D5 in every fixed dimension: lift the pin, collar, intermediate and global window bounds to d >= 2

.github/workflows/d1-cde-fulldepth-review.yml

@@ -0,0 +1,59 @@
+name: D1-C/D/E full-depth nonauthor review checks
+
+'on':
+  pull_request:
+    paths:
+      - 'reviews/d1_cde_full_depth_claude_20260929/**'
+      - '.github/workflows/d1-cde-fulldepth-review.yml'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  exact-and-probe:
+    runs-on: ubuntu-latest
+    timeout-minutes: 10
+    steps:
+      - uses: actions/checkout@11d5960a326750d5838078e36cf38b85af677262
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@a26af69be951a213d495a4c3e4e4022e16d87065
+        with:
+          python-version: '3.11.16'
+      - name: Verify sources, replay both modes, reject mutants
+        env:
+          PYTHONDONTWRITEBYTECODE: '1'
+        run: |
+          set -euo pipefail
+          python -B -S - <<'PY'
+          import hashlib, json, pathlib, subprocess, sys
+          root = pathlib.Path('reviews/d1_cde_full_depth_claude_