051684)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger413 : ℤ := Int.ofNat
+  (346364191240073554288369301353128786562528670729414528605787 * 10 ^ 60 +
+  255393949461546775270518183620198111144474747163842756471764)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger414 : ℤ := Int.ofNat
+  (162432043657677490971625416024674502981506276505535549764128 * 10 ^ 60 +
+  154111706075906554213627228752808946812699412538443898143452)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger415 : ℤ := Int.ofNat
+  (185774779055200299597637039066872805891913616382330005365634 * 10 ^ 60 +
+  322564858489359681439405230930929128070675736295524367569832)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger416 : ℤ := Int.ofNat
+  (121836662465839858902779587245156883972307161284612775045891 * 10 ^ 60 +
+  342635862568551119743852788950609840464213046754190196993876)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger417 : ℤ := Int.ofNat
+  (112813736726244676487288216958483448288164060770360077954480 * 10 ^ 60 +
+  941444678910888265899961313774305659928111270410636962381888)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger418 : ℤ := Int.ofNat
+  (58964211028813698998227126495156531254882169068355671522414 * 10 ^ 60 +
+  860945372332043774086866986840665952113513163598556586826192)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger419 : ℤ := Int.ofNat ((3 * 10 ^ 60 +
+  893202610575618597626468742037582266067694574960710376009259) * 10 ^ 60 +
+  64709942214534649472914462100244564709169493407850507473660)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger420 : ℤ := Int.ofNat ((1 * 10 ^ 60 +
+  300234417589506104231193829533435852355713730358649472891315) * 10 ^ 60 +
+  945009588151173829646616090633240007684800718424875671789688)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger421 : ℤ := Int.ofNat
+  (765329601832601589942873200498890773513036380395169846751740 * 10 ^ 60 +
+  736461669445744476224466946438674496965816359955080350616212)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger422 : ℤ := Int.ofNat ((1 * 10 ^ 60 +
+  451316409201937263044429231346018891457792810086189539754687) * 10 ^ 60 +
+  260641044820470408070139970164079694507089967247121034988804)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger423 : ℤ := Int.ofNat ((1 * 10 ^ 60 +
+  944793385005558614457395913671527408085041817940581097650695) * 10 ^ 60 +
+  443240309377523953237668342327316075536410826439942970939800)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger424 : ℤ := Int.ofNat
+  (488304695760561475717048499440944896231240868894641070555525 * 10 ^ 60 +
+  991514228508188165238879425005181785221417409673870691559800)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger425 : ℤ := Int.ofNat ((1 * 10 ^ 60 +
+  846138855061728230222545005074548039152384445581207361674791) * 10 ^ 60 +
+  905331530540480590392556056807256156358035809001907471237880)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger426 : ℤ := Int.ofNat
+  (577219766504949089074986957520579443044645876935175955706458 * 10 ^ 60 +
+  135921156452568255155581968400173303852926577313567256626440)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger427 : ℤ := Int.ofNat
+  (680213763947083940685083916540602658582545564403971324489310 * 10 ^ 60 +
+  200261587052671132116756948252525972937006827864408543308040)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger428 : ℤ := Int.ofNat
+  (128696051806663149747866291512777027257298658727954665126972 * 10 ^ 60 +
+  218628421990143290473714149488188699366387748157904680971824)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger429 : ℤ := Int.ofNat
+  (214038231895553885034008501039160062967457519663418314467531 * 10 ^ 60 +
+  130058044667775699592394718284173455847413006261264826505328)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger430 : ℤ := Int.ofNat ((6 * 10 ^ 60 +
+  450742534921895559638763328931395870259937572220587012921018) * 10 ^ 60 +
+  470952991363455707404211697355516486261679406193071076781444)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger431 : ℤ := Int.ofNat ((1 * 10 ^ 60 +
+  628117852293040139609920264618396570250304544591467243777664) * 10 ^ 60 +
+  626341081790592202732837069303358688247992236100152709390820)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger432 : ℤ := Int.ofNat
+  (472979022456280823144937229464759192523090564008574680368320 * 10 ^ 60 +
+  378253166257844411184399023327924926876041682815715407161360)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger433 : ℤ := Int.ofNat ((1 * 10 ^ 60 +
+  278833319607061484487327438571062301379390838145341964432826) * 10 ^ 60 +
+  655635672384411295254432532952962404933964501482957323139936)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger434 : ℤ := Int.ofNat ((3 * 10 ^ 60 +
+  407848891288473567507071368768427075411119325829848153764705) * 10 ^ 60 +
+  298396287945235612531669165017366976349411395277644114215140)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger435 : ℤ := Int.ofNat
+  (21696365235094477746853394780764025445199098532962468644623 * 10 ^ 60 +
+  631479864822067721920887142958058256180613577016823207108000)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger436 : ℤ := Int.ofNat
+  (900152863640129110277273318583294880846465029860788914244602 * 10 ^ 60 +
+  934434395291130095681460274448212162002340869824954108277936)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger437 : ℤ := Int.ofNat ((4 * 10 ^ 60 +
+  545110282872107304610860918776216708223825817467251434277202) * 10 ^ 60 +
+  653565247837926359703153734774048540336757625017725644345832)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger438 : ℤ := Int.ofNat
+  (726870914835771478434282344508496148799017807483044294833998 * 10 ^ 60 +
+  791187249816686044712450584385613377274076209386200084323040)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger439 : ℤ := Int.ofNat ((3 * 10 ^ 60 +
+  676941320932310874526281473228705104983902788042954480423110) * 10 ^ 60 +
+  845877158206684156589222811777808747775058197465359213897008)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger440 : ℤ := Int.ofNat ((63692 * 10 ^ 60 +
+  525548243131165413465595470183476032531233223882882838324350) * 10 ^ 60 +
+  172745283848530356016273405642961526809019461494324723542180)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger441 : ℤ := Int.ofNat ((200 * 10 ^ 60 +
+  879079056860662798170415880804865578340224377888486190565800) * 10 ^ 60 +
+  652435879404779069967334959472567127245556288918777893769702)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger442 : ℤ := Int.ofNat ((10326 * 10 ^ 60 +
+  434820290085359750314163917246317833083758358294629792069995) * 10 ^ 60 +
+  788063202684089395483596178886156356828398588358673870611884)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger443 : ℤ := Int.ofNat ((12243 * 10 ^ 60 +
+  530139122514105392136046096128731809145892538427524095726969) * 10 ^ 60 +
+  839973342181767058761209831561000101663758360825303223262480)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger444 : ℤ := Int.ofNat ((45744 * 10 ^ 60 +
+  921255268549037038970802554413251385867964724422706779114989) * 10 ^ 60 +
+  294392872917491761899607979067821326724101331373606539175176)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger445 : ℤ := Int.ofNat ((8491 * 10 ^ 60 +
+  686860643306399624092254792448709336573075078619274235853839) * 10 ^ 60 +
+  166555796344029620905825354070597652737388364202965341944160)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger446 : ℤ := Int.ofNat ((32709 * 10 ^ 60 +
+  15307965504895064710907300253488741839522856055744046126044) * 10 ^ 60 +
+  889559915273627253817630274198245079152031845636451496295048)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger447 : ℤ := Int.ofNat ((4056 * 10 ^ 60 +
+  710665942468992684190304325211763074480579080318336041007150) * 10 ^ 60 +
+  943411494685530356688456685333649130498673237045905900628000)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger448 : ℤ := Int.ofNat ((17844 * 10 ^ 60 +
+  673429739988605132829524984676177625894641791310240610635871) * 10 ^ 60 +
+  639976298922571640001879369773210262803533208059368085552756)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger449 : ℤ := Int.ofNat ((3426 * 10 ^ 60 +
+  214175153060606144335199265653013238556596855769354786700933) * 10 ^ 60 +
+  698338002862972625569100602423995852043900547552583153989900)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger450 : ℤ := Int.ofNat ((1702 * 10 ^ 60 +
+  107105235871997806522041980783242077102140857271474381773020) * 10 ^ 60 +
+  28507920485300309928704911064886577871929809989136888820650)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger451 : ℤ := Int.ofNat ((1611 * 10 ^ 60 +
+  897737269352239879478181993406809677637007414570460488068991) * 10 ^ 60 +
+  664240228261441411044836250823540744984181358477545512050970)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger452 : ℤ := Int.ofNat ((1353 * 10 ^ 60 +
+  384275994565292472818848055078328451077938205343086943831663) * 10 ^ 60 +
+  650188396360381357223346303433020781663565150810694248620968)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger453 : ℤ := Int.ofNat ((877 * 10 ^ 60 +
+  595301389085732763512656542723529774584437729265717390114020) * 10 ^ 60 +
+  781818007477766806310555552592496539025210867437894901547560)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger454 : ℤ := Int.ofNat ((617 * 10 ^ 60 +
+  542218556803321769644903206360520243083010871298396225879543) * 10 ^ 60 +
+  50344508641396018976972463897629340874613118092329401999300)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger455 : ℤ := Int.ofNat ((53740 * 10 ^ 60 +
+  957132841295423774264615881107703094983186667282395284862724) * 10 ^ 60 +
+  521880127106619461972101297067941067684506556003987892434096)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger456 : ℤ := Int.ofNat ((17853 * 10 ^ 60 +
+  557366566753564382598644667310953187904575895211402803621423) * 10 ^ 60 +
+  668968163163426650786767165547047478397984314154824474891472)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger457 : ℤ := Int.ofNat ((9901 * 10 ^ 60 +
+  455430198877246433574365169998434374592811921386746334543230) * 10 ^ 60 +
+  251667216323937908294123630262593723753947661899127269741064)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger458 : ℤ := Int.ofNat ((20197 * 10 ^ 60 +
+  121098954317967012426018769539997398644480880057546020998598) * 10 ^ 60 +
+  899368985324882182117181821035016381535132991212846653419872)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger459 : ℤ := Int.ofNat ((26861 * 10 ^ 60 +
+  917747327320849522707262640681174392040127765833634800049144) * 10 ^ 60 +
+  299254165760548794900416830815999318845970922160118597521092)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger460 : ℤ := Int.ofNat ((7106 * 10 ^ 60 +
+  897676650864720555871133218134414762789524458299097921341746) * 10 ^ 60 +
+  859652962381339972143975193840488000377853569090569242363952)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger461 : ℤ := Int.ofNat ((25901 * 10 ^ 60 +
+  687320158501376950549308886424688164875200858272103824135812) * 10 ^ 60 +
+  587527328723060506299385781216461256729391222648560116253524)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger462 : ℤ := Int.ofNat ((8542 * 10 ^ 60 +
+  219568957882817091322657240630646969775821590023612909695346) * 10 ^ 60 +
+  291380967488974004126229556095764684505605698067535325096856)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger463 : ℤ := Int.ofNat ((9487 * 10 ^ 60 +
+  896031814874189745638129869121935119541212074769376647409707) * 10 ^ 60 +
+  53361883397468272083953481965767808991869145688207156363920)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger464 : ℤ := Int.ofNat ((1555 * 10 ^ 60 +
+  916424550661198026694958889552065499996509844351156647597799) * 10 ^ 60 +
+  544070550498568751260477803959980220099544940034520746431688)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger465 : ℤ := Int.ofNat ((3108 * 10 ^ 60 +
+  434340036586888309452167053138867728996783027686958322582293) * 10 ^ 60 +
+  522943354574596572807355604156064032148417565674328673930240)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger466 : ℤ := Int.ofNat ((90634 * 10 ^ 60 +
+  55269028141293590498275191557905953477970409252114285819876) * 10 ^ 60 +
+  813259812353422815550837653174731645149166387838898020496036)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger467 : ℤ := Int.ofNat ((23269 * 10 ^ 60 +
+  756957353518597166757007622444852950662100595343655037656086) * 10 ^ 60 +
+  345026202367074946791977832405054915069793563149875156126560)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger468 : ℤ := Int.ofNat ((6240 * 10 ^ 60 +
+  345307748358278459815435175257621387874937742412421659530519) * 10 ^ 60 +
+  301452623610356325474842540664059835428413023065788151964256)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger469 : ℤ := Int.ofNat ((17958 * 10 ^ 60 +
+  266933955554691411011535019958988630230030910511427794036090) * 10 ^ 60 +
+  223626144355274524039970752103321515029736854482077207417492)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger470 : ℤ := Int.ofNat ((48133 * 10 ^ 60 +
+  745567589696039490880088663816701698297475875211833953411115) * 10 ^ 60 +
+  748838064250967235270563746866436968293659364543334135440020)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger471 : ℤ := Int.ofNat ((471 * 10 ^ 60 +
+  705758542098458521627946726638243766276816071328641653918492) * 10 ^ 60 +
+  628688249508340123849356325174991787011992379012764859066200)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger472 : ℤ := Int.ofNat ((12686 * 10 ^ 60 +
+  848613383067416414161370337642316919287153407101265476691777) * 10 ^ 60 +
+  42310423394699603417873122321971537414128795370812808771548)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger473 : ℤ := Int.ofNat ((63990 * 10 ^ 60 +
+  644527197598171231861768474023526024149025002830068584782543) * 10 ^ 60 +
+  320758857303970176574573962662275130380082879461159485842980)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger474 : ℤ := Int.ofNat ((10188 * 10 ^ 60 +
+  351021111032246582631086981708240511867496052024469744219380) * 10 ^ 60 +
+  804709150371810329482013073137098780798500755717612684924896)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger475 : ℤ := Int.ofNat ((51997 * 10 ^ 60 +
+  74911042988067647865429882655723898654783908254596977296145) * 10 ^ 60 +
+  873710175188654785772288826736528964118893211706977844105888)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger476 : ℤ := Int.ofNat ((824370435 * 10 ^ 60 +
+  367868201637367006372351242391115826788265017771082444623617) * 10 ^ 60 +
+  824379136436328275094595028259813269387693701872032696329733)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger477 : ℤ := Int.ofNat ((159791063 * 10 ^ 60 +
+  591425476576835497545554009139259012768890319027093233858982) * 10 ^ 60 +
+  989888172574177029409204131743893649084850444436683814598994)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger478 : ℤ := Int.ofNat ((76851091 * 10 ^ 60 +
+  504786427443198758092403074318829615248470464931477307053084) * 10 ^ 60 +
+  57643386039933252069119022359804400188466206268045706003070)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger479 : ℤ := Int.ofNat ((81132767 * 10 ^ 60 +
+  972933739054888093715624191000339976072314361812784069844420) * 10 ^ 60 +
+  839116300886284572116585983917380106789541316139682219388266)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger480 : ℤ := Int.ofNat ((61287233 * 10 ^ 60 +
+  460007026234593765939187958194740613964847715029533427011716) * 10 ^ 60 +
+  404793711888996954527132744681919574243640006534530255752360)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger481 : ℤ := Int.ofNat ((45309590 * 10 ^ 60 +
+  505912185563779680242063633424398552371145408376246589751959) * 10 ^ 60 +
+  262888807309993740502670277583863078778924819092152728289868)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger482 : ℤ := Int.ofNat ((27938528 * 10 ^ 60 +
+  347427474276426042351321773480220129639417166191470852749113) * 10 ^ 60 +
+  516910647511098237737184874439269110727255697329681388831500)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger483 : ℤ := Int.ofNat ((2405412654 * 10 ^ 60 +
+  178402395729491149863887705344933156816571640297912441156959) * 10 ^ 60 +
+  351477896702557210551507272594256273811948442439495877528692)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger484 : ℤ := Int.ofNat ((916516144 * 10 ^ 60 +
+  49341296833424251324666648054577564792502892394560369986600) * 10 ^ 60 +
+  556958218666646368121437570647704432044794379184452746282240)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger485 : ℤ := Int.ofNat ((114796976 * 10 ^ 60 +
+  981552219977473993833023737095763178825980155396860165197128) * 10 ^ 60 +
+  666775463898037790960901351333708489771009040341877608079888)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger486 : ℤ := Int.ofNat ((996683698 * 10 ^ 60 +
+  488956565290680056158561913667608170804137423323313472777719) * 10 ^ 60 +
+  378598274226623328270133270956761772785157840705111538947200)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger487 : ℤ := Int.ofNat ((995988363 * 10 ^ 60 +
+  800858947427127856176725299228525532508071726056603289044334) * 10 ^ 60 +
+  30094130238242264860108342376664267160658699120631542140724)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger488 : ℤ := Int.ofNat ((297943614 * 10 ^ 60 +
+  907034663034209243695576755353036274678382335521135514137777) * 10 ^ 60 +
+  276010028339653826460364307927121744095122862271875188360880)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger489 : ℤ := Int.ofNat ((1087891645 * 10 ^ 60 +
+  920332237898473246751926491321388411509034948552167897354944) * 10 ^ 60 +
+  182051192339278390953623053763375877122265048294096102030860)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger490 : ℤ := Int.ofNat ((11608161 * 10 ^ 60 +
+  275962636433821609774921642091424454528521419111050234867712) * 10 ^ 60 +
+  545580962479332966261645077380571554675138038826134683318200)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger491 : ℤ := Int.ofNat ((362915765 * 10 ^ 60 +
+  793985961280091537520682155294677374332822640095968027416456) * 10 ^ 60 +
+  686190249656082089547018118373231687227898679693436573100400)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger492 : ℤ := Int.ofNat ((362360319 * 10 ^ 60 +
+  653138980597628629221288242923903958759358187446372349723349) * 10 ^ 60 +
+  881610053585108926239337125907384870746952990008619252478040)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger493 : ℤ := Int.ofNat ((179631897 * 10 ^ 60 +
+  326253718521882474807774607744571777171800645741169757979081) * 10 ^ 60 +
+  443576952946122386073437248986516319394804670656262237385600)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger494 : ℤ := Int.ofNat ((2669328554 * 10 ^ 60 +
+  682978807711618729877302125736873493598036723810266223948861) * 10 ^ 60 +
+  810222962826643007567003478143893618725647691945222469957132)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger495 : ℤ := Int.ofNat ((793272326 * 10 ^ 60 +
+  582040933610054051240630276236160215486725762310624341624450) * 10 ^ 60 +
+  882406766997493127278933245775307620638946355915784598465120)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger496 : ℤ := Int.ofNat ((797007772 * 10 ^ 60 +
+  121370369364070471739808096381957203590772900022587053874832) * 10 ^ 60 +
+  987341132244244147190853744164869168305622330779036388856144)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger497 : ℤ := Int.ofNat ((964251478 * 10 ^ 60 +
+  998015284760020213063840016022992895694557906080194663252449) * 10 ^ 60 +
+  273699599686867942136315136870008340010069964908523874555980)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger498 : ℤ := Int.ofNat ((2171410495 * 10 ^ 60 +
+  129756819362150922956744886681831124124565531475752479355805) * 10 ^ 60 +
+  393754187929373666184956296228111947543140291065950121391500)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger499 : ℤ := Int.ofNat ((179674033 * 10 ^ 60 +
+  341619211150642037579505314487845793260307425661041205774132) * 10 ^ 60 +
+  504475218007358116793145078206148362069706538601679205236440)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger500 : ℤ := Int.ofNat ((561128503 * 10 ^ 60 +
+  400378531612058853137058011265908531094009771502855870727767) * 10 ^ 60 +
+  637224364712615327429034857702190916188742633046733189215620)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger501 : ℤ := Int.ofNat ((2180256002 * 10 ^ 60 +
+  543122762872618883138253207381693049863330995717920496253113) * 10 ^ 60 +
+  779936089788484389267562434947794018381296195390238711190668)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger502 : ℤ := Int.ofNat ((566933899 * 10 ^ 60 +
+  962512657232062592801225126259056107024793795299771359108079) * 10 ^ 60 +
+  266976045313356094009745426612408944984721704092249985430240)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger503 : ℤ := Int.ofNat ((2390257497 * 10 ^ 60 +
+  267941136638350902697699908900993808491743808403957407226073) * 10 ^ 60 +
+  453910038052493190035459729111729945278657164319382237562720)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger504 : ℤ := Int.ofNat ((30732301413893 * 10 ^ 60 +
+  967027742630606931275267866529153057914728920668080573945085) * 10 ^ 60 +
+  195612097360829355928010775436494092124348781079810565015040)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger505 : ℤ := Int.ofNat ((11669637663825 * 10 ^ 60 +
+  147666668109825945026757566962950493493235866232066950828139) * 10 ^ 60 +
+  922498392758319280733466415175727566374455218183991171094913)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger506 : ℤ := Int.ofNat ((1282268867558 * 10 ^ 60 +
+  490195371040694296372545290130076917308848833276388603290516) * 10 ^ 60 +
+  813064857762581152093628733618793740249337932571963057606975)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger507 : ℤ := Int.ofNat ((12746290325908 * 10 ^ 60 +
+  441613879783052664412859205816565565943944295044654535136147) * 10 ^ 60 +
+  433103037375936791796495001763460767641164497364439071737932)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger508 : ℤ := Int.ofNat ((12777375153911 * 10 ^ 60 +
+  781132514490053782168498187579176285834115600298547849597561) * 10 ^ 60 +
+  76857229228157214166890721803345954207475454737197756826355)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger509 : ℤ := Int.ofNat ((3926367066515 * 10 ^ 60 +
+  254085977316806188321365183003334288827820192048489585920859) * 10 ^ 60 +
+  872586972994154197870996318250893630026370896406210678843778)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger510 : ℤ := Int.ofNat ((13987820577786 * 10 ^ 60 +
+  912943382319655931698601286193440709803874350837968160861401) * 10 ^ 60 +
+  551940918172557279617285191069707317463089956245101411790686)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger511 : ℤ := Int.ofNat ((52349677778 * 10 ^ 60 +
+  685322681142002794950374321811478242124851669777932658150439) * 10 ^ 60 +
+  528128294986012388015560725833199382885259688000017553295011)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger512 : ℤ := Int.ofNat ((4623258922896 * 10 ^ 60 +
+  703197990186456365110807413733211791785623276440943457845328) * 10 ^ 60 +
+  78469783004754902756483824446696338899415211024427230573600)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger513 : ℤ := Int.ofNat ((4635348346531 * 10 ^ 60 +
+  809163007427918081576484116676362980149561542715654168720751) * 10 ^ 60 +
+  206821676529321296636911882571175950360100054236958987336692)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger514 : ℤ := Int.ofNat ((2358680716617 * 10 ^ 60 +
+  949982989353448703389091714741897479433199377297536666111621) * 10 ^ 60 +
+  109078638238230693324509982324655894229680264922587399889610)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger515 : ℤ := Int.ofNat ((34445690414068 * 10 ^ 60 +
+  629739127107936649902285522938259183823737119123324172464370) * 10 ^ 60 +
+  857598511706561117512548525093233669538531964391349904624550)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger516 : ℤ := Int.ofNat ((10345368635486 * 10 ^ 60 +
+  743367782441624708856897351403853225053056697782959258646622) * 10 ^ 60 +
+  550146731702744991038131123781281057035898268401003196401404)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger517 : ℤ := Int.ofNat ((10373363764454 * 10 ^ 60 +
+  434234590208150647284287720937469783131006667491784728610763) * 10 ^ 60 +
+  841392033320164887841455916963479617415913856013685188225458)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger518 : ℤ := Int.ofNat ((12444689146568 * 10 ^ 60 +
+  961941383417466997388555160466859258330824920572191581916467) * 10 ^ 60 +
+  652994888921070086539332750729679254837381907404698462390713)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger519 : ℤ := Int.ofNat ((28045527711007 * 10 ^ 60 +
+  320752381801104217318197938655370596405654081977467744046890) * 10 ^ 60 +
+  951200060932591337095311348780686700254961493260849550506055)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger520 : ℤ := Int.ofNat ((2281917075634 * 10 ^ 60 +
+  432386509439243830479231895970443362030089907610606601502767) * 10 ^ 60 +
+  678975668104840566245174223591067035435749795972311381949478)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger521 : ℤ := Int.ofNat ((7235785825246 * 10 ^ 60 +
+  568157229015670674527673277405395167438742996760460551766888) * 10 ^ 60 +
+  646925959958750120505859446827011911013648523467718664316197)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger522 : ℤ := Int.ofNat ((28186755283840 * 10 ^ 60 +
+  193981676196634835644801088518156271681198034392086602462362) * 10 ^ 60 +
+  326945823203532450652283892995913323247146414822222327496979)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger523 : ℤ := Int.ofNat ((7317933441108 * 10 ^ 60 +
+  411001080937674236671247075971953564746165674212360625756805) * 10 ^ 60 +
+  87672228760050914889111477820154787059506900043650764394644)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger524 : ℤ := Int.ofNat ((30924775479439 * 10 ^ 60 +
+  195185670687618096908840696847542279343553783593502345361021) * 10 ^ 60 +
+  260180050634025319805299993627739582936908227322278569945332)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger525 : ℤ := Int.ofNat ((356268811100666722 * 10 ^ 60 +
+  70883563822424175759238872955201227053952706517808674362099) * 10 ^ 60 +
+  918663592210428608141965402686833957751080971370196688180787)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger526 : ℤ := Int.ofNat ((16199982947759078 * 10 ^ 60 +
+  818145523937936059563943476458763972604501281225421846242681) * 10 ^ 60 +
+  809964914537601169859085721083953914780468119907371700855795)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger527 : ℤ := Int.ofNat ((8080351553804220 * 10 ^ 60 +
+  903370971952557336862702994415070967046956402886662260901115) * 10 ^ 60 +
+  686811740962684317508934753476314549890158450360002882770652)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger528 : ℤ := Int.ofNat ((8069692351270942 * 10 ^ 60 +
+  887620822204506324909403557616993183390591661332087840335488) * 10 ^ 60 +
+  13266213147513064094895198796279000737759991933337892540695)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger529 : ℤ := Int.ofNat ((32350026852834242 * 10 ^ 60 +
+  609137318094999721336050028490828123042049345444171947479285) * 10 ^ 60 +
+  510042868647798551462915673356547465408386562200712476167142)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger530 : ℤ := Int.ofNat ((1282131286397322282 * 10 ^ 60 +
+  463175332293781005555979547121210605627977469212983200372047) * 10 ^ 60 +
+  169684365559117521296936707579516221757010613475332367805875)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger531 : ℤ := Int.ofNat ((405498722496310550 * 10 ^ 60 +
+  161599405023106518171485251047638278943640573204668473442157) * 10 ^ 60 +
+  626582113247510879239397949349636633203048728290184007888420)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger532 : ℤ := Int.ofNat ((406590724113710002 * 10 ^ 60 +
+  286348293053969419866817406485759633786128342950041185597414) * 10 ^ 60 +
+  905700663944604881177586689895441648814577767741551280474665)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger533 : ℤ := Int.ofNat ((470041839787301730 * 10 ^ 60 +
+  15227634216705067517676889587812692898208553058273541332474) * 10 ^ 60 +
+  637401588367001760879952068334437939739384117443597079442790)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger534 : ℤ := Int.ofNat ((848448299267220129 * 10 ^ 60 +
+  617898792312990841995108252813512995897274036318552968058560) * 10 ^ 60 +
+  271610737245031878970164657419928076435648040340423545450672)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger535 : ℤ := Int.ofNat ((112492595520504467 * 10 ^ 60 +
+  531237059055993762009449963375095330407035846467535118195813) * 10 ^ 60 +
+  534430676984860715678130625477680253652916051546383976429780)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger536 : ℤ := Int.ofNat ((330456981250405111 * 10 ^ 60 +
+  925062328233890561814173038390779386546597616646349376420589) * 10 ^ 60 +
+  110597947012660284052636082592611189579683260503855561132472)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger537 : ℤ := Int.ofNat ((852750794156201423 * 10 ^ 60 +
+  861137854564905111163362844727322202350525492228294117619688) * 10 ^ 60 +
+  407029827623194454024490869329502049198475975166043206439595)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger538 : ℤ := Int.ofNat ((333667474521986954 * 10 ^ 60 +
+  43552502454941929287095474866467238157361302810717813826459) * 10 ^ 60 +
+  966898486693728857168773553956380146730982155878107949535150)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger539 : ℤ := Int.ofNat ((1134166295559693795 * 10 ^ 60 +
+  983842464905537558618945402845059317602167472515340731579523) * 10 ^ 60 +
+  714898022073390902101361704883429276050049533825560590110412)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger540 : ℤ := Int.ofNat ((14854759605665041796197 * 10 ^ 60 +
+  4766872138831741654745337406891746376339001616175844108610) * 10 ^ 60 +
+  411005911836905430582702546059142356913025381027955121594790)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger541 : ℤ := Int.ofNat ((4705064140058552846302 * 10 ^ 60 +
+  439219317259458749604213582320940000339263301293820627193142) * 10 ^ 60 +
+  199038450969750302976808005013556206237905120047725986270872)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger542 : ℤ := Int.ofNat ((4717717713698040313866 * 10 ^ 60 +
+  298268294871788044460586574890045085250128105420075279973306) * 10 ^ 60 +
+  949744858062255494006057813871563200637093649387286456615847)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger543 : ℤ := Int.ofNat ((5431977751908448636028 * 10 ^ 60 +
+  267279260007584947589945180195906660786947594902279936942161) * 10 ^ 60 +
+  262222602804899633599836727174022950038026611592942678708071)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger544 : ℤ := Int.ofNat ((9833639554324228577640 * 10 ^ 60 +
+  285205870967928751284756486256082355519633567995626464487368) * 10 ^ 60 +
+  788595244481282027329437070669993124802669258655800377739969)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger545 : ℤ := Int.ofNat ((1306209016832667234116 * 10 ^ 60 +
+  807985920213494868736436981467044355853855029432481134476060) * 10 ^ 60 +
+  590570722030478596643149483549482631327777455764610289026750)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger546 : ℤ := Int.ofNat ((3822366397433008497221 * 10 ^ 60 +
+  38000633494975132944105922468097999326515237269324702818165) * 10 ^ 60 +
+  998986071481053127709479582106954287236986682843464102442347)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger547 : ℤ := Int.ofNat ((9883522472782131462275 * 10 ^ 60 +
+  626348296409668354755574312097948144409580854311735784240070) * 10 ^ 60 +
+  725771045291584864539447210668649658822826780848142306662831)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger548 : ℤ := Int.ofNat ((3859595742251423914292 * 10 ^ 60 +
+  520094081324385441558550755740858703305597719459179369790703) * 10 ^ 60 +
+  185455465198850773890239913247603826857955675696245561020234)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger549 : ℤ := Int.ofNat ((13113939891592881047541 * 10 ^ 60 +
+  825373974826945522092601858404863363419060551630784009551030) * 10 ^ 60 +
+  446664139484803535199556222528581064132968970132652342170652)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger550 : ℤ := Int.ofNat ((347879800882038721138416467 * 10 ^ 60 +
+  602112353797827659734543032430433224591094935550996586948404) * 10 ^ 60 +
+  888233554945759499605303834492224251047973128576337014292098)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger551 : ℤ := Int.ofNat ((116767407309438697386302376 * 10 ^ 60 +
+  949424061466275506305182453930905897378473156547979139763470) * 10 ^ 60 +
+  53561838348687572727652010710329673001428849165176044615732)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger552 : ℤ := Int.ofNat ((231112393572600023752114090 * 10 ^ 60 +
+  652688292331552153429360578499527327212621779003017447184934) * 10 ^ 60 +
+  834671716597071926877651823781894578046544279411160969676366)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger553 : ℤ := Int.ofNat ((349625019320118944189646863 * 10 ^ 60 +
+  23471245748607380243598702338854465215957806785107824142699) * 10 ^ 60 +
+  596352555762941666313925972089079534948261566185170933620563)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger554 : ℤ := Int.ofNat ((232857612010680246803344486 * 10 ^ 60 +
+  74047184282331873938416248407948567837484650237128684379229) * 10 ^ 60 +
+  542790717414254093586273961378749861946832717019994889004831)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger555 : ℤ := Int.ofNat ((463970005583280270555458576 * 10 ^ 60 +
+  726735476613884027367776826907475895050106429240146131564164) * 10 ^ 60 +
+  377462434011326020463925785160644439993376996431155858681197)
+
+/-- Exact large integer shared by the full moment block and its Schur certificates. -/
+def certificateInteger556 : ℤ := Int.ofNat ((7269916010859521645129260034464 * 10 ^ 60 +
+  214540054238893602061737799320457649585412425541137343178541) * 10 ^ 60 +
+  446966955557984065288865193392562072663210906085748331482665)
+
+/-- Exact integer matrix after 0 fraction-free Schur steps in moment block Full0. -/
+def momentBlockFull0Stage0 : Fin 28 → Fin 28 → ℤ :=
+  ![![1000000000, 423308963, 71951457, 76482650, 76482117, 28193221, 31705948, 31706168,
+    148973087, 162381159, 162381048, 76574425, 23640856, -826062, -826189, 25184767, -1528158,
+    25184690, 21035273, 11656848, 21035497, 11656813, 5373335, 6700445, 13951051, 7733193,
+    7733555, 298818064],
+  ![423308963, 298818064, 28193221, 31705948, 31706168, 20333252, 21494722, 21494568, 79751621,
+    86495040, 86494935, 39889758, -9137, 1864327, 1864389, 591274, 2284387, 591309, -2998234,
+    -1514923, -2998344, -1514904, -1192529, -868051, -2410969, -1319551, -1319691, 141743481],
+  ![71951457, 28193221, 23640856, -826062, -826189, -9137, 1864327, 1864389, 27438237, 3349614,
+    3349612, 5506403, 7589636, -681088, -681283, -809987, 957561, -809686, 1370160, 455296,
+    1370265, 455102, 412026, 549857, 2599146, 126242, 126537, 20333252],
+  ![76482650, 31705948, -826062, 25184767, -1528158, 1864327, 591274, 2284387, 3349856, 30621436,
+    3504174, 5975451, -681088, -809987, 957561, 7109900, -612941, -613231, 1065984, 270523,
+    2353878, 1717831, 487649, 555248, 390599, 1403322, 19998, 21494722],
+  ![76482117, 31706168, -826189, -1528158, 25184690, 1864389, 2284387, 591309, 3349854, 3504174,
+    30621436, 5975450, -681283, 957561, -809686, -612941, -613231, 7109654, 2353567, 1717705,
+    1066067, 270288, 487668, 555251, 390534, 19621, 1403748, 21494568],
+  ![28193221, 20333252, -9137, 1864327, 1864389, 6095189, -273910, -273940, 14265654, 1411787,
+    1411790, 2769171, -1081254, 457322, 457423, 519327, -320360, 519176, -166144, 37680, -166195,
+    37777, -70012, -71505, -742651, 78463, 78319, 9365790],
+  ![31705948, 21494722, 1864327, 591274, 2284387, -273910, 6477974, -467041, 1432129, 15833908,
+    1503645, 2933691, 457322, 519327, -320360, -486932, 437258, 437401, -18413, 127362, -416222,
+    -377821, -110636, -92651, 72861, -364320, 131135, 10300379],
+  ![31706168, 21494568, 1864389, 2284387, 591309, -273940, -467041, 6477980, 1432127, 1503644,
+    15833900, 2933688, 457423, -320360, 519176, 437258, 437401, -486807, -416068, -377759, -18453,
+    127480, -110643, -92653, 72892, 131319, -364529, 10300417],
+  ![148973087, 79751621, 27438237, 3349856, 3349854, 14265654, 1432129, 1432127, 65363241,
+    6925782, 6925775, 12788775, 6365418, 202667, 202668, 307820, 305587, 307807, 1189529, 623959,
+    1189513, 623959, 291310, 474628, 1305861, 335978, 335974, 45340304],
+  ![162381159, 86495040, 3349614, 30621436, 3504174, 1411787, 15833908, 1503644, 6925782,
+    72654288, 7390663, 13722116, 315848, 196997, 310742, 7147237, 236820, 310383, 1203533, 630687,
+    1779888, 1136477, 293178, 429020, 665467, 784189, 340281, 48848306],
+  ![162381048, 86494935, 3349612, 3504174, 30621436, 1411790, 1503645, 15833900, 6925775, 7390663,
+    72654222, 13722105, 315841, 310741, 196996, 310382, 236820, 7147227, 1779896, 1136476,
+    1203525, 630686, 293173, 429020, 665471, 340280, 784192, 48848296],
+  ![76574425, 39889758, 5506403, 5975451, 5975450, 2769171, 2933691, 2933688, 12788775, 13722116,
+    13722105, 6719268, 635359, 323085, 323085, 780189, 321057, 780185, 1311683, 705659, 1311685,
+    705658, 305822, 461335, 739380, 389139, 389138, 22979581],
+  ![23640856, -9137, 7589636, -681088, -681283, -1081254, 457322, 457423, 6365418, 315848, 315841,
+    635359, 4795194, -1025445, -1025493, 1321273, 113560, 1321273, 320428, 127678, 320439, 127655,
+    194717, 89718, 1340107, 149877, 149893, 6095189],
+  ![-826062, 1864327, -681088, -809987, 957561, 457322, 519327, -320360, 202667, 196997, 310741,
+    323085, -1025445, 1321273, 113560, -1027707, 354183, 354275, 309873, 125148, -128440, -210027,
+    153598, -9261, -257922, -120319, 156445, -273910],
+  ![-826189, 1864389, -681283, 957561, -809686, 457423, -320360, 519176, 202668, 310742, 196996,
+    323085, -1025493, 113560, 1321273, 354183, 354275, -1027629, -128470, -210023, 309875, 125128,
+    153615, -9266, -257943, 156420, -120298, -273940],
+  ![25184767, 591274, -809987, 7109900, -612941, 519327, -486932, 437258, 307820, 7147237, 310382,
+    780189, 1321273, -1027707, 354183, 4647223, -1001747, 1519553, 323490, 131237, 947241, 739234,
+    200318, 77972, 215330, 807044, 179693, 6477974],
+  ![-1528158, 2284387, 957561, -612941, -613231, -320360, 437258, 437401, 305587, 236820, 236820,
+    321057, 113560, 354183, 354275, -1001747, 1519553, -1001921, -195351, -262558, -195332,
+    -262559, 195058, 78186, 210862, -143279, -143251, -467041],
+  ![25184690, 591309, -809686, -613231, 7109654, 519176, 437401, -486807, 307807, 310383, 7147227,
+    780185, 1321273, 354275, -1027629, 1519553, -1001921, 4647222, 947187, 739214, 323500, 131225,
+    200325, 77940, 215328, 179660, 807060, 6477980],
+  ![21035273, -2998234, 1370160, 1065984, 2353567, -166144, -18413, -416068, 1189529, 1203533,
+    1779896, 1311683, 320428, 309873, -128470, 323490, -195351, 947187, 2804403, 1488164, 2595168,
+    1338800, 673877, 920821, 1395420, 741344, 876755, 4872560],
+  ![11656848, -1514923, 455296, 270523, 1717705, 37680, 127362, -377759, 623959, 630687, 1136476,
+    705659, 127678, 125148, -210023, 131237, -262558, 739214, 1488164, 876755, 1338790, 725460,
+    305316, 478132, 775756, 395345, 523501, 2735066],
+  ![21035497, -2998344, 1370265, 2353878, 1066067, -166195, -416222, -18453, 1189513, 1779888,
+    1203525, 1311685, 320439, -128440, 309875, 947241, -195332, 323500, 2595168, 1338790, 2804463,
+    1488200, 673907, 920821, 1395424, 876780, 741348, 4872616],
+  ![11656813, -1514904, 455102, 1717831, 270288, 37777, -377821, 127480, 623959, 1136477, 630686,
+    705658, 127655, -210027, 125128, 739234, -262559, 131225, 1338800, 725460, 1488200, 876780,
+    305305, 478133, 775732, 523496, 395329, 2735057],
+  ![5373335, -1192529, 412026, 487649, 487668, -70012, -110636, -110643, 291310, 293178, 293173,
+    305822, 194717, 153598, 153615, 200318, 195058, 200325, 673877, 305316, 673907, 305305,
+    311051, 206949, 375018, 185908, 185909, 1188822],
+  ![6700445, -868051, 549857, 555248, 555251, -71505, -92651, -92653, 474628, 429020, 429020,
+    461335, 89718, -9261, -9266, 77972, 78186, 77940, 920821, 478132, 920821, 478133, 206949,
+    375018, 507092, 270806, 270824, 1563499],
+  ![13951051, -2410969, 2599146, 390599, 390534, -742651, 72861, 72892, 1305861, 665467, 665471,
+    739380, 1340107, -257922, -257943, 215330, 210862, 215328, 1395420, 775756, 1395424, 775732,
+    375018, 507092, 1483528, 469720, 469789, 3215208],
+  ![7733193, -1319551, 126242, 1403322, 19621, 78463, -364320, 131319, 335978, 784189, 340280,
+    389139, 149877, -120319, 156420, 807044, -143279, 179660, 741344, 395345, 876780, 523496,
+    185908, 270806, 469720, 433053, 236319, 1803902],
+  ![7733555, -1319691, 126537, 19998, 1403748, 78319, 131135, -364529, 335974, 340281, 784192,
+    389138, 149893, 156445, -120298, 179693, -143251, 807060, 876755, 523501, 741348, 395329,
+    185909, 270824, 469789, 236319, 433249, 1803955],
+  ![298818064, 141743481, 20333252, 21494722, 21494568, 9365790, 10300379, 10300417, 45340304,
+    48848306, 48848296, 22979581, 6095189, -273910, -273940, 6477974, -467041, 6477980, 4872560,
+    2735066, 4872616, 2735057, 1188822, 1563499, 3215208, 1803902, 1803955, 95993371]]
+
+/-- Exact integer matrix after 1 fraction-free Schur steps in moment block Full0. -/
+def momentBlockFull0Stage1 : Fin 27 → Fin 27 → ℤ :=
+  ![![119627585843864631, -2264475649009091, -669843258991950, -669397635314671, 8398808854860177,
+    8073310031188076, 8073062903216216, 16689978027121219, 17757639972971883, 17757581960266776,
+    7475117560928725, -10016523237792328, 2214006448593706, 2214122208832007, -10069663602166621,
+    2931269978280154, -10069596007376470, -11902653600051899, -6449371238728624,
+    -11902858421259611, -6449337422914919, -3467109866701605, -3704409424588535,
+    -8316573931570113, -4593080909508859, -4593374147353465, 15251116202492368],
+  ![-2264475649009091, 18463843835577151, -6329100102721050, -6329188752594469, -2037680328472997,
+    -416962154166236, -416915983486776, 16719406336562241, -8333946979398663, -8333940992786936,
+    -3238447687225, 5888641966072808, -621651635527666, -621837497692627, -2622067679855519,
+    1067514194626206, -2621761139593330, -143358540742761, -383431197627536, -143269657869129,
+    -383622679326541, 25406717800905, 67750219701635, 1595347553868693, -430172503612201,
+    -429903550039635, -1167143082719248],
+  ![-669843258991950, -6329100102721050, 19335171248977500, -7377712985770050, -291965254115650,
+    -1833680923802200, -140584749985200, -8044000472440550, 18202094649608650, -8915158860817200,
+    118836053773750, -2489203315148400, -746807589175700, 1020750124120850, 5183702280207450,
+    -496063426541300, -2539422830628500, -542849422513450, -621023625687200, 745027445372950,
+    826287051205550, 76682099862250, 42780210220750, -676414350765150, 811866906398550,
+    -571484780320750, -1359675402589600],
+  ![-669397635314671, -6329188752594469, -7377712985770050, 19335175779198311, -291888227128857,
+    -140551024531916, -1833645850597656, -8043923069785179, -8915080801233603, 18202189688281384,
+    118875867942275, -2489385714572152, 1020739970533254, -746497316237887, -2539125296311739,
+    -496354241049514, 5183475592811270, 744744789287059, 826164587412784, -542772342707149,
+    -621249735713121, 76703963849805, 42786781557935, -676471914854967, -571829971809581,
+    812269341664065, -1359670132561488],
+  ![8398808854860177, -2037680328472997, -291965254115650, -291888227128857, 5300331289645159,
+    -1167802798978508, -1167839001487128, 10065622835156773, -3166260901923139, -3166254772475608,
+    610291313027075, -1747765877837176, 480611348525702, 480715929064769, -190712701864507,
+    -277276303783082, -190861530986490, -759196100484333, -290964091827408, -759253415765837,
+    -290866105064673, -221503621162035, -260412126683345, -1135976064025271, -139560619284653,
+    -139714825230655, 941146282855856],
+  ![8073310031188076, -416962154166236, -1833680923802200, -140551024531916, -1167802798978508,
+    5472706861421296, -1472315113887264, -3291203949821476, 10685459416566268, -3644800064073504,
+    505826262820100, -292233751011488, 545518078816776, -294164894527828, -1285438912894116,
+    485709698083784, -361103471536120, -685356271903804, -242229416531904, -1083172374036156,
+    -747411306823724, -281002680096580, -305094960746860, -369470297551348, -609508215131964,
+    -114064692685140, 826069001355328],
+  ![8073062903216216, -416915983486776, -140584749985200, -1833645850597656, -1167839001487128,
+    -1472315113887264, 5472698910755776, -3291238723900616, -3644840307288712, 10685419212095936,
+    505806416446600, -292137951999808, -294168739449584, 545371287233752, -361254453542856,
+    485853034278544, -1285317012167920, -1083015899663864, -747352981038464, -685408001845496,
+    -242112871322584, -281010862230280, -305098434844760, -369442366782568, -113870916434424,
+    -609730394067240, 826041261381248],
+  ![16689978027121219, 16719406336562241, -8044000472440550, -8043923069785179, 10065622835156773,
+    -3291203949821476, -3291238723900616, 43170260349690431, -17264640526867833,
+    -17264630990855176, 1381246522500025, 2843566702357528, 325728006193394, 325747925775443,
+    -3444032485365729, 533241414683746, -3444034014438030, -1944160554697751, -1112597631249776,
+    -1944209924669239, -1112592417191731, -509172302435145, -523557975923715, -772470134364437,
+    -816059633576791, -816117561834285, 824454554556432],
+  ![17757639972971883, -8333946979398663, 18202094649608650, -8915080801233603, -3166260901923139,
+    10685459416566268, -3644840307288712, -17264640526867833, 46286647201816719,
+    -18976959773874632, 1287872118741425, -3522981597032104, 331133904965858, 444899527373051,
+    3057705345395047, 484964067175122, -3779136151255710, -2212199009621407, -1262165488526832,
+    -1635880383001023, -756369805186267, -579350364995265, -659006024915755, -1599920830648109,
+    -471535842110687, -915502624090245, 325882437543824],
+  ![17757581960266776, -8333940992786936, -8915158860817200, 18202189688281384, -3166254772475608,
+    -3644800064073504, 10685419212095936, -17264630990855176, -18976959773874632,
+    46286617250421696, 1287869618502600, -3522985972897088, 444877813272976, 331153435666072,
+    -3779146859095816, 484963897549584, 3057710644244880, -1635833674706104, -756375194616704,
+    -2212241048060856, -1262159511280024, -579354768555080, -659005281166360, -1599915282081448,
+    -915443983726264, -471590765665640, 325905606348928],
+  ![7475117560928725, -3238447687225, 118836053773750, 118875867942275, 610291313027075,
+    505826262820100, 505806416446600, 1381246522500025, 1287872118741425, 1287869618502600,
+    855625435919375, -1174925954707800, 386340222664350, 386349947616325, -1148320051783975,
+    438074820159150, -1148318155553250, -299080934693025, -186957432912400, -299096087364225,
+    -186955752807525, -105638037957375, -51747723119125, -328913708470675, -203025807389025,
+    -203054527330875, 97759569586800],
+  ![-10016523237792328, 5888641966072808, -2489203315148400, -2489385714572152, -1747765877837176,
+    -292233751011488, -292137951999808, 2843566702357528, -3522981597032104, -3522985972897088,
+    -1174925954707800, 4236303927587264, -1005916187210928, -1005961184822216, 725883549959448,
+    149686963223248, 725885370305360, -176863859913688, -147899864981888, -176858155465432,
+    -147922037551928, 67686761025240, -68686255380920, 1010292212260344, -32942302133208,
+    -32934860123080, -969125821222784],
+  ![2214006448593706, -621651635527666, -746807589175700, 1020739970533254, 480611348525702,
+    545518078816776, -294168739449584, 325728006193394, 331133904965858, 444877813272976,
+    386340222664350, -1005916187210928, 1320590621572156, 112877516662282, -1006902821002446,
+    352920646746204, 375079115390780, 327249439684926, 134777279172576, -111063375277186,
+    -200397749739594, 158036707856770, -3726017002410, -246397566908838, -113930903124034,
+    162833395910410, -27067752416032],
+  ![2214122208832007, -621837497692627, 1020750124120850, -746497316237887, 480715929064769,
+    -294164894527828, 545371287233752, 325747925775443, 444899527373051, 331153435666072,
+    386349947616325, -1005961184822216, 112877516662282, 1320590411736279, 374990377462963,
+    353012452670138, -1006821686153590, -111090888835403, -200392240407728, 327254296230933,
+    134758730675657, 158054390270315, -3730166045895, -246416795125361, 162809078991477,
+    -113908621928105, -27059802521904],
+  ![-10069663602166621, -2622067679855519, 5183702280207450, -2539125296311739, -190712701864507,
+    -1285438912894116, -361254453542856, -3444032485365729, 3057705345395047, -3779146859095816,
+    -1148320051783975, 725883549959448, -1006902821002446, 374990377462963, 4012950511155711,
+    -963260696830814, 885282450382770, -206278449286391, -162338000834416, 417466909325801,
+    445659880632429, 64991810012055, -90777146121315, -136023968840117, 612285336128969,
+    -15074780756685, -1047689317231088],
+  ![2931269978280154, 1067514194626206, -496063426541300, -496354241049514, -277276303783082,
+    485709698083784, 485853034278544, 533241414683746, 484964067175122, 484963897549584,
+    438074820159150, 149686963223248, 352920646746204, 353012452670138, -963260696830814,
+    1517217733127036, -963434814498980, -163205779282866, -244744494474016, -163186436975474,
+    -244745547959546, 203269304866930, 88425338630310, 232181410194058, -131461459251506,
+    -131432906058310, -10399784953888],
+  ![-10069596007376470, -2621761139593330, -2539422830628500, 5183475592811270, -190861530986490,
+    -361103471536120, -1285317012167920, -3444034014438030, -3779136151255710, 3057710644244880,
+    -1148318155553250, 725885370305360, 375079115390780, -1006821686153590, 885282450382770,
+    -963434814498980, 4012953389603900, 417420170429630, 445639896742880, -206272470940930,
+    -162348221792970, 64999223758850, -90808630187050, -136024894609190, -15098068415170,
+    612292814727050, -1047660308240160],
+  ![-11902653600051899, -143358540742761, -542849422513450, 744744789287059, -759196100484333,
+    -685356271903804, -1083015899663864, -1944160554697751, -2212199009621407, -1635833674706104,
+    -299080934693025, -176863859913688, 327249439684926, -111090888835403, -206278449286391,
+    -163205779282866, 417420170429630, 2361920289815471, 1242959020000496, 2152680577914319,
+    1093595756235051, 560847431354545, 779875310203515, 1101955833578077, 578674174083311,
+    714077559314485, -1413159553571472],
+  ![-6449371238728624, -383431197627536, -621023625687200, 826164587412784, -290964091827408,
+    -242229416531904, -747352981038464, -1112597631249776, -1262165488526832, -756375194616704,
+    -186957432912400, -147899864981888, 134777279172576, -200392240407728, -162338000834416,
+    -244744494474016, 445639896742880, 1242959020000496, 740872894704896, 1093582408866544,
+    589578302694576, 242679850651920, 400025931102640, 613130719052752, 305200344644336,
+    433352124865360, -748210751702272],
+  ![-11902858421259611, -143269657869129, 745027445372950, -542772342707149, -759253415765837,
+    -1083172374036156, -685408001845496, -1944209924669239, -1635880383001023, -2212241048060856,
+    -299096087364225, -176858155465432, -111063375277186, 327254296230933, 417466909325801,
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+  ![15251116202492368, -1167143082719248, -1359675402589600, -1359670132561488, 941146282855856,
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+    -506970932937520, 6701135627291904]]
+
+/-- Exact integer matrix after 2 fraction-free Schur steps in moment block Full0. -/
+def momentBlockFull0Stage2 : Fin 26 → Fin 26 → ℤ :=
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+
+/-- Exact integer matrix after 3 fraction-free Schur steps in moment block Full0. -/
+def momentBlockFull0Stage3 : Fin 25 → Fin 25 → ℤ :=
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+
+/-- Exact integer matrix after 4 fraction-free Schur steps in moment block Full0. -/
+def momentBlockFull0Stage4 : Fin 24 → Fin 24 → ℤ :=
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+
+/-- Exact integer matrix after 5 fraction-free Schur steps in moment block Full0. -/
+def momentBlockFull0Stage5 : Fin 23 → Fin 23 → ℤ :=
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+/-- Exact integer matrix after 6 fraction-free Schur steps in moment block Full0. -/
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+/-- Exact integer matrix after 7 fraction-free Schur steps in moment block Full0. -/
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+/-- Exact integer matrix after 8 fraction-free Schur steps in moment block Full0. -/
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+/-- Exact integer matrix after 10 fraction-free Schur steps in moment block Full0. -/
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+    -15654859399414672678724437228038374769233589170099336069292212541443950329727444041233215,
+    -7017884002199586751376750807970917030301252710677519245330132937697853716111085947357715,
+    62816173529214137131427427807203140034928879964379042528633886914625785173223698373557437,
+    8026364686969195447938500651795212254134859583172168506089847828795024934312510274640608,
+    8042589946862589910458951101357917745071023200421964853856534975074774338528746943739366,
+    1176186106793319374600724771081579212543590251690866009130365718257225903915423600197660],
+  ![-23780830434717092989202653270583122583796071121451346676572335337607008127166083545933808,
+    19481033425011637088360976879467130502717692213490596974835981190881219020847457872075168,
+    31703259715712053610894514722201658082820548205961930985420340875727177400081110417517592,
+    3170784826868432708462097832134007978026119848833170131855275287830553394627218054692584,
+    -29437152017044905123373568213117841816513407460055160833687624632383120751933639391719304,
+    -16683315633091595801901868365730351815669733440867884188745064953084174842369303544610512,
+    -4886502248262619966448164911779584351104067796042096864888835679402376128307319148410320,
+    -1445079060267680611457539323363703771154128869368192148003298226332438525844099550750632,
+    3834194111337627949042961142035060075117081182745838384818713616542973843808279771327112,
+    -8925444368309762756619568484877800817801068840882635085289144345065327327030409656802368,
+    216034086476505250548312000852685247231516966547738464067189501337303316515732582629992,
+    8026364686969195447938500651795212254134859583172168506089847828795024934312510274640608,
+    24505455266158022990584542176018144406228734545462134141296829332671196687213432179392808,
+    -5894188414889849139503821677408408727013821299385364049085599313536997252777713979297736,
+    -1849900175235478616561191485516907795031982424036997327996286566791340321651886748370456],
+  ![19487729169656622312124149165939997877268862080251222885971506844104675118931278934487690,
+    -23771075526809847418389256836601792591393738375553205209558958481249235740523293294867198,
+    -29436152638583531285744544359524214049230951761725494052145558221803665464002044563541006,
+    3192607473382126261654726553949627703810027014678942238277483185239542486396446884326900,
+    31693026751392801186532917197034956543742215494789065065977840388225117784481837765946648,
+    -1464029849889484499311793923421832279533618777109434062463823680362165342697587689336418,
+    3836805942064574318080669456022823772030574329415285407666227194109856163331316690363372,
+    -16696010318037450480176538035205494198961126276162743458329204448427855981940328738151304,
+    -4890461968174508937661654374475412918484507370348303532561666044246697599730521882400030,
+    -8934578898175895321931741195546234402270567961751424546741509376669269165195468225701474,
+    213938196990264043660737250308149500731679425407411151934251340707404358953414635279734,
+    8042589946862589910458951101357917745071023200421964853856534975074774338528746943739366,
+    -5894188414889849139503821677408408727013821299385364049085599313536997252777713979297736,
+    24560359471927945893120933884766486544954314160563584673810988325873540925267638862825564,
+    -1871016050607126263444362992053177176757466779640154424879668648373479841665080376483640],
+  ![-3350639528625291344969150433977643341811265502901285862032579159042594510903181271556556,
+    -3343342373657552203265108693511800313409013018238575317883605765158752069493617846615988,
+    -3746169599952718219001718669084845611560425321090875699697330382974931915317861380035772,
+    -734127026274934288582684443590982626775389673018282635336004772624578914356787440121856,
+    -3748610511016376992137942483916090011366308219035860924283717878612711655471491984369568,
+    62471249084080808951283755332277128712535202586221551046824676147959551999018438311956,
+    2042559805185679709335840301102521768450757062476664444970660699051993048990344688642296,
+    55716563818325870145843988757987365843397667394524625679974663843441227079065392511576,
+    2044636965483198846697854422572207569747097494823612400013650611081818588785065475448852,
+    -2604683861333914899044636173155118870061894339258839891325742775030565844238663055909932,
+    1275729683570893614014792023160172620569724797079355742217506360781162362615233259623484,
+    1176186106793319374600724771081579212543590251690866009130365718257225903915423600197660,
+    -1849900175235478616561191485516907795031982424036997327996286566791340321651886748370456,
+    -1871016050607126263444362992053177176757466779640154424879668648373479841665080376483640,
+    12526006278449888936491999288554295757678553961391116082325581193534402895351476114148176]]
+
+/-- Exact integer matrix after 14 fraction-free Schur steps in moment block Full0. -/
+def momentBlockFull0Stage14 : Fin 14 → Fin 14 → ℤ :=
+  ![![certificateInteger0, certificateInteger1, certificateInteger2, -certificateInteger3,
+    -certificateInteger4, -certificateInteger5, certificateInteger6, -certificateInteger7,
+    certificateInteger8, -certificateInteger9, -certificateInteger10, certificateInteger11,
+    -certificateInteger12, -certificateInteger13],
+  ![certificateInteger1, certificateInteger14, certificateInteger15, -certificateInteger16,
+    -certificateInteger17, -certificateInteger18, -certificateInteger19, -certificateInteger20,
+    certificateInteger21, -certificateInteger22, -certificateInteger23, certificateInteger24,
+    -certificateInteger25, -certificateInteger26],
+  ![certificateInteger2, certificateInteger15, certificateInteger27, -certificateInteger28,
+    -certificateInteger29, -certificateInteger30, -certificateInteger31, -certificateInteger32,
+    certificateInteger33, certificateInteger34, -certificateInteger35, certificateInteger36,
+    -certificateInteger37, certificateInteger38],
+  ![-certificateInteger3, -certificateInteger16, -certificateInteger28, certificateInteger39,
+    certificateInteger40, certificateInteger41, -certificateInteger42, certificateInteger43,
+    -certificateInteger44, certificateInteger45, certificateInteger46, -certificateInteger47,
+    certificateInteger48, -certificateInteger49],
+  ![-certificateInteger4, -certificateInteger17, -certificateInteger29, certificateInteger40,
+    certificateInteger50, certificateInteger51, certificateInteger52, certificateInteger53,
+    -certificateInteger54, certificateInteger55, -certificateInteger56, -certificateInteger57,
+    -certificateInteger58, certificateInteger59],
+  ![-certificateInteger5, -certificateInteger18, -certificateInteger30, certificateInteger41,
+    certificateInteger51, certificateInteger60, certificateInteger61, certificateInteger62,
+    -certificateInteger63, certificateInteger64, certificateInteger65, -certificateInteger66,
+    certificateInteger67, certificateInteger68],
+  ![certificateInteger6, -certificateInteger19, -certificateInteger31, -certificateInteger42,
+    certificateInteger52, certificateInteger61, certificateInteger69, certificateInteger70,
+    certificateInteger71, certificateInteger72, -certificateInteger73, -certificateInteger74,
+    -certificateInteger75, -certificateInteger76],
+  ![-certificateInteger7, -certificateInteger20, -certificateInteger32, certificateInteger43,
+    certificateInteger53, certificateInteger62, certificateInteger70, certificateInteger77,
+    -certificateInteger78, certificateInteger79, certificateInteger80, -certificateInteger81,
+    certificateInteger82, certificateInteger83],
+  ![certificateInteger8, certificateInteger21, certificateInteger33, -certificateInteger44,
+    -certificateInteger54, -certificateInteger63, certificateInteger71, -certificateInteger78,
+    certificateInteger84, -certificateInteger85, -certificateInteger86, -certificateInteger87,
+    -certificateInteger88, -certificateInteger89],
+  ![-certificateInteger9, -certificateInteger22, certificateInteger34, certificateInteger45,
+    certificateInteger55, certificateInteger64, certificateInteger72, certificateInteger79,
+    -certificateInteger85, certificateInteger90, -certificateInteger91, -certificateInteger92,
+    certificateInteger93, certificateInteger94],
+  ![-certificateInteger10, -certificateInteger23, -certificateInteger35, certificateInteger46,
+    -certificateInteger56, certificateInteger65, -certificateInteger73, certificateInteger80,
+    -certificateInteger86, -certificateInteger91, certificateInteger95, certificateInteger96,
+    certificateInteger97, certificateInteger98],
+  ![certificateInteger11, certificateInteger24, certificateInteger36, -certificateInteger47,
+    -certificateInteger57, -certificateInteger66, -certificateInteger74, -certificateInteger81,
+    -certificateInteger87, -certificateInteger92, certificateInteger96, certificateInteger99,
+    -certificateInteger100, -certificateInteger101],
+  ![-certificateInteger12, -certificateInteger25, -certificateInteger37, certificateInteger48,
+    -certificateInteger58, certificateInteger67, -certificateInteger75, certificateInteger82,
+    -certificateInteger88, certificateInteger93, certificateInteger97, -certificateInteger100,
+    certificateInteger102, -certificateInteger103],
+  ![-certificateInteger13, -certificateInteger26, certificateInteger38, -certificateInteger49,
+    certificateInteger59, certificateInteger68, -certificateInteger76, certificateInteger83,
+    -certificateInteger89, certificateInteger94, certificateInteger98, -certificateInteger101,
+    -certificateInteger103, certificateInteger104]]
+
+/-- Exact integer matrix after 15 fraction-free Schur steps in moment block Full0. -/
+def momentBlockFull0Stage15 : Fin 13 → Fin 13 → ℤ :=
+  ![![certificateInteger105, -certificateInteger106, -certificateInteger107,
+    -certificateInteger108, -certificateInteger109, -certificateInteger110,
+    -certificateInteger111, -certificateInteger112, -certificateInteger113,
+    -certificateInteger114, certificateInteger115, -certificateInteger116,
+    -certificateInteger117],
+  ![-certificateInteger106, certificateInteger118, -certificateInteger119, -certificateInteger120,
+    -certificateInteger121, -certificateInteger122, -certificateInteger123, certificateInteger124,
+    certificateInteger125, certificateInteger126, certificateInteger127, certificateInteger128,
+    certificateInteger129],
+  ![-certificateInteger107, -certificateInteger119, certificateInteger130, -certificateInteger131,
+    -certificateInteger132, -certificateInteger133, -certificateInteger134,
+    -certificateInteger135, -certificateInteger136, -certificateInteger137,
+    -certificateInteger138, certificateInteger139, -certificateInteger140],
+  ![-certificateInteger108, -certificateInteger120, -certificateInteger131, certificateInteger141,
+    certificateInteger142, certificateInteger143, certificateInteger144, certificateInteger145,
+    certificateInteger146, -certificateInteger147, -certificateInteger148, -certificateInteger149,
+    -certificateInteger150],
+  ![-certificateInteger109, -certificateInteger121, -certificateInteger132, certificateInteger142,
+    certificateInteger151, certificateInteger152, certificateInteger153, certificateInteger154,
+    -certificateInteger155, -certificateInteger156, -certificateInteger157,
+    -certificateInteger158, certificateInteger159],
+  ![-certificateInteger110, -certificateInteger122, -certificateInteger133, certificateInteger143,
+    certificateInteger152, certificateInteger160, certificateInteger161, certificateInteger162,
+    certificateInteger163, -certificateInteger164, -certificateInteger165, -certificateInteger166,
+    -certificateInteger167],
+  ![-certificateInteger111, -certificateInteger123, -certificateInteger134, certificateInteger144,
+    certificateInteger153, certificateInteger161, certificateInteger168, certificateInteger169,
+    -certificateInteger170, -certificateInteger171, -certificateInteger172,
+    -certificateInteger173, certificateInteger174],
+  ![-certificateInteger112, certificateInteger124, -certificateInteger135, certificateInteger145,
+    certificateInteger154, certificateInteger162, certificateInteger169, certificateInteger175,
+    -certificateInteger176, -certificateInteger177, -certificateInteger178,
+    -certificateInteger179, -certificateInteger180],
+  ![-certificateInteger113, certificateInteger125, -certificateInteger136, certificateInteger146,
+    -certificateInteger155, certificateInteger163, -certificateInteger170, -certificateInteger176,
+    certificateInteger181, -certificateInteger182, -certificateInteger183, -certificateInteger184,
+    certificateInteger185],
+  ![-certificateInteger114, certificateInteger126, -certificateInteger137, -certificateInteger147,
+    -certificateInteger156, -certificateInteger164, -certificateInteger171,
+    -certificateInteger177, -certificateInteger182, certificateInteger186, certificateInteger187,
+    certificateInteger188, certificateInteger189],
+  ![certificateInteger115, certificateInteger127, -certificateInteger138, -certificateInteger148,
+    -certificateInteger157, -certificateInteger165, -certificateInteger172,
+    -certificateInteger178, -certificateInteger183, certificateInteger187, certificateInteger190,
+    -certificateInteger191, -certificateInteger192],
+  ![-certificateInteger116, certificateInteger128, certificateInteger139, -certificateInteger149,
+    -certificateInteger158, -certificateInteger166, -certificateInteger173,
+    -certificateInteger179, -certificateInteger184, certificateInteger188, -certificateInteger191,
+    certificateInteger193, -certificateInteger194],
+  ![-certificateInteger117, certificateInteger129, -certificateInteger140, -certificateInteger150,
+    certificateInteger159, -certificateInteger167, certificateInteger174, -certificateInteger180,
+    certificateInteger185, certificateInteger189, -certificateInteger192, -certificateInteger194,
+    certificateInteger195]]
+
+/-- Exact integer matrix after 16 fraction-free Schur steps in moment block Full0. -/
+def momentBlockFull0Stage16 : Fin 12 → Fin 12 → ℤ :=
+  ![![certificateInteger196, -certificateInteger197, -certificateInteger198,
+    -certificateInteger199, -certificateInteger200, -certificateInteger201, certificateInteger202,
+    certificateInteger203, certificateInteger204, certificateInteger205, certificateInteger206,
+    certificateInteger207],
+  ![-certificateInteger197, certificateInteger208, -certificateInteger209, -certificateInteger210,
+    -certificateInteger211, -certificateInteger212, -certificateInteger213,
+    -certificateInteger214, -certificateInteger215, -certificateInteger216, certificateInteger217,
+    -certificateInteger218],
+  ![-certificateInteger198, -certificateInteger209, certificateInteger219, certificateInteger220,
+    certificateInteger221, certificateInteger222, certificateInteger223, certificateInteger224,
+    -certificateInteger225, -certificateInteger226, -certificateInteger227,
+    -certificateInteger228],
+  ![-certificateInteger199, -certificateInteger210, certificateInteger220, certificateInteger229,
+    certificateInteger230, certificateInteger231, certificateInteger232, -certificateInteger233,
+    -certificateInteger234, -certificateInteger235, -certificateInteger236,
+    certificateInteger237],
+  ![-certificateInteger200, -certificateInteger211, certificateInteger221, certificateInteger230,
+    certificateInteger238, certificateInteger239, certificateInteger240, certificateInteger241,
+    -certificateInteger242, -certificateInteger243, -certificateInteger244,
+    -certificateInteger245],
+  ![-certificateInteger201, -certificateInteger212, certificateInteger222, certificateInteger231,
+    certificateInteger239, certificateInteger246, certificateInteger247, -certificateInteger248,
+    -certificateInteger249, -certificateInteger250, -certificateInteger251,
+    certificateInteger252],
+  ![certificateInteger202, -certificateInteger213, certificateInteger223, certificateInteger232,
+    certificateInteger240, certificateInteger247, certificateInteger253, -certificateInteger254,
+    -certificateInteger255, -certificateInteger256, -certificateInteger257,
+    -certificateInteger258],
+  ![certificateInteger203, -certificateInteger214, certificateInteger224, -certificateInteger233,
+    certificateInteger241, -certificateInteger248, -certificateInteger254, certificateInteger259,
+    -certificateInteger260, certificateInteger261, -certificateInteger262, certificateInteger263],
+  ![certificateInteger204, -certificateInteger215, -certificateInteger225, -certificateInteger234,
+    -certificateInteger242, -certificateInteger249, -certificateInteger255,
+    -certificateInteger260, certificateInteger264, certificateInteger265, certificateInteger266,
+    certificateInteger267],
+  ![certificateInteger205, -certificateInteger216, -certificateInteger226, -certificateInteger235,
+    -certificateInteger243, -certificateInteger250, -certificateInteger256, certificateInteger261,
+    certificateInteger265, certificateInteger268, certificateInteger269, -certificateInteger270],
+  ![certificateInteger206, certificateInteger217, -certificateInteger227, -certificateInteger236,
+    -certificateInteger244, -certificateInteger251, -certificateInteger257,
+    -certificateInteger262, certificateInteger266, certificateInteger269, certificateInteger271,
+    -certificateInteger272],
+  ![certificateInteger207, -certificateInteger218, -certificateInteger228, certificateInteger237,
+    -certificateInteger245, certificateInteger252, -certificateInteger258, certificateInteger263,
+    certificateInteger267, -certificateInteger270, -certificateInteger272, certificateInteger273]]
+
+/-- Exact integer matrix after 17 fraction-free Schur steps in moment block Full0. -/
+def momentBlockFull0Stage17 : Fin 11 → Fin 11 → ℤ :=
+  ![![certificateInteger274, -certificateInteger275, -certificateInteger276,
+    -certificateInteger277, -certificateInteger278, -certificateInteger279,
+    -certificateInteger280, -certificateInteger281, -certificateInteger282, certificateInteger283,
+    -certificateInteger284],
+  ![-certificateInteger275, certificateInteger285, certificateInteger286, certificateInteger287,
+    certificateInteger288, certificateInteger289, certificateInteger290, -certificateInteger291,
+    -certificateInteger292, -certificateInteger293, -certificateInteger294],
+  ![-certificateInteger276, certificateInteger286, certificateInteger295, certificateInteger296,
+    certificateInteger297, certificateInteger298, -certificateInteger299, -certificateInteger300,
+    certificateInteger301, -certificateInteger302, certificateInteger303],
+  ![-certificateInteger277, certificateInteger287, certificateInteger296, certificateInteger304,
+    certificateInteger305, certificateInteger306, certificateInteger307, -certificateInteger308,
+    -certificateInteger309, -certificateInteger310, -certificateInteger311],
+  ![-certificateInteger278, certificateInteger288, certificateInteger297, certificateInteger305,
+    certificateInteger312, certificateInteger313, -certificateInteger314, -certificateInteger315,
+    certificateInteger316, -certificateInteger317, certificateInteger318],
+  ![-certificateInteger279, certificateInteger289, certificateInteger298, certificateInteger306,
+    certificateInteger313, certificateInteger319, -certificateInteger320, -certificateInteger321,
+    -certificateInteger322, -certificateInteger323, -certificateInteger324],
+  ![-certificateInteger280, certificateInteger290, -certificateInteger299, certificateInteger307,
+    -certificateInteger314, -certificateInteger320, certificateInteger325, -certificateInteger326,
+    -certificateInteger327, -certificateInteger328, -certificateInteger329],
+  ![-certificateInteger281, -certificateInteger291, -certificateInteger300,
+    -certificateInteger308, -certificateInteger315, -certificateInteger321,
+    -certificateInteger326, certificateInteger330, certificateInteger331, certificateInteger332,
+    certificateInteger333],
+  ![-certificateInteger282, -certificateInteger292, certificateInteger301, -certificateInteger309,
+    certificateInteger316, -certificateInteger322, -certificateInteger327, certificateInteger331,
+    certificateInteger334, certificateInteger335, -certificateInteger336],
+  ![certificateInteger283, -certificateInteger293, -certificateInteger302, -certificateInteger310,
+    -certificateInteger317, -certificateInteger323, -certificateInteger328, certificateInteger332,
+    certificateInteger335, certificateInteger337, -certificateInteger338],
+  ![-certificateInteger284, -certificateInteger294, certificateInteger303, -certificateInteger311,
+    certificateInteger318, -certificateInteger324, -certificateInteger329, certificateInteger333,
+    -certificateInteger336, -certificateInteger338, certificateInteger339]]
+
+/-- Exact integer matrix after 18 fraction-free Schur steps in moment block Full0. -/
+def momentBlockFull0Stage18 : Fin 10 → Fin 10 → ℤ :=
+  ![![certificateInteger340, certificateInteger341, certificateInteger342, certificateInteger343,
+    certificateInteger344, certificateInteger345, -certificateInteger346, -certificateInteger347,
+    -certificateInteger348, -certificateInteger349],
+  ![certificateInteger341, certificateInteger350, certificateInteger351, certificateInteger352,
+    certificateInteger353, -certificateInteger354, -certificateInteger355, -certificateInteger356,
+    -certificateInteger357, certificateInteger358],
+  ![certificateInteger342, certificateInteger351, certificateInteger359, certificateInteger360,
+    certificateInteger361, certificateInteger362, -certificateInteger363, -certificateInteger364,
+    -certificateInteger365, -certificateInteger366],
+  ![certificateInteger343, certificateInteger352, certificateInteger360, certificateInteger367,
+    certificateInteger368, -certificateInteger369, -certificateInteger370, -certificateInteger371,
+    -certificateInteger372, certificateInteger373],
+  ![certificateInteger344, certificateInteger353, certificateInteger361, certificateInteger368,
+    certificateInteger374, -certificateInteger375, -certificateInteger376, -certificateInteger377,
+    -certificateInteger378, -certificateInteger379],
+  ![certificateInteger345, -certificateInteger354, certificateInteger362, -certificateInteger369,
+    -certificateInteger375, certificateInteger380, -certificateInteger381, -certificateInteger382,
+    -certificateInteger383, -certificateInteger384],
+  ![-certificateInteger346, -certificateInteger355, -certificateInteger363,
+    -certificateInteger370, -certificateInteger376, -certificateInteger381, certificateInteger385,
+    certificateInteger386, certificateInteger387, -certificateInteger388],
+  ![-certificateInteger347, -certificateInteger356, -certificateInteger364,
+    -certificateInteger371, -certificateInteger377, -certificateInteger382, certificateInteger386,
+    certificateInteger389, certificateInteger390, -certificateInteger391],
+  ![-certificateInteger348, -certificateInteger357, -certificateInteger365,
+    -certificateInteger372, -certificateInteger378, -certificateInteger383, certificateInteger387,
+    certificateInteger390, certificateInteger392, -certificateInteger393],
+  ![-certificateInteger349, certificateInteger358, -certificateInteger366, certificateInteger373,
+    -certificateInteger379, -certificateInteger384, -certificateInteger388,
+    -certificateInteger391, -certificateInteger393, certificateInteger394]]
+
+/-- Exact integer matrix after 19 fraction-free Schur steps in moment block Full0. -/
+def momentBlockFull0Stage19 : Fin 9 → Fin 9 → ℤ :=
+  ![![certificateInteger395, certificateInteger396, certificateInteger397, certificateInteger398,
+    -certificateInteger399, -certificateInteger400, -certificateInteger401,
+    -certificateInteger402, certificateInteger403],
+  ![certificateInteger396, certificateInteger404, certificateInteger405, certificateInteger406,
+    certificateInteger407, -certificateInteger408, certificateInteger409, -certificateInteger410,
+    -certificateInteger411],
+  ![certificateInteger397, certificateInteger405, certificateInteger412, certificateInteger413,
+    -certificateInteger414, -certificateInteger415, -certificateInteger416,
+    -certificateInteger417, certificateInteger418],
+  ![certificateInteger398, certificateInteger406, certificateInteger413, certificateInteger419,
+    -certificateInteger420, -certificateInteger421, -certificateInteger422,
+    -certificateInteger423, -certificateInteger424],
+  ![-certificateInteger399, certificateInteger407, -certificateInteger414, -certificateInteger420,
+    certificateInteger425, -certificateInteger426, certificateInteger427, certificateInteger428,
+    certificateInteger429],
+  ![-certificateInteger400, -certificateInteger408, -certificateInteger415,
+    -certificateInteger421, -certificateInteger426, certificateInteger430, -certificateInteger431,
+    certificateInteger432, -certificateInteger433],
+  ![-certificateInteger401, certificateInteger409, -certificateInteger416, -certificateInteger422,
+    certificateInteger427, -certificateInteger431, certificateInteger434, -certificateInteger435,
+    -certificateInteger436],
+  ![-certificateInteger402, -certificateInteger410, -certificateInteger417,
+    -certificateInteger423, certificateInteger428, certificateInteger432, -certificateInteger435,
+    certificateInteger437, -certificateInteger438],
+  ![certificateInteger403, -certificateInteger411, certificateInteger418, -certificateInteger424,
+    certificateInteger429, -certificateInteger433, -certificateInteger436, -certificateInteger438,
+    certificateInteger439]]
+
+/-- Exact integer matrix after 20 fraction-free Schur steps in moment block Full0. -/
+def momentBlockFull0Stage20 : Fin 8 → Fin 8 → ℤ :=
+  ![![certificateInteger440, -certificateInteger441, certificateInteger442, certificateInteger443,
+    -certificateInteger444, certificateInteger445, -certificateInteger446,
+    -certificateInteger447],
+  ![-certificateInteger441, certificateInteger448, certificateInteger449, -certificateInteger450,
+    -certificateInteger451, -certificateInteger452, -certificateInteger453,
+    certificateInteger454],
+  ![certificateInteger442, certificateInteger449, certificateInteger455, -certificateInteger456,
+    -certificateInteger457, -certificateInteger458, -certificateInteger459,
+    -certificateInteger460],
+  ![certificateInteger443, -certificateInteger450, -certificateInteger456, certificateInteger461,
+    -certificateInteger462, certificateInteger463, certificateInteger464, certificateInteger465],
+  ![-certificateInteger444, -certificateInteger451, -certificateInteger457,
+    -certificateInteger462, certificateInteger466, -certificateInteger467, certificateInteger468,
+    -certificateInteger469],
+  ![certificateInteger445, -certificateInteger452, -certificateInteger458, certificateInteger463,
+    -certificateInteger467, certificateInteger470, -certificateInteger471,
+    -certificateInteger472],
+  ![-certificateInteger446, -certificateInteger453, -certificateInteger459, certificateInteger464,
+    certificateInteger468, -certificateInteger471, certificateInteger473, -certificateInteger474],
+  ![-certificateInteger447, certificateInteger454, -certificateInteger460, certificateInteger465,
+    -certificateInteger469, -certificateInteger472, -certificateInteger474,
+    certificateInteger475]]
+
+/-- Exact integer matrix after 21 fraction-free Schur steps in moment block Full0. -/
+def momentBlockFull0Stage21 : Fin 7 → Fin 7 → ℤ :=
+  ![![certificateInteger476, certificateInteger477, -certificateInteger478,
+    -certificateInteger479, -certificateInteger480, -certificateInteger481,
+    certificateInteger482],
+  ![certificateInteger477, certificateInteger483, -certificateInteger484, -certificateInteger485,
+    -certificateInteger486, -certificateInteger487, -certificateInteger488],
+  ![-certificateInteger478, -certificateInteger484, certificateInteger489, certificateInteger490,
+    certificateInteger491, certificateInteger492, certificateInteger493],
+  ![-certificateInteger479, -certificateInteger485, certificateInteger490, certificateInteger494,
+    -certificateInteger495, -certificateInteger496, -certificateInteger497],
+  ![-certificateInteger480, -certificateInteger486, certificateInteger491, -certificateInteger495,
+    certificateInteger498, certificateInteger499, -certificateInteger500],
+  ![-certificateInteger481, -certificateInteger487, certificateInteger492, -certificateInteger496,
+    certificateInteger499, certificateInteger501, -certificateInteger502],
+  ![certificateInteger482, -certificateInteger488, certificateInteger493, -certificateInteger497,
+    -certificateInteger500, -certificateInteger502, certificateInteger503]]
+
+/-- Exact integer matrix after 22 fraction-free Schur steps in moment block Full0. -/
+def momentBlockFull0Stage22 : Fin 6 → Fin 6 → ℤ :=
+  ![![certificateInteger504, -certificateInteger505, -certificateInteger506,
+    -certificateInteger507, -certificateInteger508, -certificateInteger509],
+  ![-certificateInteger505, certificateInteger510, certificateInteger511, certificateInteger512,
+    certificateInteger513, certificateInteger514],
+  ![-certificateInteger506, certificateInteger511, certificateInteger515, -certificateInteger516,
+    -certificateInteger517, -certificateInteger518],
+  ![-certificateInteger507, certificateInteger512, -certificateInteger516, certificateInteger519,
+    certificateInteger520, -certificateInteger521],
+  ![-certificateInteger508, certificateInteger513, -certificateInteger517, certificateInteger520,
+    certificateInteger522, -certificateInteger523],
+  ![-certificateInteger509, certificateInteger514, -certificateInteger518, -certificateInteger521,
+    -certificateInteger523, certificateInteger524]]
+
+/-- Exact integer matrix after 23 fraction-free Schur steps in moment block Full0. -/
+def momentBlockFull0Stage23 : Fin 5 → Fin 5 → ℤ :=
+  ![![certificateInteger525, -certificateInteger526, -certificateInteger527,
+    -certificateInteger528, certificateInteger529],
+  ![-certificateInteger526, certificateInteger530, -certificateInteger531, -certificateInteger532,
+    -certificateInteger533],
+  ![-certificateInteger527, -certificateInteger531, certificateInteger534, -certificateInteger535,
+    -certificateInteger536],
+  ![-certificateInteger528, -certificateInteger532, -certificateInteger535, certificateInteger537,
+    -certificateInteger538],
+  ![certificateInteger529, -certificateInteger533, -certificateInteger536, -certificateInteger538,
+    certificateInteger539]]
+
+/-- Exact integer matrix after 24 fraction-free Schur steps in moment block Full0. -/
+def momentBlockFull0Stage24 : Fin 4 → Fin 4 → ℤ :=
+  ![![certificateInteger540, -certificateInteger541, -certificateInteger542,
+    -certificateInteger543],
+  ![-certificateInteger541, certificateInteger544, -certificateInteger545, -certificateInteger546],
+  ![-certificateInteger542, -certificateInteger545, certificateInteger547, -certificateInteger548],
+  ![-certificateInteger543, -certificateInteger546, -certificateInteger548, certificateInteger549]]
+
+/-- Exact integer matrix after 25 fraction-free Schur steps in moment block Full0. -/
+def momentBlockFull0Stage25 : Fin 3 → Fin 3 → ℤ :=
+  ![![certificateInteger550, -certificateInteger551, -certificateInteger552],
+  ![-certificateInteger551, certificateInteger553, -certificateInteger554],
+  ![-certificateInteger552, -certificateInteger554, certificateInteger555]]
+
+/-- Exact integer matrix after 26 fraction-free Schur steps in moment block Full0. -/
+def momentBlockFull0Stage26 : Fin 2 → Fin 2 → ℤ :=
+  ![![certificateInteger556, -certificateInteger556],
+  ![-certificateInteger556, certificateInteger556]]
+
+/-- Exact integer matrix after 27 fraction-free Schur steps in moment block Full0. -/
+def momentBlockFull0Stage27 : Fin 1 → Fin 1 → ℤ :=
+  ![![0]]
+
+theorem momentBlockFull0Stage27_psd : IsPSD (fun i j => (momentBlockFull0Stage27 i j : ℝ)) := by
+  intro x
+  simp [quadraticForm, momentBlockFull0Stage27]
+
+theorem momentBlockFull0Stage26_psd : IsPSD (fun i j => (momentBlockFull0Stage26 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage26 momentBlockFull0Stage27 (certificateInteger550)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage27_psd
+
+theorem momentBlockFull0Stage25_psd : IsPSD (fun i j => (momentBlockFull0Stage25 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage25 momentBlockFull0Stage26 (certificateInteger540)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage26_psd
+
+theorem momentBlockFull0Stage24_psd : IsPSD (fun i j => (momentBlockFull0Stage24 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage24 momentBlockFull0Stage25 (certificateInteger525)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage25_psd
+
+theorem momentBlockFull0Stage23_psd : IsPSD (fun i j => (momentBlockFull0Stage23 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage23 momentBlockFull0Stage24 (certificateInteger504)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage24_psd
+
+theorem momentBlockFull0Stage22_psd : IsPSD (fun i j => (momentBlockFull0Stage22 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage22 momentBlockFull0Stage23 (certificateInteger476)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage23_psd
+
+theorem momentBlockFull0Stage21_psd : IsPSD (fun i j => (momentBlockFull0Stage21 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage21 momentBlockFull0Stage22 (certificateInteger440)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage22_psd
+
+theorem momentBlockFull0Stage20_psd : IsPSD (fun i j => (momentBlockFull0Stage20 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage20 momentBlockFull0Stage21 (certificateInteger395)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage21_psd
+
+theorem momentBlockFull0Stage19_psd : IsPSD (fun i j => (momentBlockFull0Stage19 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage19 momentBlockFull0Stage20 (certificateInteger340)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage20_psd
+
+theorem momentBlockFull0Stage18_psd : IsPSD (fun i j => (momentBlockFull0Stage18 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage18 momentBlockFull0Stage19 (certificateInteger274)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage19_psd
+
+theorem momentBlockFull0Stage17_psd : IsPSD (fun i j => (momentBlockFull0Stage17 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage17 momentBlockFull0Stage18 (certificateInteger196)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage18_psd
+
+theorem momentBlockFull0Stage16_psd : IsPSD (fun i j => (momentBlockFull0Stage16 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage16 momentBlockFull0Stage17 (certificateInteger105)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage17_psd
+
+theorem momentBlockFull0Stage15_psd : IsPSD (fun i j => (momentBlockFull0Stage15 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage15 momentBlockFull0Stage16 (certificateInteger0)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage16_psd
+
+theorem momentBlockFull0Stage14_psd : IsPSD (fun i j => (momentBlockFull0Stage14 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage14 momentBlockFull0Stage15
+    (241937662857451058764338007389609057488521077140633070297581497740643677390649179167977221)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage15_psd
+
+theorem momentBlockFull0Stage13_psd : IsPSD (fun i j => (momentBlockFull0Stage13 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage13 momentBlockFull0Stage14
+    (302282677391569003353895410009431779736279896258953094590784667407429716152511796424)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage14_psd
+
+theorem momentBlockFull0Stage12_psd : IsPSD (fun i j => (momentBlockFull0Stage12 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage12 momentBlockFull0Stage13
+    (755056374531704706639560641699264475888561252757247054018662644650894582588403)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage13_psd
+
+theorem momentBlockFull0Stage11_psd : IsPSD (fun i j => (momentBlockFull0Stage11 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage11 momentBlockFull0Stage12
+    (2527217969538333548343375792657934772317626846256498137010805719338681588)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage12_psd
+
+theorem momentBlockFull0Stage10_psd : IsPSD (fun i j => (momentBlockFull0Stage10 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage10 momentBlockFull0Stage11
+    (34561535069389069592098393609264156370712154364300862953273139676473)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage11_psd
+
+theorem momentBlockFull0Stage9_psd : IsPSD (fun i j => (momentBlockFull0Stage9 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage9 momentBlockFull0Stage10
+    (469013774677419966936811159834691249742394614482932476667660686)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage10_psd
+
+theorem momentBlockFull0Stage8_psd : IsPSD (fun i j => (momentBlockFull0Stage8 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage8 momentBlockFull0Stage9
+    (6257923582445758747145390762296215429555519566979662217587)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage9_psd
+
+theorem momentBlockFull0Stage7_psd : IsPSD (fun i j => (momentBlockFull0Stage7 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage7 momentBlockFull0Stage8
+    (7034453464707846749569596351075403408014983448443661)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage8_psd
+
+theorem momentBlockFull0Stage6_psd : IsPSD (fun i j => (momentBlockFull0Stage6 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage6 momentBlockFull0Stage7
+    (1923707158678150201899330964651535171639857294)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage7_psd
+
+theorem momentBlockFull0Stage5_psd : IsPSD (fun i j => (momentBlockFull0Stage5 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage5 momentBlockFull0Stage6
+    (446401646662782787320944432891295635868)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage6_psd
+
+theorem momentBlockFull0Stage4_psd : IsPSD (fun i j => (momentBlockFull0Stage4 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage4 momentBlockFull0Stage5
+    (37788621552805100777283433380138)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage5_psd
+
+theorem momentBlockFull0Stage3_psd : IsPSD (fun i j => (momentBlockFull0Stage3 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage3 momentBlockFull0Stage4 (2203657213483261276564022)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage4_psd
+
+theorem momentBlockFull0Stage2_psd : IsPSD (fun i j => (momentBlockFull0Stage2 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage2 momentBlockFull0Stage3 (119627585843864631)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage3_psd
+
+theorem momentBlockFull0Stage1_psd : IsPSD (fun i j => (momentBlockFull0Stage1 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage1 momentBlockFull0Stage2 (1000000000)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage2_psd
+
+theorem momentBlockFull0Stage0_psd : IsPSD (fun i j => (momentBlockFull0Stage0 i j : ℝ)) := by
+  apply integer_schur_step momentBlockFull0Stage0 momentBlockFull0Stage1 (1)
+  · decide
+  · decide
+  · decide +kernel
+  · decide +kernel
+  · exact momentBlockFull0Stage1_psd
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/MomentBridge.lean b/LeanPool/PersistentSOS/MomentBridge.lean
new file mode 100644
index 0000000000..f950672b88
--- /dev/null
+++ b/LeanPool/PersistentSOS/MomentBridge.lean
@@ -0,0 +1,101 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import Mathlib.Algebra.MvPolynomial.Degrees
+public import Mathlib.Basic.Real.Basic
+public import Mathlib.LinearAlgebra.Finsupp.LinearCombination
+public import Mathlib.Tactic.Convert
+public import Mathlib.Tactic.Positivity
+public import Mathlib.Tactic.Ring
+
+/-!
+# Finite monomial moment matrices
+
+A complete finite monomial basis spans bounded-degree polynomials over any
+commutative semiring. For real coefficients, positivity of its moment matrix
+implies positivity on every quadratic square, for any polynomial variable type.
+-/
+
+@[expose] public section
+namespace PersistentSOS
+open MvPolynomial
+open scoped BigOperators
+
+/-- A complete finite list of monomials of degree at most two spans every
+quadratic polynomial. Repeated entries in the list are allowed. -/
+theorem quadratic_eq_sum_monomials {σ R ι : Type*} [CommSemiring R] [Fintype ι]
+    (basis : ι → (σ →₀ ℕ))
+    (hcover : ∀ d : σ →₀ ℕ, d.sum (fun _ n => n) ≤ 2 → ∃ i, basis i = d)
+    (p : MvPolynomial σ R) (hp : p.totalDegree ≤ 2) :
+    ∃ x : ι → R, p = ∑ i, x i • (monomial (basis i) (1 : R) : MvPolynomial σ R) := by
+  classical
+  suffices hmem : p ∈ Submodule.span R
+      (Set.range fun i => (monomial (basis i) (1 : R) : MvPolynomial σ R)) by
+    obtain ⟨x, hx⟩ := (Submodule.mem_span_range_iff_exists_fun R).mp hmem
+    exact ⟨x, hx.symm⟩
+  rw [p.as_sum]
+  apply Submodule.sum_mem
+  intro d hd
+  obtain ⟨i, hi⟩ := hcover d ((le_totalDegree hd).trans hp)
+  rw [← hi]
+  have hmem : (monomial (basis i) (1 : R) : MvPolynomial σ R) ∈
+      Submodule.span R (Set.range fun j => (monomial (basis j) (1 : R) : MvPolynomial σ R)) :=
+    Submodule.subset_span (Set.mem_range_self i)
+  simpa only [smul_monomial, smul_eq_mul, mul_one] using
+    Submodule.smul_mem _ (p.coeff (basis i)) hmem
+
+/-- Positivity of the genuine monomial moment matrix implies positivity
+on the square of every quadratic polynomial. -/
+theorem nonneg_quadratic_square_of_momentMatrix {σ ι : Type*} [Fintype ι]
+    (basis : ι → (σ →₀ ℕ))
+    (hcover : ∀ d : σ →₀ ℕ, d.sum (fun _ n => n) ≤ 2 → ∃ i, basis i = d)
+    (L : MvPolynomial σ ℝ →ₗ[ℝ] ℝ)
+    (hpsd : ∀ x : ι → ℝ,
+      0 ≤ ∑ i, ∑ j, x i * L (monomial (basis i + basis j) 1) * x j)
+    (p : MvPolynomial σ ℝ) (hp : p.totalDegree ≤ 2) : 0 ≤ L (p ^ 2) := by
+  classical
+  obtain ⟨x, rfl⟩ := quadratic_eq_sum_monomials basis hcover p hp
+  convert hpsd x using 1
+  rw [pow_two, Finset.sum_mul]
+  simp_rw [Finset.mul_sum, map_sum, smul_mul_smul_comm, map_smul,
+    monomial_mul_monomial, one_mul, smul_eq_mul]
+  congr 1
+  ext i
+  congr 1
+  ext j
+  ring
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/MomentData.lean b/LeanPool/PersistentSOS/MomentData.lean
new file mode 100644
index 0000000000..9b52832833
--- /dev/null
+++ b/LeanPool/PersistentSOS/MomentData.lean
@@ -0,0 +1,1676 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.MomentGeneral
+public import LeanPool.PersistentSOS.MomentBlockFull0
+public import LeanPool.PersistentSOS.MomentBlock1
+public import LeanPool.PersistentSOS.MomentBlock2
+public import LeanPool.PersistentSOS.MomentBlock3
+public import LeanPool.PersistentSOS.MomentBlock4
+public import LeanPool.PersistentSOS.MomentBlock5
+public import LeanPool.PersistentSOS.MomentBlock6
+public import LeanPool.PersistentSOS.MomentBlock7
+public import Mathlib.Tactic.FinCases
+
+/-!
+# Explicit rational moment data
+
+Every monomial occurrence uses one base-five exponent key. All degree-four
+moments are derived from the retained rational certificate. The finite
+Gram identities and coverage are proved below by kernel reduction.
+-/
+
+
+@[expose] public section
+
+namespace PersistentSOS
+
+
+/-- Integer numerator table; unspecified keys have value zero. -/
+def momentNumerator (k : ℕ) : ℤ :=
+  if k < 19612500 then
+    if k < 109376 then
+      if k < 15876 then
+        if k < 3126 then
+          if k < 250 then
+            if k < 12 then
+              if k < 3 then
+                if k < 1 then
+                  if k = 0 then (1000000000) else 0
+                else
+                  if k < 2 then
+                    if k = 1 then (423308963) else 0
+                  else
+                    if k = 2 then (298818064) else 0
+              else
+                if k < 10 then
+                  if k < 4 then
+                    if k = 3 then (141743481) else 0
+                  else
+                    if k = 4 then (95993371) else 0
+                else
+                  if k < 11 then
+                    if k = 10 then (148973087) else 0
+                  else
+                    if k = 11 then (79751621) else 0
+            else
+              if k < 51 then
+                if k < 20 then
+                  if k = 12 then (45340304) else 0
+                else
+                  if k < 50 then
+                    if k = 20 then (65363241) else 0
+                  else
+                    if k = 50 then (162381159) else 0
+              else
+                if k < 60 then
+                  if k < 52 then
+                    if k = 51 then (86495040) else 0
+                  else
+                    if k = 52 then (48848306) else 0
+                else
+                  if k < 100 then
+                    if k = 60 then (6925782) else 0
+                  else
+                    if k = 100 then (72654288) else 0
+          else
+            if k < 1250 then
+              if k < 260 then
+                if k < 251 then
+                  if k = 250 then (162381048) else 0
+                else
+                  if k < 252 then
+                    if k = 251 then (86494935) else 0
+                  else
+                    if k = 252 then (48848296) else 0
+              else
+                if k < 500 then
+                  if k < 300 then
+                    if k = 260 then (6925775) else 0
+                  else
+                    if k = 300 then (7390663) else 0
+                else
+                  if k < 780 then
+                    if k = 500 then (72654222) else 0
+                  else
+                    if k = 780 then (9655915) else 0
+            else
+              if k < 1300 then
+                if k < 1252 then
+                  if k < 1251 then
+                    if k = 1250 then (76574425) else 0
+                  else
+                    if k = 1251 then (39889758) else 0
+                else
+                  if k < 1260 then
+                    if k = 1252 then (22979581) else 0
+                  else
+                    if k = 1260 then (12788775) else 0
+              else
+                if k < 2500 then
+                  if k < 1500 then
+                    if k = 1300 then (13722116) else 0
+                  else
+                    if k = 1500 then (13722105) else 0
+                else
+                  if k < 3125 then
+                    if k = 2500 then (6719268) else 0
+                  else
+                    if k = 3125 then (71951457) else 0
+        else
+          if k < 6300 then
+            if k < 3375 then
+              if k < 3135 then
+                if k < 3127 then
+                  if k = 3126 then (28193221) else 0
+                else
+                  if k < 3128 then
+                    if k = 3127 then (20333252) else 0
+                  else
+                    if k = 3128 then (9365790) else 0
+              else
+                if k < 3175 then
+                  if k < 3136 then
+                    if k = 3135 then (27438237) else 0
+                  else
+                    if k = 3136 then (14265654) else 0
+                else
+                  if k < 3176 then
+                    if k = 3175 then (3349614) else 0
+                  else
+                    if k = 3176 then (1411787) else 0
+            else
+              if k < 6250 then
+                if k < 4375 then
+                  if k < 3376 then
+                    if k = 3375 then (3349612) else 0
+                  else
+                    if k = 3376 then (1411790) else 0
+                else
+                  if k < 4376 then
+                    if k = 4375 then (5506403) else 0
+                  else
+                    if k = 4376 then (2769171) else 0
+              else
+                if k < 6252 then
+                  if k < 6251 then
+                    if k = 6250 then (23640856) else 0
+                  else
+                    if k = 6251 then (-9137) else 0
+                else
+                  if k < 6260 then
+                    if k = 6252 then (6095189) else 0
+                  else
+                    if k = 6260 then (6365418) else 0
+          else
+            if k < 15626 then
+              if k < 9375 then
+                if k < 6500 then
+                  if k = 6300 then (315848) else 0
+                else
+                  if k < 7500 then
+                    if k = 6500 then (315841) else 0
+                  else
+                    if k = 7500 then (635359) else 0
+              else
+                if k < 12500 then
+                  if k < 9376 then
+                    if k = 9375 then (7589636) else 0
+                  else
+                    if k = 9376 then (-1081254) else 0
+                else
+                  if k < 15625 then
+                    if k = 12500 then (4795194) else 0
+                  else
+                    if k = 15625 then (76482650) else 0
+            else
+              if k < 15636 then
+                if k < 15628 then
+                  if k < 15627 then
+                    if k = 15626 then (31705948) else 0
+                  else
+                    if k = 15627 then (21494722) else 0
+                else
+                  if k < 15635 then
+                    if k = 15628 then (10300379) else 0
+                  else
+                    if k = 15635 then (3349856) else 0
+              else
+                if k < 15676 then
+                  if k < 15675 then
+                    if k = 15636 then (1432129) else 0
+                  else
+                    if k = 15675 then (30621436) else 0
+                else
+                  if k < 15875 then
+                    if k = 15676 then (15833908) else 0
+                  else
+                    if k = 15875 then (3504174) else 0
+      else
+        if k < 78128 then
+          if k < 31252 then
+            if k < 18800 then
+              if k < 18750 then
+                if k < 16875 then
+                  if k = 15876 then (1503645) else 0
+                else
+                  if k < 16876 then
+                    if k = 16875 then (5975451) else 0
+                  else
+                    if k = 16876 then (2933691) else 0
+              else
+                if k < 18752 then
+                  if k < 18751 then
+                    if k = 18750 then (-826062) else 0
+                  else
+                    if k = 18751 then (1864327) else 0
+                else
+                  if k < 18760 then
+                    if k = 18752 then (-273910) else 0
+                  else
+                    if k = 18760 then (202667) else 0
+            else
+              if k < 21876 then
+                if k < 20000 then
+                  if k < 19000 then
+                    if k = 18800 then (196997) else 0
+                  else
+                    if k = 19000 then (310741) else 0
+                else
+                  if k < 21875 then
+                    if k = 20000 then (323085) else 0
+                  else
+                    if k = 21875 then (-681088) else 0
+              else
+                if k < 31250 then
+                  if k < 25000 then
+                    if k = 21876 then (457322) else 0
+                  else
+                    if k = 25000 then (-1025445) else 0
+                else
+                  if k < 31251 then
+                    if k = 31250 then (25184767) else 0
+                  else
+                    if k = 31251 then (591274) else 0
+          else
+            if k < 37500 then
+              if k < 31500 then
+                if k < 31260 then
+                  if k = 31252 then (6477974) else 0
+                else
+                  if k < 31300 then
+                    if k = 31260 then (307820) else 0
+                  else
+                    if k = 31300 then (7147237) else 0
+              else
+                if k < 34375 then
+                  if k < 32500 then
+                    if k = 31500 then (310382) else 0
+                  else
+                    if k = 32500 then (780189) else 0
+                else
+                  if k < 34376 then
+                    if k = 34375 then (-809987) else 0
+                  else
+                    if k = 34376 then (519327) else 0
+            else
+              if k < 62500 then
+                if k < 46876 then
+                  if k < 46875 then
+                    if k = 37500 then (1321273) else 0
+                  else
+                    if k = 46875 then (7109900) else 0
+                else
+                  if k < 50000 then
+                    if k = 46876 then (-486932) else 0
+                  else
+                    if k = 50000 then (-1027707) else 0
+              else
+                if k < 78126 then
+                  if k < 78125 then
+                    if k = 62500 then (4647223) else 0
+                  else
+                    if k = 78125 then (76482117) else 0
+                else
+                  if k < 78127 then
+                    if k = 78126 then (31706168) else 0
+                  else
+                    if k = 78127 then (21494568) else 0
+        else
+          if k < 82500 then
+            if k < 79375 then
+              if k < 78175 then
+                if k < 78135 then
+                  if k = 78128 then (10300417) else 0
+                else
+                  if k < 78136 then
+                    if k = 78135 then (3349854) else 0
+                  else
+                    if k = 78136 then (1432127) else 0
+              else
+                if k < 78375 then
+                  if k < 78176 then
+                    if k = 78175 then (3504174) else 0
+                  else
+                    if k = 78176 then (1503644) else 0
+                else
+                  if k < 78376 then
+                    if k = 78375 then (30621436) else 0
+                  else
+                    if k = 78376 then (15833900) else 0
+            else
+              if k < 81252 then
+                if k < 81250 then
+                  if k < 79376 then
+                    if k = 79375 then (5975450) else 0
+                  else
+                    if k = 79376 then (2933688) else 0
+                else
+                  if k < 81251 then
+                    if k = 81250 then (-826189) else 0
+                  else
+                    if k = 81251 then (1864389) else 0
+              else
+                if k < 81300 then
+                  if k < 81260 then
+                    if k = 81252 then (-273940) else 0
+                  else
+                    if k = 81260 then (202668) else 0
+                else
+                  if k < 81500 then
+                    if k = 81300 then (310742) else 0
+                  else
+                    if k = 81500 then (196996) else 0
+          else
+            if k < 93760 then
+              if k < 87500 then
+                if k < 84375 then
+                  if k = 82500 then (323085) else 0
+                else
+                  if k < 84376 then
+                    if k = 84375 then (-681283) else 0
+                  else
+                    if k = 84376 then (457423) else 0
+              else
+                if k < 93751 then
+                  if k < 93750 then
+                    if k = 87500 then (-1025493) else 0
+                  else
+                    if k = 93750 then (-1528158) else 0
+                else
+                  if k < 93752 then
+                    if k = 93751 then (2284387) else 0
+                  else
+                    if k = 93752 then (-467041) else 0
+            else
+              if k < 96875 then
+                if k < 94000 then
+                  if k < 93800 then
+                    if k = 93760 then (305587) else 0
+                  else
+                    if k = 93800 then (236820) else 0
+                else
+                  if k < 95000 then
+                    if k = 94000 then (236820) else 0
+                  else
+                    if k = 95000 then (321057) else 0
+              else
+                if k < 100000 then
+                  if k < 96876 then
+                    if k = 96875 then (957561) else 0
+                  else
+                    if k = 96876 then (-320360) else 0
+                else
+                  if k < 109375 then
+                    if k = 100000 then (113560) else 0
+                  else
+                    if k = 109375 then (-612941) else 0
+    else
+      if k < 2031380 then
+        if k < 468780 then
+          if k < 175000 then
+            if k < 156300 then
+              if k < 156250 then
+                if k < 112500 then
+                  if k = 109376 then (437258) else 0
+                else
+                  if k < 125000 then
+                    if k = 112500 then (354183) else 0
+                  else
+                    if k = 125000 then (-1001747) else 0
+              else
+                if k < 156252 then
+                  if k < 156251 then
+                    if k = 156250 then (25184690) else 0
+                  else
+                    if k = 156251 then (591309) else 0
+                else
+                  if k < 156260 then
+                    if k = 156252 then (6477980) else 0
+                  else
+                    if k = 156260 then (307807) else 0
+            else
+              if k < 159376 then
+                if k < 157500 then
+                  if k < 156500 then
+                    if k = 156300 then (310383) else 0
+                  else
+                    if k = 156500 then (7147227) else 0
+                else
+                  if k < 159375 then
+                    if k = 157500 then (780185) else 0
+                  else
+                    if k = 159375 then (-809686) else 0
+              else
+                if k < 171875 then
+                  if k < 162500 then
+                    if k = 159376 then (519176) else 0
+                  else
+                    if k = 162500 then (1321273) else 0
+                else
+                  if k < 171876 then
+                    if k = 171875 then (-613231) else 0
+                  else
+                    if k = 171876 then (437401) else 0
+          else
+            if k < 390655 then
+              if k < 234376 then
+                if k < 187500 then
+                  if k = 175000 then (354275) else 0
+                else
+                  if k < 234375 then
+                    if k = 187500 then (1519553) else 0
+                  else
+                    if k = 234375 then (7109654) else 0
+              else
+                if k < 250000 then
+                  if k < 237500 then
+                    if k = 234376 then (-486807) else 0
+                  else
+                    if k = 237500 then (-1027629) else 0
+                else
+                  if k < 312500 then
+                    if k = 250000 then (-1001921) else 0
+                  else
+                    if k = 312500 then (4647222) else 0
+            else
+              if k < 393780 then
+                if k < 391375 then
+                  if k < 390656 then
+                    if k = 390655 then (7457187) else 0
+                  else
+                    if k = 390656 then (3269119) else 0
+                else
+                  if k < 391376 then
+                    if k = 391375 then (10073398) else 0
+                  else
+                    if k = 391376 then (4832959) else 0
+              else
+                if k < 406280 then
+                  if k < 394500 then
+                    if k = 393780 then (608339) else 0
+                  else
+                    if k = 394500 then (615867) else 0
+                else
+                  if k < 407000 then
+                    if k = 406280 then (604148) else 0
+                  else
+                    if k = 407000 then (615337) else 0
+        else
+          if k < 812500 then
+            if k < 781500 then
+              if k < 781251 then
+                if k < 469500 then
+                  if k = 468780 then (604133) else 0
+                else
+                  if k < 781250 then
+                    if k = 469500 then (1128523) else 0
+                  else
+                    if k = 781250 then (21035273) else 0
+              else
+                if k < 781260 then
+                  if k < 781252 then
+                    if k = 781251 then (-2998234) else 0
+                  else
+                    if k = 781252 then (4872560) else 0
+                else
+                  if k < 781300 then
+                    if k = 781260 then (1189529) else 0
+                  else
+                    if k = 781300 then (1203533) else 0
+            else
+              if k < 787500 then
+                if k < 784375 then
+                  if k < 782500 then
+                    if k = 781500 then (1779896) else 0
+                  else
+                    if k = 782500 then (1311683) else 0
+                else
+                  if k < 784376 then
+                    if k = 784375 then (1370160) else 0
+                  else
+                    if k = 784376 then (-166144) else 0
+              else
+                if k < 796876 then
+                  if k < 796875 then
+                    if k = 787500 then (320428) else 0
+                  else
+                    if k = 796875 then (1065984) else 0
+                else
+                  if k < 800000 then
+                    if k = 796876 then (-18413) else 0
+                  else
+                    if k = 800000 then (309873) else 0
+          else
+            if k < 1953255 then
+              if k < 862500 then
+                if k < 859375 then
+                  if k = 812500 then (323490) else 0
+                else
+                  if k < 859376 then
+                    if k = 859375 then (2353567) else 0
+                  else
+                    if k = 859376 then (-416068) else 0
+              else
+                if k < 937500 then
+                  if k < 875000 then
+                    if k = 862500 then (-128470) else 0
+                  else
+                    if k = 875000 then (-195351) else 0
+                else
+                  if k < 1562500 then
+                    if k = 937500 then (947187) else 0
+                  else
+                    if k = 1562500 then (2804403) else 0
+            else
+              if k < 1956380 then
+                if k < 1953775 then
+                  if k < 1953256 then
+                    if k = 1953255 then (7457187) else 0
+                  else
+                    if k = 1953256 then (3269121) else 0
+                else
+                  if k < 1953776 then
+                    if k = 1953775 then (10073399) else 0
+                  else
+                    if k = 1953776 then (4832959) else 0
+              else
+                if k < 1968880 then
+                  if k < 1956900 then
+                    if k = 1956380 then (608339) else 0
+                  else
+                    if k = 1956900 then (615867) else 0
+                else
+                  if k < 1969400 then
+                    if k = 1968880 then (604133) else 0
+                  else
+                    if k = 1969400 then (1128524) else 0
+      else
+        if k < 9769380 then
+          if k < 3921876 then
+            if k < 3906260 then
+              if k < 2344380 then
+                if k < 2031900 then
+                  if k = 2031380 then (604148) else 0
+                else
+                  if k < 2343900 then
+                    if k = 2031900 then (615337) else 0
+                  else
+                    if k = 2343900 then (1201302) else 0
+              else
+                if k < 3906251 then
+                  if k < 3906250 then
+                    if k = 2344380 then (1220643) else 0
+                  else
+                    if k = 3906250 then (21035497) else 0
+                else
+                  if k < 3906252 then
+                    if k = 3906251 then (-2998344) else 0
+                  else
+                    if k = 3906252 then (4872616) else 0
+            else
+              if k < 3909375 then
+                if k < 3906500 then
+                  if k < 3906300 then
+                    if k = 3906260 then (1189513) else 0
+                  else
+                    if k = 3906300 then (1779888) else 0
+                else
+                  if k < 3907500 then
+                    if k = 3906500 then (1203525) else 0
+                  else
+                    if k = 3907500 then (1311685) else 0
+              else
+                if k < 3912500 then
+                  if k < 3909376 then
+                    if k = 3909375 then (1370265) else 0
+                  else
+                    if k = 3909376 then (-166195) else 0
+                else
+                  if k < 3921875 then
+                    if k = 3912500 then (320439) else 0
+                  else
+                    if k = 3921875 then (2353878) else 0
+          else
+            if k < 4062500 then
+              if k < 3984375 then
+                if k < 3925000 then
+                  if k = 3921876 then (-416222) else 0
+                else
+                  if k < 3937500 then
+                    if k = 3925000 then (-128440) else 0
+                  else
+                    if k = 3937500 then (947241) else 0
+              else
+                if k < 3987500 then
+                  if k < 3984376 then
+                    if k = 3984375 then (1066067) else 0
+                  else
+                    if k = 3984376 then (-18453) else 0
+                else
+                  if k < 4000000 then
+                    if k = 3987500 then (309875) else 0
+                  else
+                    if k = 4000000 then (-195332) else 0
+            else
+              if k < 9765776 then
+                if k < 7812500 then
+                  if k < 4687500 then
+                    if k = 4062500 then (323500) else 0
+                  else
+                    if k = 4687500 then (2595168) else 0
+                else
+                  if k < 9765775 then
+                    if k = 7812500 then (2804463) else 0
+                  else
+                    if k = 9765775 then (3462345) else 0
+              else
+                if k < 9766256 then
+                  if k < 9766255 then
+                    if k = 9765776 then (1400984) else 0
+                  else
+                    if k = 9766255 then (4143478) else 0
+                else
+                  if k < 9768900 then
+                    if k = 9766256 then (2022744) else 0
+                  else
+                    if k = 9768900 then (299603) else 0
+        else
+          if k < 19531251 then
+            if k < 11718780 then
+              if k < 9843900 then
+                if k < 9781400 then
+                  if k = 9769380 then (331233) else 0
+                else
+                  if k < 9781880 then
+                    if k = 9781400 then (297238) else 0
+                  else
+                    if k = 9781880 then (297189) else 0
+              else
+                if k < 10156380 then
+                  if k < 9844380 then
+                    if k = 9843900 then (297238) else 0
+                  else
+                    if k = 9844380 then (297189) else 0
+                else
+                  if k < 10156900 then
+                    if k = 10156380 then (583593) else 0
+                  else
+                    if k = 10156900 then (591740) else 0
+            else
+              if k < 12112500 then
+                if k < 12109375 then
+                  if k < 11719500 then
+                    if k = 11718780 then (583593) else 0
+                  else
+                    if k = 11719500 then (591740) else 0
+                else
+                  if k < 12109376 then
+                    if k = 12109375 then (2833858) else 0
+                  else
+                    if k = 12109376 then (-906164) else 0
+              else
+                if k < 12187500 then
+                  if k < 12125000 then
+                    if k = 12112500 then (312527) else 0
+                  else
+                    if k = 12125000 then (231540) else 0
+                else
+                  if k < 19531250 then
+                    if k = 12187500 then (231538) else 0
+                  else
+                    if k = 19531250 then (5373335) else 0
+          else
+            if k < 19534376 then
+              if k < 19531300 then
+                if k < 19531252 then
+                  if k = 19531251 then (-1192529) else 0
+                else
+                  if k < 19531260 then
+                    if k = 19531252 then (1188822) else 0
+                  else
+                    if k = 19531260 then (291310) else 0
+              else
+                if k < 19532500 then
+                  if k < 19531500 then
+                    if k = 19531300 then (293178) else 0
+                  else
+                    if k = 19531500 then (293173) else 0
+                else
+                  if k < 19534375 then
+                    if k = 19532500 then (305822) else 0
+                  else
+                    if k = 19534375 then (412026) else 0
+            else
+              if k < 19550000 then
+                if k < 19546875 then
+                  if k < 19537500 then
+                    if k = 19534376 then (-70012) else 0
+                  else
+                    if k = 19537500 then (194717) else 0
+                else
+                  if k < 19546876 then
+                    if k = 19546875 then (487649) else 0
+                  else
+                    if k = 19546876 then (-110636) else 0
+              else
+                if k < 19609375 then
+                  if k < 19562500 then
+                    if k = 19550000 then (153598) else 0
+                  else
+                    if k = 19562500 then (200318) else 0
+                else
+                  if k < 19609376 then
+                    if k = 19609375 then (487668) else 0
+                  else
+                    if k = 19609376 then (-110643) else 0
+  else
+    if k < 304687500 then
+      if k < 97675000 then
+        if k < 58593800 then
+          if k < 48906400 then
+            if k < 48828276 then
+              if k < 20312500 then
+                if k < 19625000 then
+                  if k = 19612500 then (153615) else 0
+                else
+                  if k < 19687500 then
+                    if k = 19625000 then (195058) else 0
+                  else
+                    if k = 19687500 then (200325) else 0
+              else
+                if k < 39062500 then
+                  if k < 23437500 then
+                    if k = 20312500 then (673877) else 0
+                  else
+                    if k = 23437500 then (673907) else 0
+                else
+                  if k < 48828275 then
+                    if k = 39062500 then (311051) else 0
+                  else
+                    if k = 48828275 then (5800689) else 0
+            else
+              if k < 48831400 then
+                if k < 48828755 then
+                  if k = 48828276 then (2688879) else 0
+                else
+                  if k < 48828756 then
+                    if k = 48828755 then (7594848) else 0
+                  else
+                    if k = 48828756 then (3598238) else 0
+              else
+                if k < 48843900 then
+                  if k < 48831880 then
+                    if k = 48831400 then (451763) else 0
+                  else
+                    if k = 48831880 then (900626) else 0
+                else
+                  if k < 48844380 then
+                    if k = 48843900 then (449043) else 0
+                  else
+                    if k = 48844380 then (454472) else 0
+          else
+            if k < 51171876 then
+              if k < 49219400 then
+                if k < 48906880 then
+                  if k = 48906400 then (449043) else 0
+                else
+                  if k < 49218880 then
+                    if k = 48906880 then (454472) else 0
+                  else
+                    if k = 49218880 then (883143) else 0
+              else
+                if k < 50782000 then
+                  if k < 50781280 then
+                    if k = 49219400 then (918271) else 0
+                  else
+                    if k = 50781280 then (883142) else 0
+                else
+                  if k < 51171875 then
+                    if k = 50782000 then (918271) else 0
+                  else
+                    if k = 51171875 then (3953065) else 0
+            else
+              if k < 58593750 then
+                if k < 51187500 then
+                  if k < 51175000 then
+                    if k = 51171876 then (-1199593) else 0
+                  else
+                    if k = 51175000 then (399703) else 0
+                else
+                  if k < 51250000 then
+                    if k = 51187500 then (278253) else 0
+                  else
+                    if k = 51250000 then (278254) else 0
+              else
+                if k < 58593752 then
+                  if k < 58593751 then
+                    if k = 58593750 then (6700445) else 0
+                  else
+                    if k = 58593751 then (-868051) else 0
+                else
+                  if k < 58593760 then
+                    if k = 58593752 then (1563499) else 0
+                  else
+                    if k = 58593760 then (474628) else 0
+        else
+          if k < 59375000 then
+            if k < 58609376 then
+              if k < 58596875 then
+                if k < 58594000 then
+                  if k = 58593800 then (429020) else 0
+                else
+                  if k < 58595000 then
+                    if k = 58594000 then (429020) else 0
+                  else
+                    if k = 58595000 then (461335) else 0
+              else
+                if k < 58600000 then
+                  if k < 58596876 then
+                    if k = 58596875 then (549857) else 0
+                  else
+                    if k = 58596876 then (-71505) else 0
+                else
+                  if k < 58609375 then
+                    if k = 58600000 then (89718) else 0
+                  else
+                    if k = 58609375 then (555248) else 0
+            else
+              if k < 58671876 then
+                if k < 58625000 then
+                  if k < 58612500 then
+                    if k = 58609376 then (-92651) else 0
+                  else
+                    if k = 58612500 then (-9261) else 0
+                else
+                  if k < 58671875 then
+                    if k = 58625000 then (77972) else 0
+                  else
+                    if k = 58671875 then (555251) else 0
+              else
+                if k < 58687500 then
+                  if k < 58675000 then
+                    if k = 58671876 then (-92653) else 0
+                  else
+                    if k = 58675000 then (-9266) else 0
+                else
+                  if k < 58750000 then
+                    if k = 58687500 then (78186) else 0
+                  else
+                    if k = 58750000 then (77940) else 0
+          else
+            if k < 97656300 then
+              if k < 97656250 then
+                if k < 62500000 then
+                  if k = 59375000 then (920821) else 0
+                else
+                  if k < 78125000 then
+                    if k = 62500000 then (920821) else 0
+                  else
+                    if k = 78125000 then (206949) else 0
+              else
+                if k < 97656252 then
+                  if k < 97656251 then
+                    if k = 97656250 then (13951051) else 0
+                  else
+                    if k = 97656251 then (-2410969) else 0
+                else
+                  if k < 97656260 then
+                    if k = 97656252 then (3215208) else 0
+                  else
+                    if k = 97656260 then (1305861) else 0
+            else
+              if k < 97659376 then
+                if k < 97657500 then
+                  if k < 97656500 then
+                    if k = 97656300 then (665467) else 0
+                  else
+                    if k = 97656500 then (665471) else 0
+                else
+                  if k < 97659375 then
+                    if k = 97657500 then (739380) else 0
+                  else
+                    if k = 97659375 then (2599146) else 0
+              else
+                if k < 97671875 then
+                  if k < 97662500 then
+                    if k = 97659376 then (-742651) else 0
+                  else
+                    if k = 97662500 then (1340107) else 0
+                else
+                  if k < 97671876 then
+                    if k = 97671875 then (390599) else 0
+                  else
+                    if k = 97671876 then (72861) else 0
+      else
+        if k < 246095000 then
+          if k < 244141276 then
+            if k < 98437500 then
+              if k < 97734376 then
+                if k < 97687500 then
+                  if k = 97675000 then (-257922) else 0
+                else
+                  if k < 97734375 then
+                    if k = 97687500 then (215330) else 0
+                  else
+                    if k = 97734375 then (390534) else 0
+              else
+                if k < 97750000 then
+                  if k < 97737500 then
+                    if k = 97734376 then (72892) else 0
+                  else
+                    if k = 97737500 then (-257943) else 0
+                else
+                  if k < 97812500 then
+                    if k = 97750000 then (210862) else 0
+                  else
+                    if k = 97812500 then (215328) else 0
+            else
+              if k < 195312500 then
+                if k < 117187500 then
+                  if k < 101562500 then
+                    if k = 98437500 then (1395420) else 0
+                  else
+                    if k = 101562500 then (1395424) else 0
+                else
+                  if k < 156250000 then
+                    if k = 117187500 then (375018) else 0
+                  else
+                    if k = 156250000 then (507092) else 0
+              else
+                if k < 244140756 then
+                  if k < 244140755 then
+                    if k = 195312500 then (1483528) else 0
+                  else
+                    if k = 244140755 then (4162390) else 0
+                else
+                  if k < 244141275 then
+                    if k = 244140756 then (1964657) else 0
+                  else
+                    if k = 244141275 then (5911137) else 0
+          else
+            if k < 244531400 then
+              if k < 244156380 then
+                if k < 244143880 then
+                  if k = 244141276 then (2789333) else 0
+                else
+                  if k < 244144400 then
+                    if k = 244143880 then (318997) else 0
+                  else
+                    if k = 244144400 then (326209) else 0
+              else
+                if k < 244218880 then
+                  if k < 244156900 then
+                    if k = 244156380 then (317182) else 0
+                  else
+                    if k = 244156900 then (777072) else 0
+                else
+                  if k < 244219400 then
+                    if k = 244218880 then (317179) else 0
+                  else
+                    if k = 244219400 then (326753) else 0
+            else
+              if k < 246093752 then
+                if k < 246093750 then
+                  if k < 244531880 then
+                    if k = 244531400 then (630690) else 0
+                  else
+                    if k = 244531880 then (651390) else 0
+                else
+                  if k < 246093751 then
+                    if k = 246093750 then (11656813) else 0
+                  else
+                    if k = 246093751 then (-1514904) else 0
+              else
+                if k < 246093800 then
+                  if k < 246093760 then
+                    if k = 246093752 then (2735057) else 0
+                  else
+                    if k = 246093760 then (623959) else 0
+                else
+                  if k < 246094000 then
+                    if k = 246093800 then (1136477) else 0
+                  else
+                    if k = 246094000 then (630686) else 0
+        else
+          if k < 253906280 then
+            if k < 246125000 then
+              if k < 246100000 then
+                if k < 246096875 then
+                  if k = 246095000 then (705658) else 0
+                else
+                  if k < 246096876 then
+                    if k = 246096875 then (455102) else 0
+                  else
+                    if k = 246096876 then (37777) else 0
+              else
+                if k < 246109376 then
+                  if k < 246109375 then
+                    if k = 246100000 then (127655) else 0
+                  else
+                    if k = 246109375 then (1717831) else 0
+                else
+                  if k < 246112500 then
+                    if k = 246109376 then (-377821) else 0
+                  else
+                    if k = 246112500 then (-210027) else 0
+            else
+              if k < 246187500 then
+                if k < 246171876 then
+                  if k < 246171875 then
+                    if k = 246125000 then (739234) else 0
+                  else
+                    if k = 246171875 then (270288) else 0
+                else
+                  if k < 246175000 then
+                    if k = 246171876 then (127480) else 0
+                  else
+                    if k = 246175000 then (125128) else 0
+              else
+                if k < 246875000 then
+                  if k < 246250000 then
+                    if k = 246187500 then (-262559) else 0
+                  else
+                    if k = 246250000 then (131225) else 0
+                else
+                  if k < 250000000 then
+                    if k = 246875000 then (1338800) else 0
+                  else
+                    if k = 250000000 then (1488200) else 0
+          else
+            if k < 265625000 then
+              if k < 254296876 then
+                if k < 253907000 then
+                  if k = 253906280 then (301842) else 0
+                else
+                  if k < 254296875 then
+                    if k = 253907000 then (318788) else 0
+                  else
+                    if k = 254296875 then (1418658) else 0
+              else
+                if k < 254312500 then
+                  if k < 254300000 then
+                    if k = 254296876 then (-442446) else 0
+                  else
+                    if k = 254300000 then (124516) else 0
+                else
+                  if k < 254375000 then
+                    if k = 254312500 then (82775) else 0
+                  else
+                    if k = 254375000 then (79776) else 0
+            else
+              if k < 293359376 then
+                if k < 292969500 then
+                  if k < 292968780 then
+                    if k = 265625000 then (305305) else 0
+                  else
+                    if k = 292968780 then (470215) else 0
+                else
+                  if k < 293359375 then
+                    if k = 292969500 then (486284) else 0
+                  else
+                    if k = 293359375 then (2037393) else 0
+              else
+                if k < 293375000 then
+                  if k < 293362500 then
+                    if k = 293359376 then (-607622) else 0
+                  else
+                    if k = 293362500 then (197247) else 0
+                else
+                  if k < 293437500 then
+                    if k = 293375000 then (129317) else 0
+                  else
+                    if k = 293437500 then (130613) else 0
+    else
+      if k < 1225000000 then
+        if k < 1220703875 then
+          if k < 488312500 then
+            if k < 488281500 then
+              if k < 488281251 then
+                if k < 343750000 then
+                  if k = 304687500 then (478133) else 0
+                else
+                  if k < 488281250 then
+                    if k = 343750000 then (775732) else 0
+                  else
+                    if k = 488281250 then (7733193) else 0
+              else
+                if k < 488281260 then
+                  if k < 488281252 then
+                    if k = 488281251 then (-1319551) else 0
+                  else
+                    if k = 488281252 then (1803902) else 0
+                else
+                  if k < 488281300 then
+                    if k = 488281260 then (335978) else 0
+                  else
+                    if k = 488281300 then (784189) else 0
+            else
+              if k < 488287500 then
+                if k < 488284375 then
+                  if k < 488282500 then
+                    if k = 488281500 then (340280) else 0
+                  else
+                    if k = 488282500 then (389139) else 0
+                else
+                  if k < 488284376 then
+                    if k = 488284375 then (126242) else 0
+                  else
+                    if k = 488284376 then (78463) else 0
+              else
+                if k < 488296876 then
+                  if k < 488296875 then
+                    if k = 488287500 then (149877) else 0
+                  else
+                    if k = 488296875 then (1403322) else 0
+                else
+                  if k < 488300000 then
+                    if k = 488296876 then (-364320) else 0
+                  else
+                    if k = 488300000 then (-120319) else 0
+          else
+            if k < 492187500 then
+              if k < 488362500 then
+                if k < 488359375 then
+                  if k = 488312500 then (807044) else 0
+                else
+                  if k < 488359376 then
+                    if k = 488359375 then (19621) else 0
+                  else
+                    if k = 488359376 then (131319) else 0
+              else
+                if k < 488437500 then
+                  if k < 488375000 then
+                    if k = 488362500 then (156420) else 0
+                  else
+                    if k = 488375000 then (-143279) else 0
+                else
+                  if k < 489062500 then
+                    if k = 488437500 then (179660) else 0
+                  else
+                    if k = 489062500 then (741344) else 0
+            else
+              if k < 734375000 then
+                if k < 546875000 then
+                  if k < 507812500 then
+                    if k = 492187500 then (876780) else 0
+                  else
+                    if k = 507812500 then (185908) else 0
+                else
+                  if k < 585937500 then
+                    if k = 546875000 then (270806) else 0
+                  else
+                    if k = 585937500 then (469720) else 0
+              else
+                if k < 1220703155 then
+                  if k < 976562500 then
+                    if k = 734375000 then (523496) else 0
+                  else
+                    if k = 976562500 then (433053) else 0
+                else
+                  if k < 1220703156 then
+                    if k = 1220703155 then (4162390) else 0
+                  else
+                    if k = 1220703156 then (1964655) else 0
+        else
+          if k < 1221096875 then
+            if k < 1220782000 then
+              if k < 1220707000 then
+                if k < 1220703876 then
+                  if k = 1220703875 then (5911137) else 0
+                else
+                  if k < 1220706280 then
+                    if k = 1220703876 then (2789334) else 0
+                  else
+                    if k = 1220706280 then (318998) else 0
+              else
+                if k < 1220719500 then
+                  if k < 1220718780 then
+                    if k = 1220707000 then (326209) else 0
+                  else
+                    if k = 1220718780 then (317179) else 0
+                else
+                  if k < 1220781280 then
+                    if k = 1220719500 then (326753) else 0
+                  else
+                    if k = 1220781280 then (317183) else 0
+            else
+              if k < 1221093760 then
+                if k < 1221093751 then
+                  if k < 1221093750 then
+                    if k = 1220782000 then (777071) else 0
+                  else
+                    if k = 1221093750 then (11656848) else 0
+                else
+                  if k < 1221093752 then
+                    if k = 1221093751 then (-1514923) else 0
+                  else
+                    if k = 1221093752 then (2735066) else 0
+              else
+                if k < 1221094000 then
+                  if k < 1221093800 then
+                    if k = 1221093760 then (623959) else 0
+                  else
+                    if k = 1221093800 then (630687) else 0
+                else
+                  if k < 1221095000 then
+                    if k = 1221094000 then (1136476) else 0
+                  else
+                    if k = 1221095000 then (705659) else 0
+          else
+            if k < 1221171875 then
+              if k < 1221109375 then
+                if k < 1221096876 then
+                  if k = 1221096875 then (455296) else 0
+                else
+                  if k < 1221100000 then
+                    if k = 1221096876 then (37680) else 0
+                  else
+                    if k = 1221100000 then (127678) else 0
+              else
+                if k < 1221112500 then
+                  if k < 1221109376 then
+                    if k = 1221109375 then (270523) else 0
+                  else
+                    if k = 1221109376 then (127362) else 0
+                else
+                  if k < 1221125000 then
+                    if k = 1221112500 then (125148) else 0
+                  else
+                    if k = 1221125000 then (131237) else 0
+            else
+              if k < 1221250000 then
+                if k < 1221175000 then
+                  if k < 1221171876 then
+                    if k = 1221171875 then (1717705) else 0
+                  else
+                    if k = 1221171876 then (-377759) else 0
+                else
+                  if k < 1221187500 then
+                    if k = 1221175000 then (-210023) else 0
+                  else
+                    if k = 1221187500 then (-262558) else 0
+              else
+                if k < 1222656400 then
+                  if k < 1221875000 then
+                    if k = 1221250000 then (739214) else 0
+                  else
+                    if k = 1221875000 then (1488164) else 0
+                else
+                  if k < 1222656880 then
+                    if k = 1222656400 then (630691) else 0
+                  else
+                    if k = 1222656880 then (651390) else 0
+      else
+        if k < 1513750000 then
+          if k < 1271562500 then
+            if k < 1232500000 then
+              if k < 1232421875 then
+                if k < 1230468880 then
+                  if k = 1225000000 then (1338790) else 0
+                else
+                  if k < 1230469400 then
+                    if k = 1230468880 then (301842) else 0
+                  else
+                    if k = 1230469400 then (318788) else 0
+              else
+                if k < 1232425000 then
+                  if k < 1232421876 then
+                    if k = 1232421875 then (1418815) else 0
+                  else
+                    if k = 1232421876 then (-442523) else 0
+                else
+                  if k < 1232437500 then
+                    if k = 1232425000 then (124519) else 0
+                  else
+                    if k = 1232437500 then (79784) else 0
+            else
+              if k < 1271484375 then
+                if k < 1269531380 then
+                  if k < 1240625000 then
+                    if k = 1232500000 then (82777) else 0
+                  else
+                    if k = 1240625000 then (305316) else 0
+                else
+                  if k < 1269531900 then
+                    if k = 1269531380 then (470216) else 0
+                  else
+                    if k = 1269531900 then (486285) else 0
+              else
+                if k < 1271487500 then
+                  if k < 1271484376 then
+                    if k = 1271484375 then (2037568) else 0
+                  else
+                    if k = 1271484376 then (-607709) else 0
+                else
+                  if k < 1271500000 then
+                    if k = 1271487500 then (197239) else 0
+                  else
+                    if k = 1271500000 then (130616) else 0
+          else
+            if k < 1474609376 then
+              if k < 1464843900 then
+                if k < 1279687500 then
+                  if k = 1271562500 then (129312) else 0
+                else
+                  if k < 1318750000 then
+                    if k = 1279687500 then (478132) else 0
+                  else
+                    if k = 1318750000 then (775756) else 0
+              else
+                if k < 1467187500 then
+                  if k < 1464844380 then
+                    if k = 1464843900 then (338068) else 0
+                  else
+                    if k = 1464844380 then (344016) else 0
+                else
+                  if k < 1474609375 then
+                    if k = 1467187500 then (725460) else 0
+                  else
+                    if k = 1474609375 then (752865) else 0
+            else
+              if k < 1513671875 then
+                if k < 1474625000 then
+                  if k < 1474612500 then
+                    if k = 1474609376 then (-233311) else 0
+                  else
+                    if k = 1474612500 then (78020) else 0
+                else
+                  if k < 1474687500 then
+                    if k = 1474625000 then (54692) else 0
+                  else
+                    if k = 1474687500 then (54684) else 0
+              else
+                if k < 1513675000 then
+                  if k < 1513671876 then
+                    if k = 1513671875 then (1065899) else 0
+                  else
+                    if k = 1513671876 then (-315518) else 0
+                else
+                  if k < 1513687500 then
+                    if k = 1513675000 then (105630) else 0
+                  else
+                    if k = 1513687500 then (68507) else 0
+        else
+          if k < 2441437500 then
+            if k < 2441406500 then
+              if k < 2441406251 then
+                if k < 1709375000 then
+                  if k = 1513750000 then (68496) else 0
+                else
+                  if k < 2441406250 then
+                    if k = 1709375000 then (395345) else 0
+                  else
+                    if k = 2441406250 then (7733555) else 0
+              else
+                if k < 2441406260 then
+                  if k < 2441406252 then
+                    if k = 2441406251 then (-1319691) else 0
+                  else
+                    if k = 2441406252 then (1803955) else 0
+                else
+                  if k < 2441406300 then
+                    if k = 2441406260 then (335974) else 0
+                  else
+                    if k = 2441406300 then (340281) else 0
+            else
+              if k < 2441412500 then
+                if k < 2441409375 then
+                  if k < 2441407500 then
+                    if k = 2441406500 then (784192) else 0
+                  else
+                    if k = 2441407500 then (389138) else 0
+                else
+                  if k < 2441409376 then
+                    if k = 2441409375 then (126537) else 0
+                  else
+                    if k = 2441409376 then (78319) else 0
+              else
+                if k < 2441421876 then
+                  if k < 2441421875 then
+                    if k = 2441412500 then (149893) else 0
+                  else
+                    if k = 2441421875 then (19998) else 0
+                else
+                  if k < 2441425000 then
+                    if k = 2441421876 then (131135) else 0
+                  else
+                    if k = 2441425000 then (156445) else 0
+          else
+            if k < 2445312500 then
+              if k < 2441487500 then
+                if k < 2441484375 then
+                  if k = 2441437500 then (179693) else 0
+                else
+                  if k < 2441484376 then
+                    if k = 2441484375 then (1403748) else 0
+                  else
+                    if k = 2441484376 then (-364529) else 0
+              else
+                if k < 2441562500 then
+                  if k < 2441500000 then
+                    if k = 2441487500 then (-120298) else 0
+                  else
+                    if k = 2441500000 then (-143251) else 0
+                else
+                  if k < 2442187500 then
+                    if k = 2441562500 then (807060) else 0
+                  else
+                    if k = 2442187500 then (876755) else 0
+            else
+              if k < 2687500000 then
+                if k < 2500000000 then
+                  if k < 2460937500 then
+                    if k = 2445312500 then (741348) else 0
+                  else
+                    if k = 2460937500 then (185909) else 0
+                else
+                  if k < 2539062500 then
+                    if k = 2500000000 then (270824) else 0
+                  else
+                    if k = 2539062500 then (469789) else 0
+              else
+                if k < 3662500000 then
+                  if k < 2929687500 then
+                    if k = 2687500000 then (395329) else 0
+                  else
+                    if k = 2929687500 then (236319) else 0
+                else
+                  if k < 4882812500 then
+                    if k = 3662500000 then (523501) else 0
+                  else
+                    if k = 4882812500 then (433249) else 0
+
+/-- Dimensions of the eight exact moment-matrix blocks. -/
+def blockSize : Fin 8 → ℕ
+  | 0 => 28
+  | 1 => 11
+  | 2 => 11
+  | 3 => 16
+  | 4 => 11
+  | 5 => 16
+  | 6 => 16
+  | 7 => 11
+
+/-- Pairs of padded variable indices forming each quadratic monomial block. -/
+def basisPair : (c : Fin 8) → Fin (blockSize c) → Fin 15 × Fin 15
+  | 0 => ![(0, 0), (0, 1), (0, 6), (0, 7), (0, 8), (1, 6), (1, 7), (1, 8), (2, 2), (3, 3), (4, 4),
+    (5, 5), (6, 6), (6, 7), (6, 8), (7, 7), (7, 8), (8, 8), (9, 9), (9, 14), (10, 10), (10, 13),
+    (11, 11), (11, 12), (12, 12), (13, 13), (14, 14), (1, 1)]
+  | 1 => ![(0, 2), (1, 2), (2, 6), (2, 7), (2, 8), (3, 9), (3, 14), (4, 10), (4, 13), (5, 11), (5,
+    12)]
+  | 2 => ![(0, 3), (1, 3), (2, 9), (2, 14), (3, 6), (3, 7), (3, 8), (4, 11), (4, 12), (5, 10), (5,
+    13)]
+  | 3 => ![(0, 9), (0, 14), (1, 9), (1, 14), (2, 3), (4, 5), (6, 9), (6, 14), (7, 9), (7, 14), (8,
+    9), (8, 14), (10, 11), (10, 12), (11, 13), (12, 13)]
+  | 4 => ![(0, 4), (1, 4), (2, 10), (2, 13), (3, 11), (3, 12), (4, 6), (4, 7), (4, 8), (5, 9), (5,
+    14)]
+  | 5 => ![(0, 10), (0, 13), (1, 10), (1, 13), (2, 4), (3, 5), (6, 10), (6, 13), (7, 10), (7, 13),
+    (8, 10), (8, 13), (9, 11), (9, 12), (11, 14), (12, 14)]
+  | 6 => ![(0, 11), (0, 12), (1, 11), (1, 12), (2, 5), (3, 4), (6, 11), (6, 12), (7, 11), (7, 12),
+    (8, 11), (8, 12), (9, 10), (9, 13), (10, 14), (13, 14)]
+  | 7 => ![(0, 5), (1, 5), (2, 11), (2, 12), (3, 10), (3, 13), (4, 9), (4, 14), (5, 6), (5, 7),
+    (5, 8)]
+
+/-- Integer moment matrices, with the common denominator kept separate. -/
+def blockNumerator : (c : Fin 8) → Fin (blockSize c) → Fin (blockSize c) → ℤ
+  | 0 => momentBlockFull0Stage0
+  | 1 => momentBlock1Stage0
+  | 2 => momentBlock2Stage0
+  | 3 => momentBlock3Stage0
+  | 4 => momentBlock4Stage0
+  | 5 => momentBlock5Stage0
+  | 6 => momentBlock6Stage0
+  | 7 => momentBlock7Stage0
+
+theorem blockNumerator_psd (c : Fin 8) : IsPSD (fun i j => (blockNumerator c i j : ℝ)) := by
+  fin_cases c
+  · exact momentBlockFull0Stage0_psd
+  · exact momentBlock1Stage0_psd
+  · exact momentBlock2Stage0_psd
+  · exact momentBlock3Stage0_psd
+  · exact momentBlock4Stage0_psd
+  · exact momentBlock5Stage0_psd
+  · exact momentBlock6Stage0_psd
+  · exact momentBlock7Stage0_psd
+
+/-- A zero index pads a monomial of degree less than two. -/
+noncomputable def variableExponent (i : Fin 15) : Exponent :=
+  if h : i = 0 then 0 else Finsupp.single ⟨i.val - 1, by
+    have hi := i.isLt
+    have hn : i.val ≠ 0 := by simpa using h
+    omega⟩ 1
+
+/-- Base-five key of a variable, with zero representing the constant monomial. -/
+def variableKey (i : Fin 15) : ℕ := if i = 0 then 0 else 5 ^ (i.val - 1)
+
+/-- Exponent vector of a quadratic monomial in the complete block basis. -/
+noncomputable def momentBasis (b : (c : Fin 8) × Fin (blockSize c)) : Exponent :=
+  variableExponent (basisPair b.1 b.2).1 + variableExponent (basisPair b.1 b.2).2
+
+/-- Moment-table key of a quadratic basis monomial. -/
+def basisKey (c : Fin 8) (i : Fin (blockSize c)) : ℕ :=
+  variableKey (basisPair c i).1 + variableKey (basisPair c i).2
+
+@[simp] theorem exponentKey_variableExponent (i : Fin 15) :
+    exponentKey (variableExponent i) = variableKey i := by
+  simp only [variableExponent, variableKey]
+  split_ifs <;> simp
+
+@[simp] theorem exponentKey_momentBasis (b : (c : Fin 8) × Fin (blockSize c)) :
+    exponentKey (momentBasis b) = basisKey b.1 b.2 := by
+  simp [momentBasis, basisKey]
+
+theorem moment_block_0 : ∀ i j : Fin (blockSize 0),
+    momentNumerator (basisKey 0 i + basisKey 0 j) = blockNumerator 0 i j := by
+  decide +kernel
+
+theorem moment_block_1 : ∀ i j : Fin (blockSize 1),
+    momentNumerator (basisKey 1 i + basisKey 1 j) = blockNumerator 1 i j := by
+  decide +kernel
+
+theorem moment_block_2 : ∀ i j : Fin (blockSize 2),
+    momentNumerator (basisKey 2 i + basisKey 2 j) = blockNumerator 2 i j := by
+  decide +kernel
+
+theorem moment_block_3 : ∀ i j : Fin (blockSize 3),
+    momentNumerator (basisKey 3 i + basisKey 3 j) = blockNumerator 3 i j := by
+  decide +kernel
+
+theorem moment_block_4 : ∀ i j : Fin (blockSize 4),
+    momentNumerator (basisKey 4 i + basisKey 4 j) = blockNumerator 4 i j := by
+  decide +kernel
+
+theorem moment_block_5 : ∀ i j : Fin (blockSize 5),
+    momentNumerator (basisKey 5 i + basisKey 5 j) = blockNumerator 5 i j := by
+  decide +kernel
+
+theorem moment_block_6 : ∀ i j : Fin (blockSize 6),
+    momentNumerator (basisKey 6 i + basisKey 6 j) = blockNumerator 6 i j := by
+  decide +kernel
+
+theorem moment_block_7 : ∀ i j : Fin (blockSize 7),
+    momentNumerator (basisKey 7 i + basisKey 7 j) = blockNumerator 7 i j := by
+  decide +kernel
+
+theorem moment_block : ∀ c (i j : Fin (blockSize c)),
+    momentNumerator (basisKey c i + basisKey c j) = blockNumerator c i j := by
+  intro c
+  fin_cases c
+  · exact moment_block_0
+  · exact moment_block_1
+  · exact moment_block_2
+  · exact moment_block_3
+  · exact moment_block_4
+  · exact moment_block_5
+  · exact moment_block_6
+  · exact moment_block_7
+
+theorem moment_cross_0 : ∀ d : Fin 8, 0 ≠ d → ∀ (i : Fin (blockSize 0)) (j : Fin (blockSize d)),
+    momentNumerator (basisKey 0 i + basisKey d j) = 0 := by
+  decide +kernel
+
+theorem moment_cross_1 : ∀ d : Fin 8, 1 ≠ d → ∀ (i : Fin (blockSize 1)) (j : Fin (blockSize d)),
+    momentNumerator (basisKey 1 i + basisKey d j) = 0 := by
+  decide +kernel
+
+theorem moment_cross_2 : ∀ d : Fin 8, 2 ≠ d → ∀ (i : Fin (blockSize 2)) (j : Fin (blockSize d)),
+    momentNumerator (basisKey 2 i + basisKey d j) = 0 := by
+  decide +kernel
+
+theorem moment_cross_3 : ∀ d : Fin 8, 3 ≠ d → ∀ (i : Fin (blockSize 3)) (j : Fin (blockSize d)),
+    momentNumerator (basisKey 3 i + basisKey d j) = 0 := by
+  decide +kernel
+
+theorem moment_cross_4 : ∀ d : Fin 8, 4 ≠ d → ∀ (i : Fin (blockSize 4)) (j : Fin (blockSize d)),
+    momentNumerator (basisKey 4 i + basisKey d j) = 0 := by
+  decide +kernel
+
+theorem moment_cross_5 : ∀ d : Fin 8, 5 ≠ d → ∀ (i : Fin (blockSize 5)) (j : Fin (blockSize d)),
+    momentNumerator (basisKey 5 i + basisKey d j) = 0 := by
+  decide +kernel
+
+theorem moment_cross_6 : ∀ d : Fin 8, 6 ≠ d → ∀ (i : Fin (blockSize 6)) (j : Fin (blockSize d)),
+    momentNumerator (basisKey 6 i + basisKey d j) = 0 := by
+  decide +kernel
+
+theorem moment_cross_7 : ∀ d : Fin 8, 7 ≠ d → ∀ (i : Fin (blockSize 7)) (j : Fin (blockSize d)),
+    momentNumerator (basisKey 7 i + basisKey d j) = 0 := by
+  decide +kernel
+
+theorem moment_cross : ∀ c d : Fin 8, c ≠ d → ∀ (i : Fin (blockSize c)) (j : Fin (blockSize d)),
+    momentNumerator (basisKey c i + basisKey d j) = 0 := by
+  intro c
+  fin_cases c
+  · exact moment_cross_0
+  · exact moment_cross_1
+  · exact moment_cross_2
+  · exact moment_cross_3
+  · exact moment_cross_4
+  · exact moment_cross_5
+  · exact moment_cross_6
+  · exact moment_cross_7
+
+theorem moment_quadratic_numerator_sum :
+    (∑ i : Fin 14, momentNumerator (2 * 5 ^ i.val)) = 1000000000 := by
+  decide +kernel
+
+theorem moment_quartic_numerator_sum :
+    (∑ i : Fin 14, ∑ j : Fin 14, momentNumerator (2 * 5 ^ i.val + 2 * 5 ^ j.val)) =
+      1000000000 := by
+  decide +kernel
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/MomentGeneral.lean b/LeanPool/PersistentSOS/MomentGeneral.lean
new file mode 100644
index 0000000000..8ef9e07b72
--- /dev/null
+++ b/LeanPool/PersistentSOS/MomentGeneral.lean
@@ -0,0 +1,90 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.PSD
+public import LeanPool.PersistentSOS.Definitions
+
+/-!
+# Linear moment functionals and finite Gram forms
+
+A single exponent-indexed function supplies every occurrence of a monomial.
+-/
+
+
+@[expose] public section
+
+namespace PersistentSOS
+
+open scoped BigOperators
+
+/-- Exponent vectors of ordinary polynomials in fourteen variables. -/
+abbrev Exponent := Fin 14 →₀ ℕ
+
+/-- A base - five key used only to index the explicit finite moment table. -/
+def exponentKey (d : Exponent) : ℕ := ∑ i : Fin 14, d i * 5 ^ i.val
+
+@[simp] theorem exponentKey_zero : exponentKey 0 = 0 := by
+  simp [exponentKey]
+
+@[simp] theorem exponentKey_add (d e : Exponent) :
+    exponentKey (d + e) = exponentKey d + exponentKey e := by
+  simp [exponentKey, add_mul, Finset.sum_add_distrib]
+
+@[simp] theorem exponentKey_single (i : Fin 14) (n : ℕ) :
+    exponentKey (Finsupp.single i n) = n * 5 ^ i.val := by
+  classical
+  simp [exponentKey, Finsupp.single_apply, ite_mul]
+
+/-- Extend any moment table linearly to ordinary real multivariate polynomials. -/
+noncomputable def momentLinearMap (m : ℕ → ℤ) : Poly →ₗ[ℝ] ℝ :=
+  (Finsupp.linearCombination ℝ (fun d : Exponent => (m (exponentKey d) : ℝ) / 1000000000)).comp
+    (AddMonoidAlgebra.coeffLinearEquiv ℝ).toLinearMap
+
+@[simp] theorem momentLinearMap_monomial (m : ℕ → ℤ) (d : Exponent) (c : ℝ) :
+    momentLinearMap m (MvPolynomial.monomial d c) =
+      c * (m (exponentKey d) : ℝ) / 1000000000 := by
+  simp [momentLinearMap, LinearMap.comp_apply, MvPolynomial.monomial,
+    Finsupp.linearCombination_single, smul_eq_mul,
+    mul_div_assoc]
+
+/-- A block - diagonal collection of nonnegative quadratic forms is nonnegative. -/
+theorem block_nonneg {κ : Type*} [Fintype κ] (size : κ → ℕ)
+    (A : (k : κ) → Fin (size k) → Fin (size k) → ℝ)
+    (hA : ∀ k, IsPSD (A k)) (x : (k : κ) × Fin (size k) → ℝ) :
+    0 ≤ ∑ k, quadraticForm (A k) (fun i => x ⟨k, i⟩) := by
+  exact Finset.sum_nonneg (fun k _ => hA k _)
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/Moments.lean b/LeanPool/PersistentSOS/Moments.lean
new file mode 100644
index 0000000000..ef7196ef7a
--- /dev/null
+++ b/LeanPool/PersistentSOS/Moments.lean
@@ -0,0 +1,181 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.MomentData
+public import LeanPool.PersistentSOS.MomentBridge
+public import LeanPool.PersistentSOS.QuadraticMonomials
+public import Mathlib.Tactic.Convert
+public import Mathlib.Tactic.NormNum
+public import Mathlib.Tactic.Ring
+
+/-!
+# A positive sphere moment functional with strict cubic separation
+
+The rational moment table is interpreted on ordinary multivariate polynomials.
+Positivity follows from the exact finite block certificates and complete
+coverage of all monomials of total degree at most two.
+-/
+
+
+@[expose] public section
+
+namespace PersistentSOS
+
+open scoped BigOperators
+
+
+/-- Indices of the complete quadratic monomial basis across all eight blocks. -/
+abbrev MomentIndex := (c : Fin 8) × Fin (blockSize c)
+
+/-- The normalized exact moment functional separating the cubic from its sphere bound. -/
+noncomputable def sphereFunctional : Poly →ₗ[ℝ] ℝ := momentLinearMap momentNumerator
+
+@[simp] theorem sphereFunctional_monomial (d : Exponent) (c : ℝ) :
+    sphereFunctional (MvPolynomial.monomial d c) =
+      c * (momentNumerator (exponentKey d) : ℝ) / 1000000000 :=
+  momentLinearMap_monomial _ _ _
+
+theorem basisPair_covers : ∀ i j : Fin 15, ∃ b : MomentIndex,
+    basisPair b.1 b.2 = (i, j) ∨ basisPair b.1 b.2 = (j, i) := by
+  decide +kernel
+
+@[simp] theorem variableExponent_zero : variableExponent 0 = 0 := by
+  simp [variableExponent]
+
+@[simp] theorem variableExponent_succ (i : Fin 14) :
+    variableExponent i.succ = Finsupp.single i 1 := by
+  simp [variableExponent, Fin.succ_ne_zero]
+
+theorem momentBasis_zero : ∃ b : MomentIndex, momentBasis b = 0 := by
+  obtain ⟨b, h | h⟩ := basisPair_covers 0 0
+  all_goals exact ⟨b, by simp [momentBasis, h]⟩
+
+theorem momentBasis_single (i : Fin 14) :
+    ∃ b : MomentIndex, momentBasis b = Finsupp.single i 1 := by
+  obtain ⟨b, h | h⟩ := basisPair_covers 0 i.succ
+  · exact ⟨b, by simp [momentBasis, h]⟩
+  · exact ⟨b, by simp [momentBasis, h]⟩
+
+theorem momentBasis_pair (i j : Fin 14) :
+    ∃ b : MomentIndex, momentBasis b = Finsupp.single i 1 + Finsupp.single j 1 := by
+  obtain ⟨b, h | h⟩ := basisPair_covers i.succ j.succ
+  · exact ⟨b, by simp [momentBasis, h]⟩
+  · exact ⟨b, by simp [momentBasis, h, add_comm]⟩
+
+theorem momentBasis_covers (d : Exponent) (hd : d.sum (fun _ n => n) ≤ 2) :
+    ∃ b : MomentIndex, momentBasis b = d := by
+  rcases exponent_degree_le_two d hd with h | ⟨i, h⟩ | ⟨i, j, h⟩
+  · simpa [h] using momentBasis_zero
+  · simpa [h] using momentBasis_single i
+  · simpa [h] using momentBasis_pair i j
+
+lemma moment_inner_sum (x : MomentIndex → ℝ) (c : Fin 8) (i : Fin (blockSize c)) :
+    (∑ d : Fin 8, ∑ j : Fin (blockSize d), x ⟨c, i⟩ *
+      (momentNumerator (basisKey c i + basisKey d j) : ℝ) * x ⟨d, j⟩) =
+    ∑ j : Fin (blockSize c), x ⟨c, i⟩ * (blockNumerator c i j : ℝ) * x ⟨c, j⟩ := by
+  rw [Finset.sum_eq_single c]
+  · simp only [moment_block]
+  · intro d _ hdc
+    simp only [moment_cross c d hdc.symm, Int.cast_zero, mul_zero, zero_mul, Finset.sum_const_zero]
+  · simp
+
+lemma moment_gram_nonneg (x : MomentIndex → ℝ) :
+    0 ≤ ∑ i, ∑ j, x i * sphereFunctional
+      (MvPolynomial.monomial (momentBasis i + momentBasis j) 1) * x j := by
+  simp only [sphereFunctional_monomial, one_mul, exponentKey_add, exponentKey_momentBasis]
+  have hnum : (∑ i : MomentIndex, ∑ j : MomentIndex,
+      x i * (momentNumerator (basisKey i.1 i.2 + basisKey j.1 j.2) : ℝ) * x j) =
+      ∑ c : Fin 8, quadraticForm (fun i j => (blockNumerator c i j : ℝ))
+        (fun i => x ⟨c, i⟩) := by
+    simp only [Fintype.sum_sigma, quadraticForm]
+    apply Finset.sum_congr rfl
+    intro c _
+    apply Finset.sum_congr rfl
+    intro i _
+    exact moment_inner_sum x c i
+  have hpos : 0 ≤ ∑ i : MomentIndex, ∑ j : MomentIndex,
+      x i * (momentNumerator (basisKey i.1 i.2 + basisKey j.1 j.2) : ℝ) * x j := by
+    rw [hnum]
+    exact block_nonneg blockSize (fun c i j => (blockNumerator c i j : ℝ))
+      blockNumerator_psd x
+  convert div_nonneg hpos (by norm_num : (0:ℝ) ≤ 1000000000) using 1
+  simp only [Finset.sum_div]
+  apply Finset.sum_congr rfl
+  intro i _
+  apply Finset.sum_congr rfl
+  intro j _
+  ring
+
+theorem moment_square_nonneg (h : Poly) (hd : h.totalDegree ≤ 2) :
+    0 ≤ sphereFunctional (h ^ 2) :=
+  nonneg_quadratic_square_of_momentMatrix momentBasis momentBasis_covers sphereFunctional
+    moment_gram_nonneg h hd
+
+theorem moment_one : sphereFunctional 1 = 1 := by
+  change sphereFunctional (MvPolynomial.monomial 0 1) = 1
+  rw [sphereFunctional_monomial, exponentKey_zero]
+  norm_num [momentNumerator]
+
+theorem moment_q : sphereFunctional qPoly = 1 := by
+  simp only [qPoly, map_sum, MvPolynomial.X_pow_eq_monomial,
+    sphereFunctional_monomial, exponentKey_single, one_mul]
+  have h : (∑ i : Fin 14, (momentNumerator (2 * 5 ^ i.val) : ℝ)) = 1000000000 := by
+    exact_mod_cast moment_quadratic_numerator_sum
+  rw [← Finset.sum_div, h]
+  norm_num
+
+theorem moment_q_sq : sphereFunctional (qPoly ^ 2) = 1 := by
+  rw [pow_two]
+  simp only [qPoly, Finset.sum_mul, Finset.mul_sum, map_sum,
+    MvPolynomial.X_pow_eq_monomial, MvPolynomial.monomial_mul_monomial,
+    sphereFunctional_monomial, exponentKey_add, exponentKey_single, one_mul]
+  have h : (∑ i : Fin 14, ∑ j : Fin 14,
+      (momentNumerator (2 * 5 ^ i.val + 2 * 5 ^ j.val) : ℝ)) = 1000000000 := by
+    exact_mod_cast moment_quartic_numerator_sum
+  simp only [← Finset.sum_div]
+  rw [Finset.sum_comm, h]
+  norm_num
+
+theorem moment_cubic : sphereFunctional cubicPoly = 500753357629 / 500000000000 := by
+  have h3 : (3 : Poly) = MvPolynomial.C (3 : ℝ) :=
+    (map_natCast MvPolynomial.C 3).symm
+  simp only [cubicPoly, map_add, map_sub, MvPolynomial.X_pow_eq_monomial]
+  simp only [h3, MvPolynomial.X, MvPolynomial.C_mul_monomial,
+    MvPolynomial.monomial_mul_monomial]
+  simp only [sphereFunctional_monomial, exponentKey_add, exponentKey_single]
+  norm_num [momentNumerator]
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/PSD.lean b/LeanPool/PersistentSOS/PSD.lean
new file mode 100644
index 0000000000..565a6a3205
--- /dev/null
+++ b/LeanPool/PersistentSOS/PSD.lean
@@ -0,0 +1,127 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import Mathlib.Basic.Real.Basic
+public import Mathlib.Algebra.BigOperators.Fin
+public import Mathlib.Algebra.Order.BigOperators.Ring.Finset
+public import Mathlib.Data.Fin.VecNotation
+public import Mathlib.Tactic.Linarith
+public import Mathlib.Tactic.LinearCombination
+public import Mathlib.Tactic.NormNum
+public import Mathlib.Tactic.Ring
+
+/-!
+# Exact positive semidefinite certificate calculus
+
+Integer fraction-free Schur certificates are checked by the Lean kernel.
+-/
+
+@[expose] public section
+
+
+namespace PersistentSOS
+
+open scoped BigOperators
+
+/-- The quadratic form of a real matrix. -/
+def quadraticForm {n : ℕ} (A : Fin n → Fin n → ℝ) (x : Fin n → ℝ) : ℝ :=
+  ∑ i, ∑ j, x i * A i j * x j
+
+/-- Nonnegativity of the quadratic form; symmetry is verified independently. -/
+def IsPSD {n : ℕ} (A : Fin n → Fin n → ℝ) : Prop :=
+  ∀ x, 0 ≤ quadraticForm A x
+
+lemma quadraticForm_zero (A : Fin 0 → Fin 0 → ℝ) : IsPSD A := by
+  intro x
+  simp [quadraticForm]
+
+/-- One fraction - free Schur step, with an independently checked previous pivot. -/
+lemma schur_step {n : ℕ} (A : Fin (n + 1) → Fin (n + 1) → ℝ)
+    (B : Fin n → Fin n → ℝ) (p : ℝ)
+    (hp : 0 < p) (ha : 0 < A 0 0)
+    (hsym : ∀ i : Fin n, A i.succ 0 = A 0 i.succ)
+    (hstep : ∀ i j, p * B i j = A 0 0 * A i.succ j.succ -
+      A i.succ 0 * A 0 j.succ) (hB : IsPSD B) : IsPSD A := by
+  intro x
+  let y : Fin n → ℝ := fun i => x i.succ
+  let v : ℝ := ∑ i : Fin n, A 0 i.succ * y i
+  have htail : A 0 0 * quadraticForm (fun i j : Fin n => A i.succ j.succ) y =
+      p * quadraticForm B y + v ^ 2 := by
+    simp only [quadraticForm, v, pow_two, Finset.mul_sum, Finset.sum_mul]
+    rw [← Finset.sum_add_distrib]
+    apply Finset.sum_congr rfl
+    intro i _
+    rw [← Finset.sum_add_distrib]
+    apply Finset.sum_congr rfl
+    intro j _
+    have h := hstep i j
+    rw [hsym] at h
+    linear_combination -(y i * y j) * h
+  have hleft : (∑ i : Fin n, x 0 * A 0 i.succ * x i.succ) = x 0 * v := by
+    simp [v, y, Finset.mul_sum, mul_assoc]
+  have hright : (∑ i : Fin n, x i.succ * A i.succ 0 * x 0) = x 0 * v := by
+    simp only [v, y, Finset.mul_sum, hsym]
+    apply Finset.sum_congr rfl
+    intro i _
+    ring
+  have hfull : quadraticForm A x = A 0 0 * x 0 ^ 2 + 2 * x 0 * v +
+      quadraticForm (fun i j : Fin n => A i.succ j.succ) y := by
+    simp only [quadraticForm, Fin.sum_univ_succ, Finset.sum_add_distrib]
+    rw [hleft, hright]
+    dsimp [y]
+    ring
+  have hnonneg := hB y
+  have hsquare := sq_nonneg (A 0 0 * x 0 + v)
+  have hscaled : 0 ≤ A 0 0 * quadraticForm A x := by
+    rw [hfull]
+    nlinarith [mul_nonneg hp.le hnonneg]
+  exact nonneg_of_mul_nonneg_right hscaled ha
+
+/-- Integer identities suffice for a Schur step over the reals. -/
+lemma integer_schur_step {n : ℕ} (A : Fin (n + 1) → Fin (n + 1) → ℤ)
+    (B : Fin n → Fin n → ℤ) (p : ℤ)
+    (hp : 0 < p) (ha : 0 < A 0 0)
+    (hsym : ∀ i : Fin n, A i.succ 0 = A 0 i.succ)
+    (hstep : ∀ i j, p * B i j = A 0 0 * A i.succ j.succ -
+      A i.succ 0 * A 0 j.succ)
+    (hB : IsPSD (fun i j => (B i j : ℝ))) :
+    IsPSD (fun i j => (A i j : ℝ)) := by
+  apply schur_step _ _ (p : ℝ) (by exact_mod_cast hp) (by exact_mod_cast ha)
+    (fun i => by exact_mod_cast hsym i) _ hB
+  intro i j
+  exact_mod_cast hstep i j
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/Polynomial.lean b/LeanPool/PersistentSOS/Polynomial.lean
new file mode 100644
index 0000000000..2cf7a3c13c
--- /dev/null
+++ b/LeanPool/PersistentSOS/Polynomial.lean
@@ -0,0 +1,246 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.Definitions
+public import LeanPool.PersistentSOS.SOSDegree
+public import Mathlib.Algebra.MvPolynomial.PDeriv
+public import Mathlib.Tactic.Ring
+
+/-!
+# Polynomial
+
+Part of the explicit persistent quartic SOS counterexample.
+-/
+
+@[expose] public section
+
+namespace PersistentSOS
+open MvPolynomial
+open scoped BigOperators
+
+/-- Substitution of a common real scale in every polynomial variable. -/
+noncomputable def scalePoly (r : ℝ) : Poly →ₐ[ℝ] Poly :=
+  MvPolynomial.aeval (fun i => MvPolynomial.C r * MvPolynomial.X i)
+
+theorem scalePoly_C (r c : ℝ) : scalePoly r (MvPolynomial.C c) = MvPolynomial.C c := by
+  simp [scalePoly]
+
+@[simp] theorem scalePoly_X (r : ℝ) (i : Fin 14) :
+    scalePoly r (MvPolynomial.X i) = MvPolynomial.C r * MvPolynomial.X i := by
+  simp [scalePoly]
+
+/-- Common scaling cannot increase total degree. -/
+theorem totalDegree_scalePoly_le (r : ℝ) (p : Poly) :
+    (scalePoly r p).totalDegree ≤ p.totalDegree := by
+  classical
+  nth_rw 1 [p.as_sum]
+  rw [map_sum]
+  apply totalDegree_finsetSum_le
+  intro d hd
+  apply le_trans ?_ (le_totalDegree hd)
+  rw [scalePoly, aeval_monomial]
+  apply (totalDegree_mul _ _).trans
+  simp only [algebraMap_eq, totalDegree_C, zero_add, Finsupp.prod, Finsupp.sum]
+  apply (totalDegree_finsetProd _ _).trans
+  apply Finset.sum_le_sum
+  intro i hi
+  apply (totalDegree_pow _ _).trans
+  have h := totalDegree_mul (MvPolynomial.C r : Poly) (MvPolynomial.X i)
+  simp only [totalDegree_C, totalDegree_X, zero_add] at h
+  simpa using Nat.mul_le_mul_left (d i) h
+
+@[simp] theorem scalePoly_qPoly (r : ℝ) :
+    scalePoly r qPoly = MvPolynomial.C (r ^ 2) * qPoly := by
+  simp [qPoly, map_sum, mul_pow, Finset.mul_sum]
+
+@[simp] theorem scalePoly_cubicPoly (r : ℝ) :
+    scalePoly r cubicPoly = MvPolynomial.C (r ^ 3) * cubicPoly := by
+  simp only [cubicPoly, map_add, map_sub, map_mul, map_pow, map_ofNat, scalePoly_X,
+    scalePoly_C]
+  ring
+
+/-- The quartic, quadratic, and cubic terms scale with their literal degrees. -/
+theorem scalePoly_quarticPoly (r σ a b : ℝ) :
+    scalePoly r (quarticPoly σ a b) =
+      MvPolynomial.C (σ / 4 * r ^ 4) * qPoly ^ 2 -
+      MvPolynomial.C (a / 2 * r ^ 2) * qPoly -
+      MvPolynomial.C (b * r ^ 3) * cubicPoly := by
+  simp only [quarticPoly, map_sub, map_mul, map_pow, scalePoly_C,
+    scalePoly_qPoly, scalePoly_cubicPoly]
+  ring
+
+/-- Degree of the squared Euclidean norm polynomial. -/
+theorem totalDegree_qPoly_le : qPoly.totalDegree ≤ 2 := by
+  apply totalDegree_finsetSum_le
+  intro i hi
+  simp
+
+/-- The displayed 25 - term cubic has total degree at most three. -/
+private theorem degree_add_le_three {p q : Poly} (hp : p.totalDegree ≤ 3)
+    (hq : q.totalDegree ≤ 3) : (p + q).totalDegree ≤ 3 :=
+  (totalDegree_add p q).trans (max_le hp hq)
+
+private theorem degree_sub_le_three {p q : Poly} (hp : p.totalDegree ≤ 3)
+    (hq : q.totalDegree ≤ 3) : (p - q).totalDegree ≤ 3 :=
+  (totalDegree_sub p q).trans (max_le hp hq)
+
+private theorem degree_mul_le {p q : Poly} {m n : ℕ} (hp : p.totalDegree ≤ m)
+    (hq : q.totalDegree ≤ n) : (p * q).totalDegree ≤ m + n :=
+  (totalDegree_mul p q).trans (Nat.add_le_add hp hq)
+
+private theorem degree_three_square (i j : Fin 14) :
+    (3 * MvPolynomial.X i * MvPolynomial.X j ^ 2 : Poly).totalDegree ≤ 3 := by
+  have hnum : (3 : Poly).totalDegree ≤ 0 := by
+    rw [← map_ofNat MvPolynomial.C 3, totalDegree_C]
+  exact degree_mul_le (degree_mul_le hnum (totalDegree_X i).le)
+    (totalDegree_X_pow j 2).le
+
+private theorem degree_coefficient_square (c : ℝ) (i j : Fin 14) :
+    (MvPolynomial.C c * MvPolynomial.X i * MvPolynomial.X j ^ 2).totalDegree ≤ 3 :=
+  degree_mul_le (degree_mul_le (totalDegree_C c).le (totalDegree_X i).le)
+    (totalDegree_X_pow j 2).le
+
+private theorem degree_coefficient_product (c : ℝ) (i j k : Fin 14) :
+    (MvPolynomial.C c * MvPolynomial.X i * MvPolynomial.X j *
+      MvPolynomial.X k).totalDegree ≤ 3 :=
+  degree_mul_le (degree_mul_le (degree_mul_le (totalDegree_C c).le
+    (totalDegree_X i).le) (totalDegree_X j).le) (totalDegree_X k).le
+
+private noncomputable def cubicPart0 : Poly :=
+  MvPolynomial.X 0 ^ 3
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 5 ^ 2
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 6 ^ 2
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 7 ^ 2
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 8 ^ 2
+
+private theorem cubicPart0_degree : cubicPart0.totalDegree ≤ 3 := by
+  unfold cubicPart0
+  exact degree_sub_le_three (degree_sub_le_three (degree_sub_le_three (degree_sub_le_three
+    ((totalDegree_X_pow (0 : Fin 14) 3).le) (degree_three_square 0 5)) (degree_three_square 0 6))
+    (degree_three_square 0 7)) (degree_three_square 0 8)
+
+private noncomputable def cubicPart1 : Poly :=
+  -(3 * MvPolynomial.X 0 * MvPolynomial.X 9 ^ 2)
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 10 ^ 2
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 11 ^ 2
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 12 ^ 2
+  - 3 * MvPolynomial.X 0 * MvPolynomial.X 13 ^ 2
+
+private theorem cubicPart1_degree : cubicPart1.totalDegree ≤ 3 := by
+  unfold cubicPart1
+  exact degree_sub_le_three (degree_sub_le_three (degree_sub_le_three (degree_sub_le_three ((by
+    simpa only [totalDegree_neg] using degree_three_square 0 9)) (degree_three_square 0 10))
+    (degree_three_square 0 11)) (degree_three_square 0 12)) (degree_three_square 0 13)
+
+private noncomputable def cubicPart2 : Poly :=
+  MvPolynomial.C (3 / 2) * MvPolynomial.X 0 * MvPolynomial.X 1 ^ 2
+  + MvPolynomial.C (3 / 2) * MvPolynomial.X 0 * MvPolynomial.X 2 ^ 2
+  + MvPolynomial.C (3 / 2) * MvPolynomial.X 0 * MvPolynomial.X 3 ^ 2
+  + MvPolynomial.C (3 / 2) * MvPolynomial.X 0 * MvPolynomial.X 4 ^ 2
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 5 * MvPolynomial.X 1 ^ 2
+
+private theorem cubicPart2_degree : cubicPart2.totalDegree ≤ 3 := by
+  unfold cubicPart2
+  exact degree_add_le_three (degree_add_le_three (degree_add_le_three (degree_add_le_three
+    (degree_coefficient_square (3 / 2) 0 1) (degree_coefficient_square (3 / 2) 0 2))
+    (degree_coefficient_square (3 / 2) 0 3)) (degree_coefficient_square (3 / 2) 0 4))
+    (degree_coefficient_square (259 / 100) 5 1)
+
+private noncomputable def cubicPart3 : Poly :=
+  MvPolynomial.C (259 / 100) * MvPolynomial.X 6 * MvPolynomial.X 2 ^ 2
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 7 * MvPolynomial.X 3 ^ 2
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 8 * MvPolynomial.X 1 * MvPolynomial.X 2
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 8 * MvPolynomial.X 3 * MvPolynomial.X 4
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 9 * MvPolynomial.X 1 * MvPolynomial.X 3
+
+private theorem cubicPart3_degree : cubicPart3.totalDegree ≤ 3 := by
+  unfold cubicPart3
+  exact degree_add_le_three (degree_add_le_three (degree_add_le_three (degree_add_le_three
+    (degree_coefficient_square (259 / 100) 6 2) (degree_coefficient_square (259 / 100) 7 3))
+    (degree_coefficient_product (259 / 100) 8 1 2)) (degree_coefficient_product (259 / 100) 8 3
+    4)) (degree_coefficient_product (259 / 100) 9 1 3)
+
+private noncomputable def cubicPart4 : Poly :=
+  MvPolynomial.C (259 / 100) * MvPolynomial.X 9 * MvPolynomial.X 2 * MvPolynomial.X 4
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 10 * MvPolynomial.X 2 * MvPolynomial.X 3
+  + MvPolynomial.C (1813 / 500) * MvPolynomial.X 11 * MvPolynomial.X 1 * MvPolynomial.X 4
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 12 * MvPolynomial.X 2 * MvPolynomial.X 4
+  + MvPolynomial.C (259 / 100) * MvPolynomial.X 13 * MvPolynomial.X 3 * MvPolynomial.X 4
+
+private theorem cubicPart4_degree : cubicPart4.totalDegree ≤ 3 := by
+  unfold cubicPart4
+  exact degree_add_le_three (degree_add_le_three (degree_add_le_three (degree_add_le_three
+    (degree_coefficient_product (259 / 100) 9 2 4) (degree_coefficient_product (259 / 100) 10 2
+    3)) (degree_coefficient_product (1813 / 500) 11 1 4)) (degree_coefficient_product (259 / 100)
+    12 2 4)) (degree_coefficient_product (259 / 100) 13 3 4)
+
+private theorem cubicPoly_parts :
+    cubicPoly = cubicPart0 + cubicPart1 + cubicPart2 + cubicPart3 + cubicPart4 := by
+  unfold cubicPoly cubicPart0 cubicPart1 cubicPart2 cubicPart3 cubicPart4
+  ring
+
+/-- The cubic has degree at most three, using separately checked sparse components. -/
+theorem totalDegree_cubicPoly_le : cubicPoly.totalDegree ≤ 3 := by
+  rw [cubicPoly_parts]
+  exact degree_add_le_three
+    (degree_add_le_three
+      (degree_add_le_three (degree_add_le_three cubicPart0_degree cubicPart1_degree)
+        cubicPart2_degree) cubicPart3_degree) cubicPart4_degree
+
+/-- The objective is a quartic polynomial for all parameter values. -/
+theorem totalDegree_quarticPoly_le (σ a b : ℝ) : (quarticPoly σ a b).totalDegree ≤ 4 := by
+  unfold quarticPoly
+  apply (totalDegree_sub _ _).trans
+  apply max_le
+  · apply (totalDegree_sub _ _).trans
+    apply max_le
+    · apply (totalDegree_mul _ _).trans
+      simp only [totalDegree_C, zero_add]
+      exact (totalDegree_pow _ _).trans (by have := totalDegree_qPoly_le; omega)
+    · apply (totalDegree_mul _ _).trans
+      simp only [totalDegree_C, zero_add]
+      exact totalDegree_qPoly_le.trans (by decide)
+  · apply (totalDegree_mul _ _).trans
+    simp only [totalDegree_C, zero_add]
+    exact totalDegree_cubicPoly_le.trans (by decide)
+
+
+/-- Subtracting a real lower bound preserves the quartic degree bound. -/
+theorem totalDegree_shiftedQuartic_le (σ a b γ : ℝ) :
+    (quarticPoly σ a b - MvPolynomial.C γ).totalDegree ≤ 4 := by
+  exact (totalDegree_sub _ _).trans (max_le (totalDegree_quarticPoly_le σ a b) (by simp))
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/QuadraticMonomials.lean b/LeanPool/PersistentSOS/QuadraticMonomials.lean
new file mode 100644
index 0000000000..2b5251ab38
--- /dev/null
+++ b/LeanPool/PersistentSOS/QuadraticMonomials.lean
@@ -0,0 +1,74 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import Mathlib.Data.Finsupp.Multiset
+public import Mathlib.Tactic.IntervalCases
+
+/-!
+# Quadratic Monomials
+
+Part of the explicit persistent quartic SOS counterexample.
+-/
+
+public section
+namespace PersistentSOS
+
+/-- Every monomial of total degree at most two is constant, a variable,
+or a product of two variables (allowing a repeated variable). -/
+theorem exponent_degree_le_two {σ : Type*} (d : σ →₀ ℕ)
+    (h : d.sum (fun _ n => n) ≤ 2) :
+    d = 0 ∨ (∃ i, d = Finsupp.single i 1) ∨
+      (∃ i j, d = Finsupp.single i 1 + Finsupp.single j 1) := by
+  classical
+  have hc : d.toMultiset.card ≤ 2 := by simpa only [Finsupp.card_toMultiset, Function.id_def]
+    using h
+  interval_cases hcard : d.toMultiset.card
+  · left
+    have hm : d.toMultiset = 0 := Multiset.card_eq_zero.mp hcard
+    have := congrArg Multiset.toFinsupp hm
+    simpa using this
+  · right; left
+    obtain ⟨i, hi⟩ := Multiset.card_eq_one.mp hcard
+    refine ⟨i, ?_⟩
+    have := congrArg Multiset.toFinsupp hi
+    simpa using this
+  · right; right
+    obtain ⟨i, j, hij⟩ := Multiset.card_eq_two.mp hcard
+    refine ⟨i, j, ?_⟩
+    have := congrArg Multiset.toFinsupp hij
+    simpa [← Multiset.singleton_add, map_add] using this
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/Radial.lean b/LeanPool/PersistentSOS/Radial.lean
new file mode 100644
index 0000000000..40c5f7a5f4
--- /dev/null
+++ b/LeanPool/PersistentSOS/Radial.lean
@@ -0,0 +1,115 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.Definitions
+public import Mathlib.Tactic.FieldSimp
+public import Mathlib.Tactic.Linarith
+public import Mathlib.Tactic.LinearCombination
+public import Mathlib.Tactic.Positivity
+public import Mathlib.Tactic.Ring
+
+/-!
+# Radial
+
+Part of the explicit persistent quartic SOS counterexample.
+-/
+
+@[expose] public section
+
+namespace PersistentSOS
+
+/-- The one - variable radial lower envelope. -/
+noncomputable def radialValue (σ a b r : ℝ) : ℝ := σ / 4 * r ^ 4 - b * r ^ 3 - a / 2 * r ^ 2
+
+theorem minimizingRadius_pos {σ a b : ℝ} (hσ : 0 < σ) (ha : 0 < a) (hb : 0 < b) :
+    0 < minimizingRadius σ a b := by
+  unfold minimizingRadius
+  positivity
+
+theorem minimizingRadius_equation {σ a b : ℝ} (hσ : 0 < σ) (ha : 0 < a) :
+    σ * minimizingRadius σ a b ^ 2 = 3 * b * minimizingRadius σ a b + a := by
+  have hd : 0 ≤ 9 * b ^ 2 + 4 * a * σ := by positivity
+  have hs := Real.sq_sqrt hd
+  unfold minimizingRadius
+  field_simp
+  ring_nf at hs ⊢
+  nlinarith
+
+theorem radial_at_minimizingRadius {σ a b : ℝ} (hσ : 0 < σ) (ha : 0 < a) :
+    radialValue σ a b (minimizingRadius σ a b) = minimumValue σ a b := by
+  have he := minimizingRadius_equation (b := b) hσ ha
+  unfold radialValue minimumValue
+  linear_combination (minimizingRadius σ a b) ^ 2 / 4 * he
+
+theorem radial_factorization {σ a b r s : ℝ} (he : σ * r ^ 2 = 3 * b * r + a) :
+    radialValue σ a b s + (b * r ^ 3 + a * r ^ 2) / 4 =
+      (s - r) ^ 2 * (σ * s ^ 2 + (2 * σ * r - 4 * b) * s + b * r + a) / 4 := by
+  unfold radialValue
+  linear_combination (3 * s ^ 2 - 2 * r * s) / 4 * he
+
+theorem radial_global_minimum {σ a b : ℝ} (hσ : 0 < σ) (ha : 0 < a)
+    (hb : 0 < b) {s : ℝ} (hs : 0 ≤ s) :
+    minimumValue σ a b ≤ radialValue σ a b s := by
+  set r := minimizingRadius σ a b with hrdef
+  have hr : 0 < r := minimizingRadius_pos hσ ha hb
+  have he : σ * r ^ 2 = 3 * b * r + a := minimizingRadius_equation hσ ha
+  have hcoef : 0 < 2 * σ * r - 4 * b := by nlinarith
+  have hbr : 0 ≤ σ * s ^ 2 + (2 * σ * r - 4 * b) * s + b * r + a := by positivity
+  have hprod := mul_nonneg (sq_nonneg (s - r)) hbr
+  have hf := radial_factorization (s := s) he
+  change -(b * r ^ 3 + a * r ^ 2) / 4 ≤ _
+  linarith
+
+/-- The radial minimizer is unique among nonnegative radii. -/
+theorem radial_minimum_eq_iff {σ a b : ℝ} (hσ : 0 < σ) (ha : 0 < a)
+    (hb : 0 < b) {s : ℝ} (hs : 0 ≤ s) :
+    radialValue σ a b s = minimumValue σ a b ↔ s = minimizingRadius σ a b := by
+  set r := minimizingRadius σ a b with hrdef
+  have hr : 0 < r := minimizingRadius_pos hσ ha hb
+  have he : σ * r ^ 2 = 3 * b * r + a := minimizingRadius_equation hσ ha
+  have hcoef : 0 < 2 * σ * r - 4 * b := by nlinarith
+  have hbr : 0 < σ * s ^ 2 + (2 * σ * r - 4 * b) * s + b * r + a := by positivity
+  constructor
+  · intro h
+    have hf := radial_factorization (s := s) he
+    change radialValue σ a b s = -(b * r ^ 3 + a * r ^ 2) / 4 at h
+    have hz : (s - r) ^ 2 * (σ * s ^ 2 + (2 * σ * r - 4 * b) * s + b * r + a) = 0 := by linarith
+    have hsq := (mul_eq_zero.mp hz).resolve_right (ne_of_gt hbr)
+    nlinarith [sq_nonneg (s - r)]
+  · rintro rfl
+    exact radial_at_minimizingRadius hσ ha
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/SOSDegree.lean b/LeanPool/PersistentSOS/SOSDegree.lean
new file mode 100644
index 0000000000..37109f2c81
--- /dev/null
+++ b/LeanPool/PersistentSOS/SOSDegree.lean
@@ -0,0 +1,143 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import Mathlib.RingTheory.MvPolynomial.MonomialOrder.DegLex
+public import Mathlib.Algebra.MvPolynomial.NoZeroDivisors
+public import Mathlib.Basic.Real.Basic
+
+/-! # Degree bounds for ordinary sums of squares
+
+A finite sum of squares of real polynomials cannot cancel its highest
+terms. Consequently, every summand of an SOS polynomial of degree at most
+`2 * d` has degree at most `d`. The SOS representations in this result
+are unrestricted ordinary polynomial representations.
+-/
+
+
+public section
+
+namespace PersistentSOS
+
+open MvPolynomial
+open scoped BigOperators MonomialOrder
+
+private theorem degree_add_of_nonneg_leadingCoeff {σ : Type*}
+    (m : MonomialOrder σ) (f g : MvPolynomial σ ℝ)
+    (hf : 0 ≤ m.leadingCoeff f) (hg : 0 ≤ m.leadingCoeff g) :
+    m.toSyn (m.degree (f + g)) =
+      m.toSyn (m.degree f) ⊔ m.toSyn (m.degree g) ∧
+      0 ≤ m.leadingCoeff (f + g) := by
+  rcases lt_trichotomy (m.toSyn (m.degree f)) (m.toSyn (m.degree g)) with h | h | h
+  · constructor
+    · rw [m.degree_add_eq_right_of_lt h, sup_eq_right.mpr h.le]
+    · rw [add_comm, m.leadingCoeff_add_of_lt h]
+      exact hg
+  · have heq : m.degree f = m.degree g := m.toSyn.injective h
+    by_cases hf0 : f = 0
+    · simp_all
+    have hpos : 0 < m.leadingCoeff f :=
+      lt_of_le_of_ne hf (Ne.symm (m.leadingCoeff_ne_zero_iff.mpr hf0))
+    have hcoeff : (f + g).coeff (m.degree f) ≠ 0 := by
+      rw [AddMonoidAlgebra.coeff_add, Finsupp.add_apply]
+      simpa only [MonomialOrder.leadingCoeff, heq] using
+        ne_of_gt (add_pos_of_pos_of_nonneg hpos hg)
+    have hd : m.degree (f + g) = m.degree f := by
+      apply m.toSyn.injective
+      apply le_antisymm
+      · exact m.degree_add_le.trans (by simp [h])
+      · exact m.le_degree (mem_support_iff.mpr hcoeff)
+    constructor
+    · simp [hd, h]
+    · rw [MonomialOrder.leadingCoeff, hd, AddMonoidAlgebra.coeff_add, Finsupp.add_apply]
+      simpa only [MonomialOrder.leadingCoeff, heq] using add_nonneg hf hg
+  · constructor
+    · rw [m.degree_add_of_lt h, sup_eq_left.mpr h.le]
+    · rw [m.leadingCoeff_add_of_lt h]
+      exact hf
+
+private theorem degree_sum_of_nonneg_leadingCoeff {σ ι : Type*}
+    (m : MonomialOrder σ) (s : Finset ι) (f : ι → MvPolynomial σ ℝ)
+    (hf : ∀ i ∈ s, 0 ≤ m.leadingCoeff (f i)) :
+    m.toSyn (m.degree (∑ i ∈ s, f i)) = s.sup (fun i => m.toSyn (m.degree (f i))) ∧
+      0 ≤ m.leadingCoeff (∑ i ∈ s, f i) := by
+  classical
+  induction s using Finset.induction_on with
+  | empty => simp
+  | @insert i s hi ih =>
+    have his := ih (fun j hj => hf j (Finset.mem_insert_of_mem hj))
+    have hadd := degree_add_of_nonneg_leadingCoeff m (f i) (∑ j ∈ s, f j)
+      (hf i (Finset.mem_insert_self i s)) his.2
+    simpa [Finset.sum_insert hi, Finset.sup_insert, his.1] using hadd
+
+/-- Each square in an ordinary finite sum of squares has total degree no
+larger than the sum. This includes representations with arbitrary - degree
+polynomial summands. -/
+theorem totalDegree_sq_le_sum_sq {σ ι : Type*} [LinearOrder σ] [WellFoundedGT σ]
+    (s : Finset ι) (f : ι → MvPolynomial σ ℝ) {i : ι} (hi : i ∈ s) :
+    (f i ^ 2).totalDegree ≤ (∑ j ∈ s, f j ^ 2).totalDegree := by
+  classical
+  have hsum := degree_sum_of_nonneg_leadingCoeff MonomialOrder.degLex s
+    (fun j => f j ^ 2) (by
+      intro j hj
+      rw [MonomialOrder.leadingCoeff_pow]
+      exact sq_nonneg _)
+  apply degLex_totalDegree_monotone
+  rw [hsum.1]
+  exact Finset.le_sup (f := fun j => MonomialOrder.degLex.toSyn (MonomialOrder.degLex.degree (f j
+    ^ 2))) hi
+
+/-- Ordinary SOS degree bridge, valid for every even total - degree bound. -/
+theorem totalDegree_le_of_sum_sq {σ ι : Type*} [LinearOrder σ] [WellFoundedGT σ]
+    (s : Finset ι) (f : ι → MvPolynomial σ ℝ) (d : ℕ)
+    (h : (∑ j ∈ s, f j ^ 2).totalDegree ≤ 2 * d) {i : ι} (hi : i ∈ s) :
+    (f i).totalDegree ≤ d := by
+  by_cases hi0 : f i = 0
+  · simp [hi0]
+  have hsq := (totalDegree_sq_le_sum_sq s f hi).trans h
+  rw [pow_two, totalDegree_mul_of_isDomain hi0 hi0] at hsq
+  omega
+
+/-- In particular, every summand in any ordinary quartic SOS
+representation is a polynomial of total degree at most two. -/
+theorem quartic_sos_summand_degree {σ : Type*} [LinearOrder σ] [WellFoundedGT σ]
+    {p : MvPolynomial σ ℝ} (hp : p.totalDegree ≤ 4)
+    {m : ℕ} {f : Fin m → MvPolynomial σ ℝ} (h : p = ∑ i, f i ^ 2) (i : Fin m) :
+    (f i).totalDegree ≤ 2 := by
+  apply totalDegree_le_of_sum_sq Finset.univ f 2
+  · simpa [← h] using hp
+  · exact Finset.mem_univ i
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/Sphere.lean b/LeanPool/PersistentSOS/Sphere.lean
new file mode 100644
index 0000000000..b0eeb63faf
--- /dev/null
+++ b/LeanPool/PersistentSOS/Sphere.lean
@@ -0,0 +1,357 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.Definitions
+public import Mathlib.Tactic.Convert
+public import Mathlib.Tactic.FieldSimp
+public import Mathlib.Tactic.Linarith
+public import Mathlib.Tactic.NormNum
+public import Mathlib.Tactic.Positivity
+public import Mathlib.Tactic.Ring
+
+/-!
+# Sphere
+
+Part of the explicit persistent quartic SOS counterexample.
+-/
+
+@[expose] public section
+
+namespace PersistentSOS
+
+theorem Q_nonneg (z : Fin 14 → ℝ) : 0 ≤ Q z := by
+  rw [Q_eq_sum]
+  exact Finset.sum_nonneg fun i _ => sq_nonneg (z i)
+
+theorem radius_nonneg (z : Fin 14 → ℝ) : 0 ≤ radius z := Real.sqrt_nonneg _
+
+theorem radius_sq (z : Fin 14 → ℝ) : radius z ^ 2 = Q z :=
+  Real.sq_sqrt (Q_nonneg z)
+
+theorem Q_eq_norm_sq (z : Fin 14 → ℝ) :
+    Q z = ‖(WithLp.toLp 2 z : EuclideanSpace ℝ (Fin 14))‖ ^ 2 := by
+  simp [Q_eq_sum, PiLp.norm_sq_eq_of_L2, Real.norm_eq_abs, sq_abs]
+
+theorem radius_eq_norm (z : Fin 14 → ℝ) :
+    radius z = ‖(WithLp.toLp 2 z : EuclideanSpace ℝ (Fin 14))‖ := by
+  rw [radius, Q_eq_norm_sq, Real.sqrt_sq (norm_nonneg _)]
+
+/-- Squared norm of the four coordinates used by the quadratic map. -/
+noncomputable def xSq (z : Fin 14 → ℝ) : ℝ :=
+  z 1 ^ 2 + z 2 ^ 2 + z 3 ^ 2 + z 4 ^ 2
+
+/-- Squared norm of the nine coordinates paired with the quadratic map. -/
+noncomputable def ySq (z : Fin 14 → ℝ) : ℝ :=
+  z 5 ^ 2 + z 6 ^ 2 + z 7 ^ 2 + z 8 ^ 2 + z 9 ^ 2 + z 10 ^ 2
+    + z 11 ^ 2 + z 12 ^ 2 + z 13 ^ 2
+
+/-- The nine-component rational quadratic map appearing in the cubic. -/
+noncomputable def quadMap (z : Fin 14 → ℝ) : Fin 9 → ℝ :=
+  ![z 1 ^ 2, z 2 ^ 2, z 3 ^ 2, z 1 * z 2 + z 3 * z 4,
+    z 1 * z 3 + z 2 * z 4, z 2 * z 3, 7 / 5 * z 1 * z 4,
+    z 2 * z 4, z 3 * z 4]
+
+/-- The nine coordinates paired with the quadratic map. -/
+noncomputable def yVec (z : Fin 14 → ℝ) : Fin 9 → ℝ :=
+  ![z 5, z 6, z 7, z 8, z 9, z 10, z 11, z 12, z 13]
+
+/-- Pairing of the nine-coordinate vector with the quadratic map. -/
+noncomputable def dotTerm (z : Fin 14 → ℝ) : ℝ := ∑ i, yVec z i * quadMap z i
+
+theorem xSq_nonneg (z : Fin 14 → ℝ) : 0 ≤ xSq z := by unfold xSq; positivity
+theorem ySq_nonneg (z : Fin 14 → ℝ) : 0 ≤ ySq z := by unfold ySq; positivity
+
+theorem Q_decomp (z : Fin 14 → ℝ) : Q z = z 0 ^ 2 + xSq z + ySq z := by
+  simp [Q_eq_sum, Fin.sum_univ_succ, xSq, ySq]
+  ring
+
+theorem C_decomp (z : Fin 14 → ℝ) :
+    C z = z 0 ^ 3 - 3 * z 0 * ySq z + 3 / 2 * z 0 * xSq z
+      + 259 / 100 * dotTerm z := by
+  simp [C, cubicPoly, dotTerm, quadMap, yVec, Fin.sum_univ_succ, xSq, ySq]
+  ring
+
+theorem choiLam_nonneg (a b c d : ℝ) :
+    0 ≤ a ^ 2 * b ^ 2 + a ^ 2 * c ^ 2 + b ^ 2 * c ^ 2 + d ^ 4 - 4 * a * b * c * d := by
+  by_cases h : 0 ≤ b * c
+  · nlinarith [sq_nonneg (a * b - a * c), sq_nonneg (b * c - d ^ 2),
+      mul_nonneg h (sq_nonneg (a - d))]
+  · have hn : 0 ≤ -(b * c) := le_of_lt (neg_pos.mpr (lt_of_not_ge h))
+    nlinarith [sq_nonneg (a * b + a * c), sq_nonneg (b * c + d ^ 2),
+      mul_nonneg hn (sq_nonneg (a + d))]
+
+theorem quadMap_contraction (z : Fin 14 → ℝ) :
+    (∑ i, quadMap z i ^ 2) ≤ xSq z ^ 2 := by
+  have h := choiLam_nonneg (z 1) (z 2) (z 3) (z 4)
+  simp [quadMap, xSq, Fin.sum_univ_succ]
+  nlinarith [sq_nonneg (z 1 * z 4)]
+
+theorem dotTerm_bound (z : Fin 14 → ℝ) : dotTerm z ≤ Real.sqrt (ySq z) * xSq z := by
+  have hcs := Finset.sum_mul_sq_le_sq_mul_sq Finset.univ (yVec z) (quadMap z)
+  have hy : (∑ i, yVec z i ^ 2) = ySq z := by
+    simp [yVec, ySq, Fin.sum_univ_succ]; ring
+  have hm := mul_le_mul_of_nonneg_left (quadMap_contraction z) (ySq_nonneg z)
+  rw [hy] at hcs
+  have hs := Real.sq_sqrt (ySq_nonneg z)
+  have hx := xSq_nonneg z
+  have hy' := Real.sqrt_nonneg (ySq z)
+  change dotTerm z ^ 2 ≤ _ at hcs
+  have hprod : 0 ≤ Real.sqrt (ySq z) * xSq z := mul_nonneg hy' hx
+  nlinarith [sq_nonneg (dotTerm z - Real.sqrt (ySq z) * xSq z)]
+
+theorem cubic_unit_refined_upper (z : Fin 14 → ℝ) (hQ : Q z = 1) :
+    C z + (3 / 2 * Real.sqrt 3 - 259 / 100) * (Real.sqrt (ySq z) * xSq z) ≤ 1 := by
+  let Y := Real.sqrt (ySq z)
+  let s := Real.sqrt 3
+  let t := z 0
+  let v := (t + s * Y) / 2
+  have hY : 0 ≤ Y := Real.sqrt_nonneg _
+  have hY2 : Y ^ 2 = ySq z := Real.sq_sqrt (ySq_nonneg z)
+  have hs : 0 ≤ s := Real.sqrt_nonneg _
+  have hs2 : s ^ 2 = 3 := Real.sq_sqrt (by norm_num)
+  have hs3 : s ^ 3 = 3 * s := by calc
+    s ^ 3 = s ^ 2 * s := by ring
+    _ = 3 * s := by rw [hs2]
+  have hx := xSq_nonneg z
+  have hsplit : t ^ 2 + xSq z + Y ^ 2 = 1 := by
+    simpa only [t, hY2, ← Q_decomp] using hQ
+  have hk : (259 / 100 : ℝ) ≤ 3 / 2 * s := by nlinarith
+  have hupper : C z + (3 / 2 * s - 259 / 100) * (Y * xSq z) ≤
+      t ^ 3 - 3 * t * Y ^ 2 + 3 / 2 * (t + s * Y) * xSq z := by
+    have hd := dotTerm_bound z
+    have hm := mul_nonneg (sub_nonneg.mpr hk) (mul_nonneg hY hx)
+    rw [C_decomp, ← hY2]
+    change dotTerm z ≤ Y * xSq z at hd
+    dsimp [t]
+    nlinarith [hd]
+  have hcs : (t + s * Y) ^ 2 + (s * t - Y) ^ 2 = 4 * (t ^ 2 + Y ^ 2) := by
+    calc
+      _ = (1 + s ^ 2) * (t ^ 2 + Y ^ 2) := by ring
+      _ = _ := by rw [hs2]; ring
+  have hv : -1 ≤ v := by
+    dsimp [v]
+    nlinarith [sq_nonneg (s * t - Y)]
+  have hid : t ^ 3 - 3 * t * Y ^ 2 + 3 / 2 * (t + s * Y) * xSq z
+      = 3 * v - 4 * v ^ 3 := by
+    have heq : xSq z = 1 - t ^ 2 - Y ^ 2 := by linarith
+    rw [heq]
+    dsimp [v]
+    ring_nf
+    rw [hs2, hs3]
+    ring
+  have hf : 0 ≤ (v + 1) * (2 * v - 1) ^ 2 :=
+    mul_nonneg (by linarith) (sq_nonneg _)
+  rw [hid] at hupper
+  change C z + (3 / 2 * s - 259 / 100) * (Y * xSq z) ≤ 1
+  nlinarith
+
+theorem coefficient_strict : (259 / 100 : ℝ) < 3 / 2 * Real.sqrt 3 := by
+  have hs := Real.sqrt_nonneg (3 : ℝ)
+  have hs2 : Real.sqrt (3 : ℝ) ^ 2 = 3 := Real.sq_sqrt (by norm_num)
+  nlinarith
+
+theorem cubic_unit_upper (z : Fin 14 → ℝ) (hQ : Q z = 1) : C z ≤ 1 := by
+  have h := cubic_unit_refined_upper z hQ
+  have hp := mul_nonneg (sub_nonneg.mpr (le_of_lt coefficient_strict))
+    (mul_nonneg (Real.sqrt_nonneg (ySq z)) (xSq_nonneg z))
+  linarith
+
+theorem C_scale (z : Fin 14 → ℝ) (r : ℝ) :
+    C (fun i => r * z i) = r ^ 3 * C z := by
+  simp [C, cubicPoly]
+  ring
+
+theorem Q_scale (z : Fin 14 → ℝ) (r : ℝ) :
+    Q (fun i => r * z i) = r ^ 2 * Q z := by
+  simp only [Q_eq_sum, mul_pow, ← Finset.mul_sum]
+
+theorem C_neg (z : Fin 14 → ℝ) : C (fun i => -z i) = -C z := by
+  convert C_scale z (-1) using 1 <;> norm_num
+
+theorem cubic_unit_abs (z : Fin 14 → ℝ) (hQ : Q z = 1) : |C z| ≤ 1 := by
+  have hu := cubic_unit_upper z hQ
+  have hQn : Q (fun i => -z i) = 1 := by
+    simpa using (Q_scale z (-1)).trans (by simpa using hQ)
+  have hl := cubic_unit_upper (fun i => -z i) hQn
+  rw [C_neg] at hl
+  exact abs_le.mpr ⟨by linarith, hu⟩
+
+theorem Q_eq_zero_iff (z : Fin 14 → ℝ) : Q z = 0 ↔ z = 0 := by
+  rw [Q_eq_norm_sq, sq_eq_zero_iff, norm_eq_zero]
+  exact WithLp.toLp_eq_zero 2
+
+theorem cubic_abs_le (z : Fin 14 → ℝ) : |C z| ≤ radius z ^ 3 := by
+  by_cases hz : Q z = 0
+  · have heq := (Q_eq_zero_iff z).mp hz
+    subst z
+    simp [C, cubicPoly, radius, Q_eq_sum]
+  · have hr : 0 < radius z := Real.sqrt_pos.mpr (lt_of_le_of_ne (Q_nonneg z) (Ne.symm hz))
+    have hr0 : radius z ≠ 0 := ne_of_gt hr
+    have hn : Q (fun i => (radius z)⁻¹ * z i) = 1 := by
+      rw [Q_scale, ← radius_sq]
+      field_simp
+    have hu := cubic_unit_abs (fun i => (radius z)⁻¹ * z i) hn
+    rw [C_scale, abs_mul, abs_of_nonneg (by positivity : 0 ≤ ((radius z)⁻¹) ^ 3)] at hu
+    have hh := mul_le_mul_of_nonneg_left hu (le_of_lt (pow_pos hr 3))
+    have hi : radius z ^ 3 * ((radius z)⁻¹ ^ 3 * |C z|) = |C z| := by
+      field_simp
+    rw [hi] at hh
+    simpa using hh
+
+theorem Q_axis (r : ℝ) : Q (axis r) = r ^ 2 := by
+  simp [Q_eq_sum, axis]
+
+@[simp] theorem C_axis (r : ℝ) : C (axis r) = r ^ 3 := by
+  norm_num [C, cubicPoly, axis]
+
+theorem unit_sphere_attainment : Q (axis 1) = 1 ∧ C (axis 1) = 1 := by
+  rw [Q_axis, C_axis]
+  norm_num
+
+theorem dotTerm_sq_le (z : Fin 14 → ℝ) : dotTerm z ^ 2 ≤ ySq z * xSq z ^ 2 := by
+  have hcs := Finset.sum_mul_sq_le_sq_mul_sq Finset.univ (yVec z) (quadMap z)
+  have hy : (∑ i, yVec z i ^ 2) = ySq z := by
+    simp [yVec, ySq, Fin.sum_univ_succ]; ring
+  rw [hy] at hcs
+  exact le_trans hcs (mul_le_mul_of_nonneg_left (quadMap_contraction z) (ySq_nonneg z))
+
+theorem dotTerm_zero_of_xSq_zero (z : Fin 14 → ℝ) (h : xSq z = 0) : dotTerm z = 0 := by
+  have hd := dotTerm_sq_le z
+  rw [h] at hd
+  nlinarith [sq_nonneg (dotTerm z)]
+
+theorem dotTerm_zero_of_ySq_zero (z : Fin 14 → ℝ) (h : ySq z = 0) : dotTerm z = 0 := by
+  have hd := dotTerm_sq_le z
+  rw [h] at hd
+  nlinarith [sq_nonneg (dotTerm z)]
+
+/-- Exact equality classification on the unit sphere. The four `x` coordinates vanish;
+    the first coordinate is either `1` or `-1 / 2`. The sphere equation then determines
+    the squared length of the nine `y` coordinates as `0` or `3 / 4`, respectively. -/
+theorem cubic_unit_maximizers (z : Fin 14 → ℝ) (hQ : Q z = 1) :
+    C z = 1 ↔ xSq z = 0 ∧ (z 0 = 1 ∨ z 0 = -1 / 2) := by
+  constructor
+  · intro hC
+    have hu := cubic_unit_refined_upper z hQ
+    have hd : 0 < 3 / 2 * Real.sqrt 3 - 259 / 100 := sub_pos.mpr coefficient_strict
+    have hprod : Real.sqrt (ySq z) * xSq z = 0 := by
+      have hn := mul_nonneg (Real.sqrt_nonneg (ySq z)) (xSq_nonneg z)
+      rw [hC] at hu
+      nlinarith
+    rcases mul_eq_zero.mp hprod with hy | hx
+    · have hy0 : ySq z = 0 := by
+        have hs := Real.sq_sqrt (ySq_nonneg z)
+        rw [hy] at hs
+        simpa using hs.symm
+      have hdot := dotTerm_zero_of_ySq_zero z hy0
+      have hsplit := Q_decomp z
+      rw [hQ, hy0] at hsplit
+      have hxs : xSq z = 1 - z 0 ^ 2 := by linarith
+      have hc := C_decomp z
+      rw [hC, hy0, hdot, hxs] at hc
+      have hf : (z 0 - 1) ^ 2 * (z 0 + 2) = 0 := by nlinarith [hc]
+      have ht : -1 ≤ z 0 := by nlinarith [xSq_nonneg z]
+      have ht2 : z 0 + 2 ≠ 0 := by linarith
+      have ht1 : z 0 = 1 := by
+        have hh := (mul_eq_zero.mp hf).resolve_right ht2
+        nlinarith [sq_nonneg (z 0 - 1)]
+      exact ⟨by rw [hxs, ht1]; norm_num, Or.inl ht1⟩
+    · refine ⟨hx, ?_⟩
+      have hdot := dotTerm_zero_of_xSq_zero z hx
+      have hsplit := Q_decomp z
+      rw [hQ, hx] at hsplit
+      have hys : ySq z = 1 - z 0 ^ 2 := by linarith
+      have hc := C_decomp z
+      rw [hC, hx, hdot, hys] at hc
+      have hf : (z 0 - 1) * (2 * z 0 + 1) ^ 2 = 0 := by nlinarith [hc]
+      rcases mul_eq_zero.mp hf with h | h
+      · exact Or.inl (by linarith)
+      · exact Or.inr (by nlinarith [sq_nonneg (2 * z 0 + 1)])
+  · rintro ⟨hx, ht | ht⟩
+    all_goals
+      have hdot := dotTerm_zero_of_xSq_zero z hx
+      have hsplit := Q_decomp z
+      rw [hQ, hx, ht] at hsplit
+      rw [C_decomp, hx, ht, hdot]
+      nlinarith
+
+theorem xSq_zero_iff (z : Fin 14 → ℝ) :
+    xSq z = 0 ↔ z 1 = 0 ∧ z 2 = 0 ∧ z 3 = 0 ∧ z 4 = 0 := by
+  unfold xSq
+  constructor
+  · intro h
+    have h1 := sq_nonneg (z 1)
+    have h2 := sq_nonneg (z 2)
+    have h3 := sq_nonneg (z 3)
+    have h4 := sq_nonneg (z 4)
+    exact ⟨by nlinarith, by nlinarith, by nlinarith, by nlinarith⟩
+  · rintro ⟨h1, h2, h3, h4⟩
+    simp [h1, h2, h3, h4]
+
+theorem cubic_unit_maximizers_coordinates (z : Fin 14 → ℝ) (hQ : Q z = 1) :
+    C z = 1 ↔ (z 1 = 0 ∧ z 2 = 0 ∧ z 3 = 0 ∧ z 4 = 0) ∧
+      (z 0 = 1 ∨ z 0 = -1 / 2) := by
+  rw [cubic_unit_maximizers z hQ, xSq_zero_iff]
+
+theorem xSq_scale (z : Fin 14 → ℝ) (r : ℝ) :
+    xSq (fun i => r * z i) = r ^ 2 * xSq z := by
+  unfold xSq
+  ring
+
+/-- Global equality classification for the sharp homogeneous cubic bound. -/
+theorem cubic_upper_equality (z : Fin 14 → ℝ) :
+    C z = radius z ^ 3 ↔ xSq z = 0 ∧
+      (z 0 = radius z ∨ z 0 = -radius z / 2) := by
+  by_cases hz : Q z = 0
+  · have heq := (Q_eq_zero_iff z).mp hz
+    subst z
+    simp [C, cubicPoly, radius, Q_eq_sum, xSq]
+  · have hr : 0 < radius z := Real.sqrt_pos.mpr (lt_of_le_of_ne (Q_nonneg z) (Ne.symm hz))
+    have hr0 : radius z ≠ 0 := ne_of_gt hr
+    have hn : Q (fun i => (radius z)⁻¹ * z i) = 1 := by
+      rw [Q_scale, ← radius_sq]
+      field_simp
+    have hc := cubic_unit_maximizers (fun i => (radius z)⁻¹ * z i) hn
+    rw [C_scale, xSq_scale] at hc
+    field_simp [hr0] at hc
+    simpa only [mul_zero, eq_div_iff (by norm_num : (2 : ℝ) ≠ 0)] using hc
+
+theorem cubic_upper_equality_coordinates (z : Fin 14 → ℝ) :
+    C z = radius z ^ 3 ↔ (z 1 = 0 ∧ z 2 = 0 ∧ z 3 = 0 ∧ z 4 = 0) ∧
+      (z 0 = radius z ∨ z 0 = -radius z / 2) := by
+  rw [cubic_upper_equality, xSq_zero_iff]
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/Transfer.lean b/LeanPool/PersistentSOS/Transfer.lean
new file mode 100644
index 0000000000..660e36bcd1
--- /dev/null
+++ b/LeanPool/PersistentSOS/Transfer.lean
@@ -0,0 +1,127 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.Definitions
+public import LeanPool.PersistentSOS.Radial
+public import LeanPool.PersistentSOS.SOSDegree
+public import LeanPool.PersistentSOS.Polynomial
+public import LeanPool.PersistentSOS.Sphere
+public import Mathlib.Tactic.Convert
+public import Mathlib.Tactic.Linarith
+public import Mathlib.Tactic.NormNum
+public import Mathlib.Tactic.Ring
+
+/-!
+# Transfer
+
+Part of the explicit persistent quartic SOS counterexample.
+-/
+
+@[expose] public section
+
+namespace PersistentSOS
+
+/-- The strict rational separation of the fixed cubic from its sphere bound. -/
+noncomputable def separation : ℝ := 753357629 / 500000000000
+
+theorem separation_pos : 0 < separation := by norm_num [separation]
+
+/-- An abstract linear - separation calculation, used with a separately verified
+ordinary moment functional. The public explicit theorem supplies that witness. -/
+theorem functional_separation (L : Poly →ₗ[ℝ] ℝ)
+    (h1 : L 1 = 1) (hQ : L qPoly = 1) (hQQ : L (qPoly ^ 2) = 1)
+    (hC : L cubicPoly = 1 + separation) (σ a b r γ : ℝ) :
+    L (MvPolynomial.C (σ / 4 * r ^ 4) * qPoly ^ 2 -
+       MvPolynomial.C (a / 2 * r ^ 2) * qPoly -
+       MvPolynomial.C (b * r ^ 3) * cubicPoly - MvPolynomial.C γ) =
+      radialValue σ a b r - b * separation * r ^ 3 - γ := by
+  have hscale (c : ℝ) (p : Poly) : L (MvPolynomial.C c * p) = c * L p := by
+    rw [← MvPolynomial.smul_eq_C_mul, map_smul, smul_eq_mul]
+  have hconst (c : ℝ) : L (MvPolynomial.C c) = c := by
+    simpa [h1] using hscale c 1
+  simp only [map_sub, hscale, hconst, hQ, hQQ, hC]
+  unfold radialValue
+  ring
+
+/-- Positivity for an ordinary quartic SOS, after any common coordinate scaling. -/
+theorem scaled_sos_nonneg (L : Poly →ₗ[ℝ] ℝ)
+    (hL : ∀ h : Poly, h.totalDegree ≤ 2 → 0 ≤ L (h ^ 2))
+    {p : Poly} (hp : p.totalDegree ≤ 4) (hsos : IsSOS p) (r : ℝ) :
+    0 ≤ L (scalePoly r p) := by
+  rcases hsos with ⟨m, f, hf⟩
+  rw [hf, map_sum, map_sum]
+  apply Finset.sum_nonneg
+  intro i hi
+  rw [map_pow]
+  exact hL _ ((totalDegree_scalePoly_le r (f i)).trans
+    (quartic_sos_summand_degree hp hf i))
+
+/-- Exact global lower bound for every positive parameter. -/
+theorem objective_global_lower_bound {σ a b : ℝ} (hσ : 0 < σ)
+    (ha : 0 < a) (hb : 0 < b) (z : Fin 14 → ℝ) :
+    minimumValue σ a b ≤ objective σ a b z := by
+  have hc := (le_abs_self (C z)).trans (cubic_abs_le z)
+  have hscaled := mul_le_mul_of_nonneg_left hc (le_of_lt hb)
+  have hrad := radial_global_minimum hσ ha hb (radius_nonneg z)
+  rw [objective_eq]
+  rw [← radius_sq z]
+  unfold radialValue at hrad
+  nlinarith
+
+/-- The distinguished axis point attains the exact global minimum. -/
+theorem objective_axis_attainment {σ a b : ℝ} (hσ : 0 < σ) (ha : 0 < a) :
+    objective σ a b (axis (minimizingRadius σ a b)) = minimumValue σ a b := by
+  rw [objective_eq, Q_axis, C_axis]
+  convert radial_at_minimizingRadius (b := b) hσ ha using 1
+  unfold radialValue
+  ring
+
+/-- The abstract moment - to - SOS transfer. The explicit theorem below instantiates
+all witness hypotheses by exact certificate proofs. -/
+theorem moment_quantitative_transfer (L : Poly →ₗ[ℝ] ℝ)
+    (h1 : L 1 = 1) (hQ : L qPoly = 1) (hQQ : L (qPoly ^ 2) = 1)
+    (hC : L cubicPoly = 1 + separation)
+    (hL : ∀ h : Poly, h.totalDegree ≤ 2 → 0 ≤ L (h ^ 2))
+    {σ a b γ : ℝ} (hσ : 0 < σ) (ha : 0 < a)
+    (hsos : IsSOS (quarticPoly σ a b - MvPolynomial.C γ)) :
+    γ ≤ minimumValue σ a b - b * separation * minimizingRadius σ a b ^ 3 := by
+  have hn := scaled_sos_nonneg L hL (totalDegree_shiftedQuartic_le σ a b γ)
+    hsos (minimizingRadius σ a b)
+  rw [map_sub, scalePoly_C, scalePoly_quarticPoly] at hn
+  rw [functional_separation L h1 hQ hQQ hC, radial_at_minimizingRadius hσ ha] at hn
+  linarith
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/UniqueDerivatives.lean b/LeanPool/PersistentSOS/UniqueDerivatives.lean
new file mode 100644
index 0000000000..7adef19415
--- /dev/null
+++ b/LeanPool/PersistentSOS/UniqueDerivatives.lean
@@ -0,0 +1,219 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.Derivatives
+public import LeanPool.PersistentSOS.Sphere
+public import LeanPool.PersistentSOS.Radial
+public import Mathlib.LinearAlgebra.Matrix.PosDef
+public import Mathlib.Algebra.Order.Star.Real
+public import Mathlib.Tactic.FinCases
+public import Mathlib.Tactic.Linarith
+public import Mathlib.Tactic.LinearCombination
+public import Mathlib.Tactic.NormNum
+public import Mathlib.Tactic.Positivity
+public import Mathlib.Tactic.Ring
+
+/-! # Derivatives of the quartic with a unique global minimizer
+
+The Hessian is computed from the literal polynomial using `MvPolynomial.pderiv`.
+At its minimizing axis point it is a strictly positive diagonal matrix.
+-/
+
+
+@[expose] public section
+namespace PersistentSOS
+open MvPolynomial
+
+
+private theorem constantCoeff_two : constantCoeff (2 : Poly) = 2 := by
+  rw [← map_ofNat MvPolynomial.C 2]
+  simp
+
+@[simp] private theorem pderiv_thousand (i : Fin 14) :
+    pderiv i (1000 : Poly) = 0 := by
+  rw [← map_ofNat MvPolynomial.C 1000]
+  exact pderiv_C
+
+@[simp] private theorem pderiv_two (i : Fin 14) :
+    pderiv i (2 : Poly) = 0 := by
+  rw [← map_ofNat MvPolynomial.C 2]
+  exact pderiv_C
+
+@[simp] private theorem pderiv_three (i : Fin 14) :
+    pderiv i (3 : Poly) = 0 := by
+  rw [← map_ofNat MvPolynomial.C 3]
+  exact pderiv_C
+
+@[simp] private theorem eval_ite_poly (z : Fin 14 → ℝ) (c : Prop) [Decidable c]
+    (u v : Poly) : eval z (if c then u else v) = if c then eval z u else eval z v := by
+  split_ifs <;> rfl
+
+@[simp] private theorem pderiv_ite_poly (i : Fin 14) (c : Prop) [Decidable c]
+    (u v : Poly) : pderiv i (if c then u else v) = if c then pderiv i u else pderiv i v := by
+  split_ifs <;> rfl
+
+@[simp] private theorem eval_qPoly_axis (r : ℝ) :
+    eval (axis r) qPoly = r ^ 2 := Q_axis r
+
+/-- The new cubic has no first - order contribution at the origin. -/
+theorem unique_cubic_first_at_zero (i : Fin 14) :
+    eval (0 : Fin 14 → ℝ) (pderiv i uniqueCubicPoly) = 0 := by
+  have hc : constantCoeff (pderiv i cubicPoly) = 0 := by
+    simpa using cubic_first_at_zero i
+  simp [uniqueCubicPoly, qPoly, hc]
+
+/-- The new cubic has no second - order contribution at the origin. -/
+theorem unique_cubic_second_at_zero (i j : Fin 14) :
+    eval (0 : Fin 14 → ℝ) (pderiv j (pderiv i uniqueCubicPoly)) = 0 := by
+  have hc : constantCoeff (pderiv j (pderiv i cubicPoly)) = 0 := by
+    simpa using cubic_second_at_zero i j
+  simp [uniqueCubicPoly, qPoly, hc]
+
+/-- The origin remains stationary for every choice of the parameters. -/
+theorem unique_stationary_origin (σ a b : ℝ) (i : Fin 14) :
+    eval (0 : Fin 14 → ℝ) (pderiv i (uniqueQuarticPoly σ a b)) = 0 := by
+  have hc : constantCoeff (pderiv i uniqueCubicPoly) = 0 := by
+    simpa using unique_cubic_first_at_zero i
+  have hq : constantCoeff qPoly = 0 := by simp [qPoly]
+  simp [uniqueQuarticPoly, q_first, hc, hq]
+
+/-- The Hessian at the stationary origin remains the negative scalar matrix. -/
+theorem unique_hessian_origin (σ a b : ℝ) (i j : Fin 14) :
+    eval (0 : Fin 14 → ℝ) (pderiv j (pderiv i (uniqueQuarticPoly σ a b))) =
+      if i = j then -a else 0 := by
+  have hc : constantCoeff (pderiv j (pderiv i uniqueCubicPoly)) = 0 := by
+    simpa using unique_cubic_second_at_zero i j
+  have hq : constantCoeff qPoly = 0 := by simp [qPoly]
+  simp [uniqueQuarticPoly, q_first, hc, Pi.single_apply, constantCoeff_two]
+  split_ifs <;> simp_all [constantCoeff_two]
+
+/-- The second derivatives of the original cubic at an arbitrary axis point. -/
+theorem cubic_second_axis (r : ℝ) (i j : Fin 14) :
+    eval (axis r) (pderiv j (pderiv i cubicPoly)) =
+      if i = j then (if i = 0 then 6 * r else if i.val ≤ 4 then 3 * r else -6 * r)
+      else 0 := by
+  fin_cases i <;>
+    norm_num [cubicPoly, axis, Pi.single_apply] <;> split_ifs <;> try simp_all
+  all_goals ring
+
+/-- The selected cubic's Hessian on the distinguished axis. -/
+theorem unique_cubic_second_axis (r : ℝ) (i j : Fin 14) :
+    eval (axis r) (pderiv j (pderiv i uniqueCubicPoly)) =
+      if i = j then
+        (if i = 0 then 6 * r else if i.val ≤ 4 then 3002 * r / 1001 else -5998 * r / 1001)
+      else 0 := by
+  simp [uniqueCubicPoly, q_first, cubic_second_axis, axis, Pi.single_apply]
+  by_cases hij : i = j
+  · subst j
+    by_cases hi : i = 0
+    · subst i
+      norm_num
+      ring
+    · by_cases hix : i.val ≤ 4
+      · simp [hi, Ne.symm hi, hix]
+        ring
+      · simp [hi, Ne.symm hi, hix]
+        ring
+  · by_cases hi : i = 0
+    · subst i
+      simp [hij, Ne.symm hij]
+    · simp [hij, hi, Ne.symm hi]
+
+/-- The actual Hessian entries at the explicit minimizing radius. -/
+theorem unique_hessian_minimizer {σ a b : ℝ} (hσ : 0 < σ) (ha : 0 < a)
+    (i j : Fin 14) :
+    eval (axis (minimizingRadius σ a b))
+      (pderiv j (pderiv i (uniqueQuarticPoly σ a b))) =
+      if i = j then
+        (if i = 0 then 2 * a + 3 * b * minimizingRadius σ a b
+         else if i.val ≤ 4 then b * minimizingRadius σ a b / 1001
+         else 9001 * b * minimizingRadius σ a b / 1001)
+      else 0 := by
+  have he := minimizingRadius_equation (b := b) hσ ha
+  simp [uniqueQuarticPoly, q_first, unique_cubic_second_axis,
+    axis, Pi.single_apply]
+  split_ifs <;> simp_all <;> nlinarith
+
+/-- The Hessian at the unique global minimizer is positive definite for
+all positive real regularization, quadratic, and cubic strengths. -/
+theorem unique_hessian_posDef {σ a b : ℝ} (hσ : 0 < σ) (ha : 0 < a) (hb : 0 < b) :
+    Matrix.PosDef (fun i j : Fin 14 =>
+      eval (axis (minimizingRadius σ a b))
+        (pderiv j (pderiv i (uniqueQuarticPoly σ a b)))) := by
+  have hr := minimizingRadius_pos hσ ha hb
+  have hdiag :
+      (fun i j : Fin 14 => eval (axis (minimizingRadius σ a b))
+        (pderiv j (pderiv i (uniqueQuarticPoly σ a b)))) =
+      Matrix.diagonal (fun i : Fin 14 =>
+        if i = 0 then 2 * a + 3 * b * minimizingRadius σ a b
+        else if i.val ≤ 4 then b * minimizingRadius σ a b / 1001
+        else 9001 * b * minimizingRadius σ a b / 1001) := by
+    funext i j
+    rw [unique_hessian_minimizer hσ ha]
+    rfl
+  rw [hdiag]
+  apply Matrix.PosDef.diagonal
+  intro i
+  split_ifs <;> positivity
+
+/-- First derivatives of the original cubic on its distinguished axis. -/
+theorem cubic_first_axis (r : ℝ) (i : Fin 14) :
+    eval (axis r) (pderiv i cubicPoly) = if i = 0 then 3 * r ^ 2 else 0 := by
+  fin_cases i <;> norm_num [cubicPoly, axis, Pi.single_apply]
+
+/-- The selected cubic has the same axial gradient as the original cubic. -/
+theorem unique_cubic_first_axis (r : ℝ) (i : Fin 14) :
+    eval (axis r) (pderiv i uniqueCubicPoly) = if i = 0 then 3 * r ^ 2 else 0 := by
+  simp [uniqueCubicPoly, q_first, cubic_first_axis, axis, Pi.single_apply]
+  by_cases hi : i = 0
+  · subst i
+    norm_num
+    ring
+  · simp [hi, Ne.symm hi]
+
+/-- The explicitly specified unique minimizer is stationary. -/
+theorem unique_stationary_minimizer {σ a b : ℝ} (hσ : 0 < σ) (ha : 0 < a)
+    (i : Fin 14) :
+    eval (axis (minimizingRadius σ a b))
+      (pderiv i (uniqueQuarticPoly σ a b)) = 0 := by
+  have he := minimizingRadius_equation (b := b) hσ ha
+  simp [uniqueQuarticPoly, q_first, unique_cubic_first_axis, axis]
+  by_cases hi : i = 0
+  · simp [hi]
+    linear_combination minimizingRadius σ a b * he
+  · simp [hi]
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/UniqueGeometry.lean b/LeanPool/PersistentSOS/UniqueGeometry.lean
new file mode 100644
index 0000000000..160165496e
--- /dev/null
+++ b/LeanPool/PersistentSOS/UniqueGeometry.lean
@@ -0,0 +1,219 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.Geometry
+public import Mathlib.Tactic.Convert
+public import Mathlib.Tactic.Linarith
+public import Mathlib.Tactic.NormNum
+public import Mathlib.Tactic.Ring
+
+/-!
+# Unique Geometry
+
+Part of the explicit persistent quartic SOS counterexample.
+-/
+
+@[expose] public section
+
+namespace PersistentSOS
+
+/-- The selected cubic is the explicit convex combination of the original
+cubic and the first coordinate times the squared Euclidean norm. -/
+theorem unique_cubic_eq (z : Fin 14 → ℝ) :
+    uniqueCubic z = (1000 * C z + z 0 * Q z) / 1001 := by
+  simp [uniqueCubic, uniqueCubicPoly, C, Q]
+  ring
+
+/-- The selected quartic is evaluated on ordinary real vectors. -/
+theorem unique_objective_eq (σ a b : ℝ) (z : Fin 14 → ℝ) :
+    uniqueObjective σ a b z = σ / 4 * Q z ^ 2 - a / 2 * Q z - b * uniqueCubic z := by
+  simp [uniqueObjective, uniqueQuarticPoly, Q, uniqueCubic]
+
+/-- Every coordinate has absolute value bounded by the Euclidean radius. -/
+theorem coordinate_abs_le_radius (z : Fin 14 → ℝ) (i : Fin 14) :
+    |z i| ≤ radius z := by
+  have hi : z i ^ 2 ≤ Q z := by
+    rw [Q_eq_sum]
+    exact Finset.single_le_sum (fun j _ => sq_nonneg (z j)) (Finset.mem_univ i)
+  have hr := radius_nonneg z
+  have hs := radius_sq z
+  exact abs_le.mpr ⟨by nlinarith, by nlinarith⟩
+
+/-- Squared distance to a point on the distinguished axis. -/
+theorem Q_sub_axis (z : Fin 14 → ℝ) (r : ℝ) :
+    Q (fun i => z i - axis r i) = Q z - 2 * r * z 0 + r ^ 2 := by
+  simp [Q_eq_sum, axis, Fin.sum_univ_succ]
+  ring
+
+/-- Equality of the first coordinate with the radius forces all transverse
+coordinates to vanish. -/
+theorem eq_axis_of_first_eq_radius (z : Fin 14 → ℝ) (h : z 0 = radius z) :
+    z = axis (radius z) := by
+  have hq : Q (fun i => z i - axis (radius z) i) = 0 := by
+    rw [Q_sub_axis, ← radius_sq, h]
+    ring
+  have hv := (Q_eq_zero_iff _).mp hq
+  funext i
+  have hi := congrFun hv i
+  simpa only [Pi.zero_apply, sub_eq_zero] using hi
+
+/-- The deficit separates into two nonnegative terms. -/
+theorem unique_cubic_deficit (z : Fin 14 → ℝ) :
+    radius z ^ 3 - uniqueCubic z =
+      (1000 * (radius z ^ 3 - C z) + radius z ^ 2 * (radius z - z 0)) / 1001 := by
+  rw [unique_cubic_eq, ← radius_sq]
+  ring
+
+/-- The original sharp bound and a coordinate bound give the same upper
+bound for the selected cubic. -/
+theorem unique_cubic_le (z : Fin 14 → ℝ) : uniqueCubic z ≤ radius z ^ 3 := by
+  have hc := (le_abs_self (C z)).trans (cubic_abs_le z)
+  have ht := (le_abs_self (z 0)).trans (coordinate_abs_le_radius z 0)
+  apply sub_nonneg.mp
+  rw [unique_cubic_deficit]
+  exact div_nonneg (add_nonneg (mul_nonneg (by norm_num) (sub_nonneg.mpr hc))
+    (mul_nonneg (sq_nonneg _) (sub_nonneg.mpr ht))) (by norm_num)
+
+/-- The selected cubic remains homogeneous of degree three. -/
+theorem unique_cubic_scale (z : Fin 14 → ℝ) (r : ℝ) :
+    uniqueCubic (fun i => r * z i) = r ^ 3 * uniqueCubic z := by
+  rw [unique_cubic_eq, C_scale, Q_scale, unique_cubic_eq]
+  ring
+
+theorem unique_cubic_neg (z : Fin 14 → ℝ) :
+    uniqueCubic (fun i => -z i) = -uniqueCubic z := by
+  convert unique_cubic_scale z (-1) using 1 <;> norm_num
+
+theorem radius_neg (z : Fin 14 → ℝ) : radius (fun i => -z i) = radius z := by
+  unfold radius
+  congr 1
+  convert Q_scale z (-1) using 1 <;> norm_num
+
+/-- The selected cubic has the sharp global homogeneous bound. -/
+theorem unique_cubic_abs_le (z : Fin 14 → ℝ) : |uniqueCubic z| ≤ radius z ^ 3 := by
+  have hu := unique_cubic_le z
+  have hl := unique_cubic_le (fun i => -z i)
+  rw [unique_cubic_neg, radius_neg] at hl
+  exact abs_le.mpr ⟨by linarith, hu⟩
+
+@[simp] theorem unique_cubic_axis (r : ℝ) : uniqueCubic (axis r) = r ^ 3 := by
+  rw [unique_cubic_eq, C_axis, Q_axis]
+  simp [axis]
+  ring
+
+/-- Equality in the upper cubic bound occurs exactly on the nonnegative
+part of the distinguished coordinate axis, including the origin. -/
+theorem unique_cubic_upper_equality (z : Fin 14 → ℝ) :
+    uniqueCubic z = radius z ^ 3 ↔ z = axis (radius z) := by
+  constructor
+  · intro heq
+    by_cases hz : radius z = 0
+    · have hQ : Q z = 0 := by rw [← radius_sq, hz]; norm_num
+      have hv := (Q_eq_zero_iff z).mp hQ
+      rw [hz, hv]
+      funext i
+      simp [axis]
+    · have hc := (le_abs_self (C z)).trans (cubic_abs_le z)
+      have ht := (le_abs_self (z 0)).trans (coordinate_abs_le_radius z 0)
+      have hd := unique_cubic_deficit z
+      rw [heq, sub_self] at hd
+      have hp := mul_nonneg (sq_nonneg (radius z)) (sub_nonneg.mpr ht)
+      have hs : radius z ^ 2 * (radius z - z 0) = 0 := by nlinarith
+      have hfirst := (mul_eq_zero.mp hs).resolve_left (pow_ne_zero 2 hz)
+      exact eq_axis_of_first_eq_radius z (by linarith)
+  · intro h
+    calc
+      uniqueCubic z = uniqueCubic (axis (radius z)) := congrArg uniqueCubic h
+      _ = radius z ^ 3 := unique_cubic_axis _
+
+/-- The selected cubic attains its unit - sphere maximum only at the first
+coordinate unit vector. -/
+theorem unique_cubic_unit_maximizer (z : Fin 14 → ℝ) (hQ : Q z = 1) :
+    uniqueCubic z = 1 ↔ z = axis 1 := by
+  have hr : radius z = 1 := by rw [radius, hQ]; norm_num
+  simpa only [hr, one_pow] using unique_cubic_upper_equality z
+
+/-- Decomposition into the radial envelope and the selected cubic deficit. -/
+theorem unique_objective_radial_decomposition (σ a b : ℝ) (z : Fin 14 → ℝ) :
+    uniqueObjective σ a b z = radialValue σ a b (radius z) +
+      b * (radius z ^ 3 - uniqueCubic z) := by
+  rw [unique_objective_eq, ← radius_sq]
+  unfold radialValue
+  ring
+
+/-- Global optimality for every positive real regularization, quadratic
+strength and cubic strength. -/
+theorem unique_objective_global_lower_bound {σ a b : ℝ} (hσ : 0 < σ)
+    (ha : 0 < a) (hb : 0 < b) (z : Fin 14 → ℝ) :
+    minimumValue σ a b ≤ uniqueObjective σ a b z := by
+  have hc := unique_cubic_le z
+  have hscaled := mul_le_mul_of_nonneg_left hc (le_of_lt hb)
+  have hrad := radial_global_minimum hσ ha hb (radius_nonneg z)
+  rw [unique_objective_eq, ← radius_sq z]
+  unfold radialValue at hrad
+  nlinarith
+
+/-- The distinguished point attains the explicit minimum. -/
+theorem unique_objective_axis_attainment {σ a b : ℝ} (hσ : 0 < σ) (ha : 0 < a) :
+    uniqueObjective σ a b (axis (minimizingRadius σ a b)) = minimumValue σ a b := by
+  rw [unique_objective_eq, Q_axis, unique_cubic_axis]
+  calc
+    _ = radialValue σ a b (minimizingRadius σ a b) := by unfold radialValue; ring
+    _ = minimumValue σ a b := radial_at_minimizingRadius hσ ha
+
+/-- The global minimizer is unique for every positive choice of all three
+real parameters. -/
+theorem unique_objective_minimizer {σ a b : ℝ} (hσ : 0 < σ)
+    (ha : 0 < a) (hb : 0 < b) (z : Fin 14 → ℝ) :
+    uniqueObjective σ a b z = minimumValue σ a b ↔
+      z = axis (minimizingRadius σ a b) := by
+  constructor
+  · intro hobj
+    have hrad := radial_global_minimum hσ ha hb (radius_nonneg z)
+    have hc := unique_cubic_le z
+    have hdef := mul_nonneg (le_of_lt hb) (sub_nonneg.mpr hc)
+    have hid := unique_objective_radial_decomposition σ a b z
+    have heq : radialValue σ a b (radius z) = minimumValue σ a b := by linarith
+    have hr := (radial_minimum_eq_iff hσ ha hb (radius_nonneg z)).mp heq
+    have hzero : b * (radius z ^ 3 - uniqueCubic z) = 0 := by linarith
+    have hd := (mul_eq_zero.mp hzero).resolve_left (ne_of_gt hb)
+    have hu : uniqueCubic z = radius z ^ 3 := by linarith
+    have hz := (unique_cubic_upper_equality z).mp hu
+    simpa only [hr] using hz
+  · rintro rfl
+    exact unique_objective_axis_attainment hσ ha
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/UniqueMain.lean b/LeanPool/PersistentSOS/UniqueMain.lean
new file mode 100644
index 0000000000..10f5c27b3c
--- /dev/null
+++ b/LeanPool/PersistentSOS/UniqueMain.lean
@@ -0,0 +1,72 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.UniqueGeometry
+public import LeanPool.PersistentSOS.UniqueMoments
+public import LeanPool.PersistentSOS.UniqueDerivatives
+
+/-!
+# Unique Main
+
+Part of the explicit persistent quartic SOS counterexample.
+-/
+
+@[expose] public section
+namespace PersistentSOS
+
+/-- The selected quartic's exact minimum shift is globally nonnegative. -/
+theorem unique_minimum_shift_nonnegative {σ a b : ℝ} (hσ : 0 < σ) (ha : 0 < a)
+    (hb : 0 < b) (z : Fin 14 → ℝ) :
+    0 ≤ MvPolynomial.eval z
+      (uniqueQuarticPoly σ a b - MvPolynomial.C (minimumValue σ a b)) := by
+  simpa only [map_sub, MvPolynomial.eval_C, sub_nonneg, uniqueObjective]
+    using unique_objective_global_lower_bound hσ ha hb z
+
+/-- Persistent ordinary - SOS failure with a unique global minimizer and
+positive - definite Hessian there, for every positive real parameter. -/
+theorem unique_persistent_failure {σ a b : ℝ} (hσ : 0 < σ) (ha : 0 < a) (hb : 0 < b) :
+    (∀ z : Fin 14 → ℝ, minimumValue σ a b ≤ uniqueObjective σ a b z) ∧
+    (∀ z : Fin 14 → ℝ, uniqueObjective σ a b z = minimumValue σ a b ↔
+      z = axis (minimizingRadius σ a b)) ∧
+    Matrix.PosDef (fun i j : Fin 14 =>
+      MvPolynomial.eval (axis (minimizingRadius σ a b))
+        (MvPolynomial.pderiv j (MvPolynomial.pderiv i (uniqueQuarticPoly σ a b)))) ∧
+    ¬ IsSOS (uniqueQuarticPoly σ a b - MvPolynomial.C (minimumValue σ a b)) :=
+  ⟨unique_objective_global_lower_bound hσ ha hb,
+    unique_objective_minimizer hσ ha hb, unique_hessian_posDef hσ ha hb,
+    unique_minimum_shift_not_sos hσ ha hb⟩
+
+end PersistentSOS
diff --git a/LeanPool/PersistentSOS/UniqueMoments.lean b/LeanPool/PersistentSOS/UniqueMoments.lean
new file mode 100644
index 0000000000..05dc51f906
--- /dev/null
+++ b/LeanPool/PersistentSOS/UniqueMoments.lean
@@ -0,0 +1,208 @@
+/-
+Copyright (c) 2026 JD Jones. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: JD Jones
+-/
+
+/-
+Adapted from JD-Jones-ASES/persistent-sos, commit
+d432ff9a67594cc0fa7a7af1913320b46d2a86db.
+Original MIT notice (retained under the permission to sublicense):
+
+MIT License
+
+Copyright (c) 2026 JD Jones
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+-/
+
+module
+
+public import LeanPool.PersistentSOS.Localizers
+public import LeanPool.PersistentSOS.Transfer
+public import Mathlib.Tactic.Linarith
+public import Mathlib.Tactic.NormNum
+public import Mathlib.Tactic.Positivity
+public import Mathlib.Tactic.Ring
+
+/-! # The same moment certificate separates a cubic with a unique maximizer
+
+No new moment data are required. The existing sphere localizer identifies
+`L(tQ)` with `L(t)`, giving a positive exact gap for the selected cubic.
+The ordinary SOS degree bridge then transfers that gap at every positive
+regularization parameter.
+-/
+
+
+@[expose] public section
+
+namespace PersistentSOS
+open MvPolynomial
+
+/-- The exact first - coordinate moment from the retained rational certificate. -/
+theorem moment_first_coordinate : sphereFunctional (X 0) = 423308963 / 1000000000 := by
+  simp only [X, sphereFunctional_monomial, exponentKey_single]
+  norm_num [momentNumerator]
+
+/-- Multiplication by the sphere equation preserves the first - coordinate moment. -/
+theorem moment_first_coordinate_q :
+    sphereFunctional (X 0 * qPoly) = 423308963 / 1000000000 := by
+  have h := moment_sphere_localizer (X 0) (by simp)
+  rw [sub_mul, one_mul, map_sub] at h
+  rw [mul_comm, ← moment_first_coordinate]
+  exact sub_eq_zero.mp h
+
+/-- Constants act by ordinary scalar multiplication under the moment functional. -/
+lemma unique_moment_C_mul (c : ℝ) (p : Poly) :
+    sphereFunctional (MvPolynomial.C c * p) = c * sphereFunctional p := by
+  rw [← smul_eq_C_mul, map_smul, smul_eq_mul]
+
+/-- The separation for the selected cubic is strictly positive. -/
+theorem uniqueSeparation_pos : 0 < uniqueSeparation := by
+  norm_num [uniqueSeparation]
+
+/-- The exact gap for the selected cubic, using the unchanged functional. -/
+theorem moment_unique_cubic : sphereFunctional uniqueCubicPoly = 1 + uniqueSeparation := by
+  have h1000 : (1000 : Poly) = MvPolynomial.C (1000 : ℝ) :=
+    (map_natCast MvPolynomial.C 1000).symm
+  unfold uniqueCubicPoly
+  rw [unique_moment_C_mul, map_add, h1000, unique_moment_C_mul,
+    moment_cubic, moment_first_coordinate_q]
+  norm_num [uniqueSeparation]
+
+/-- The selected cubic's exact rational moment value. -/
+theorem moment_unique_cubic_exact :
+    sphereFunctional uniqueCubicPoly = 143132860603 / 143000000000 := by
+  rw [moment_unique_cubic]
+  norm_num [uniqueSeparation]
+
+/-- The selected cubic still exceeds its unit - sphere bound under the functional. -/
+theorem moment_unique_cubic_gt_one : 1 < sphereFunctional uniqueCubicPoly := by
+  rw [moment_unique_cubic]
+  linarith [uniqueSeparation_pos]
+
+/-- Common scaling respects the degree - three homogeneity of the selected cubic. -/
+@[simp] theorem scalePoly_uniqueCubicPoly (r : ℝ) :
+    scalePoly r uniqueCubicPoly = MvPolynomial.C (r ^ 3) * uniqueCubicPoly := by
+  simp only [uniqueCubicPoly, map_mul, map_add, map_pow, map_ofNat,
+    scalePoly_C, scalePoly_X, scalePoly_qPoly, scalePoly_cubicPoly]
+  ring
+
+/-- Exact scaling identity for the selected quartic. -/
+theorem scalePoly_uniqueQuarticPoly (r σ a b : ℝ) :
+    scalePoly r (uniqueQuarticPoly σ a b) =
+      MvPolynomial.C (σ / 4 * r ^ 4) * qPoly ^ 2 -
+      MvPolynomial.C (a / 2 * r ^ 2) * qPoly -
+      MvPolynomial.C (b * r ^ 3) * uniqueCubicPoly := by
+  simp only [uniqueQuarticPoly, map_sub, map_mul, map_pow, scalePoly_C,
+    scalePoly_qPoly, scalePoly_uniqueCubicPoly]
+  ring
+
+/-- The selected polynomial remains a cubic. -/
+theorem totalDegree_uniqueCubicPoly_le : uniqueCubicPoly.totalDegree ≤ 3 := by
+  have hnum : (1000 : Poly).totalDegree = 0 := by
+    rw [← map_ofNat MvPolynomial.C 1000, totalDegree_C]
+  unfold uniqueCubicPoly
+  apply (totalDegree_mul _ _).trans
+  simp only [totalDegree_C, zero_add]
+  apply (totalDegree_add _ _).trans
+  apply max_le
+  · apply (totalDegree_mul _ _).trans
+    simpa only [hnum, zero_add] using totalDegree_cubicPoly_le
+  · have h := totalDegree_mul (X 0 : Poly) qPoly
+    have hq := totalDegree_qPoly_le
+    simp only [totalDegree_X] at h
+    omega
+
+/-- The selected objective has degree at most four. -/
+theorem totalDegree_uniqueQuarticPoly_le (σ a b : ℝ) :
+    (uniqueQuarticPoly σ a b).totalDegree ≤ 4 := by
+  unfold uniqueQuarticPoly
+  apply (totalDegree_sub _ _).trans
+  apply max_le
+  · apply (totalDegree_sub _ _).trans
+    apply max_le
+    · apply (totalDegree_mul _ _).trans
+      simp only [totalDegree_C, zero_add]
+      exact (totalDegree_pow _ _).trans (by have := totalDegree_qPoly_le; omega)
+    · apply (totalDegree_mul _ _).trans
+      simp only [totalDegree_C, zero_add]
+      exact totalDegree_qPoly_le.trans (by decide)
+  · apply (totalDegree_mul _ _).trans
+    simp only [totalDegree_C, zero_add]
+    exact totalDegree_uniqueCubicPoly_le.trans (by decide)
+
+/-- Subtracting a real lower bound preserves the selected quartic degree bound. -/
+theorem totalDegree_shiftedUniqueQuartic_le (σ a b γ : ℝ) :
+    (uniqueQuarticPoly σ a b - MvPolynomial.C γ).totalDegree ≤ 4 := by
+  exact (totalDegree_sub _ _).trans
+    (max_le (totalDegree_uniqueQuarticPoly_le σ a b) (by simp))
+
+/-- The scaled functional evaluates the selected quartic shift exactly. -/
+theorem unique_functional_separation (σ a b r γ : ℝ) :
+    sphereFunctional (MvPolynomial.C (σ / 4 * r ^ 4) * qPoly ^ 2 -
+      MvPolynomial.C (a / 2 * r ^ 2) * qPoly -
+      MvPolynomial.C (b * r ^ 3) * uniqueCubicPoly - MvPolynomial.C γ) =
+      radialValue σ a b r - b * uniqueSeparation * r ^ 3 - γ := by
+  have hconst (c : ℝ) : sphereFunctional (MvPolynomial.C c) = c := by
+    simpa only [mul_one, moment_one] using unique_moment_C_mul c 1
+  simp only [map_sub, unique_moment_C_mul, hconst, moment_q, moment_q_sq,
+    moment_unique_cubic]
+  unfold radialValue
+  ring
+
+/-- Every ordinary SOS lower bound for the selected quartic has the exact gap. -/
+theorem unique_quantitative_sos_gap {σ a b γ : ℝ} (hσ : 0 < σ) (ha : 0 < a)
+    (hsos : IsSOS (uniqueQuarticPoly σ a b - MvPolynomial.C γ)) :
+    γ ≤ minimumValue σ a b - b * uniqueSeparation * minimizingRadius σ a b ^ 3 := by
+  have hn := scaled_sos_nonneg sphereFunctional moment_square_nonneg
+    (totalDegree_shiftedUniqueQuartic_le σ a b γ) hsos (minimizingRadius σ a b)
+  rw [map_sub, scalePoly_C, scalePoly_uniqueQuarticPoly, unique_functional_separation,
+    radial_at_minimizingRadius hσ ha] at hn
+  linarith
+
+/-- The selected cubic gives a strict SOS gap for every positive parameter. -/
+theorem unique_quantitative_sos_strict {σ a b γ : ℝ} (hσ : 0 < σ) (ha : 0 < a)
+    (hb : 0 < b) (hsos : IsSOS (uniqueQuarticPoly σ a b - MvPolynomial.C γ)) :
+    γ < minimumValue σ a b := by
+  have h := unique_quantitative_sos_gap hσ ha hsos
+  have hr := minimizingRadius_pos hσ ha hb
+  have hd := uniqueSeparation_pos
+  have hp : 0 < b * uniqueSeparation * minimizingRadius σ a b ^ 3 := by positivity
+  linarith
+
+/-- The selected quartic's exact minimum shift is not an ordinary polynomial SOS. -/
+theorem unique_minimum_shift_not_sos {σ a b : ℝ} (hσ : 0 < σ) (ha : 0 < a) (hb : 0 < b) :
+    ¬ IsSOS (uniqueQuarticPoly σ a b - MvPolynomial.C (minimumValue σ a b)) := by
+  intro h
+  exact (lt_irrefl _) (unique_quantitative_sos_strict hσ ha hb h)
+
+/-- A common ordinary - polynomial functional certifies both exact cubic values,
+all truncated sphere relations, and positivity on every quadratic square. -/
+theorem unique_sphere_moment_gap : ∃ L : Poly →ₗ[ℝ] ℝ,
+    L 1 = 1 ∧ L qPoly = 1 ∧ L (qPoly ^ 2) = 1 ∧
+    (∀ h : Poly, h.totalDegree ≤ 2 → 0 ≤ L (h ^ 2)) ∧
+    (∀ h : Poly, h.totalDegree ≤ 2 → L ((qPoly - 1) * h) = 0) ∧
+    L cubicPoly = 500753357629 / 500000000000 ∧
+    L (X 0) = 423308963 / 1000000000 ∧
+    L uniqueCubicPoly = 143132860603 / 143000000000 :=
+  ⟨sphereFunctional, moment_one, moment_q, moment_q_sq, moment_square_nonneg,
+    moment_sphere_localizer, moment_cubic, moment_first_coordinate, moment_unique_cubic_exact⟩
+
+end PersistentSOS
diff --git a/LeanPool/projects/persistent-sos.yaml b/LeanPool/projects/persistent-sos.yaml
new file mode 100644
index 0000000000..b6ab1084bb
--- /dev/null
+++ b/LeanPool/projects/persistent-sos.yaml
@@ -0,0 +1,54 @@
+slug: persistent-sos
+title: Persistent failure of quartic sum-of-squares exactness
+summary: Constructs explicit rational cubics in fourteen real variables whose
+  Euclidean quartic regularizations have a strict ordinary sum-of-squares gap
+  for every positive regularization, quadratic, and cubic parameter. A companion
+  construction has a unique global minimizer and a positive-definite Hessian
+  there. Exact moment certificates and a general SOS degree bridge certify the
+  gap for arbitrary finite sums of squares of real polynomials.
+branch: polynomial optimization and real algebraic geometry
+entry_module: LeanPool.PersistentSOS
+authors:
+- JD Jones
+source:
+  title: Persistent SOS failure with an explicit unique global minimizer
+  authors:
+  - JD Jones
+  url: https://github.com/JD-Jones-ASES/persistent-sos
+  github_repo: JD-Jones-ASES/persistent-sos
+  commit: d432ff9a67594cc0fa7a7af1913320b46d2a86db
+license: MIT
+status: verified
+provenance: AI
+main_declarations:
+- PersistentSOS.persistent_failure
+- PersistentSOS.unique_persistent_failure
+main_results:
+- declaration: PersistentSOS.persistent_failure
+  informal: For every positive sigma, a, and b, the explicit fourteen-variable
+    quartic sigma/4 times the Euclidean norm to the fourth power minus
+    a/2 times the squared norm minus b times the displayed cubic has the stated
+    attained global minimum, and subtracting that minimum is not an ordinary
+    finite sum of squares of real polynomials.
+- declaration: PersistentSOS.unique_persistent_failure
+  informal: For all three positive parameters, the companion quartic has exactly
+    one global minimizer, its actual polynomial Hessian is positive definite
+    there, and its shift by the attained minimum is not an ordinary sum of squares.
+- declaration: PersistentSOS.quantitative_sos_gap
+  informal: For positive sigma and a and any real b, every ordinary
+    sum-of-squares lower bound is at most the stated minimum-value expression
+    minus b times 753357629/500000000000 times the cube of the stated radius.
+    When b is positive, that expression is the attained global minimum.
+- declaration: PersistentSOS.sphere_moment_gap
+  informal: An explicit linear functional on real polynomials has normalized
+    radial moments, is nonnegative on all quadratic squares, annihilates the
+    quadratic sphere localizers, and evaluates the cubic to
+    500753357629/500000000000, strictly above its sphere maximum of one.
+tags:
+- sum-of-squares
+- polynomial-optimization
+- exact-certificates
+msc:
+- 90C22
+- 90C26
+- 14P10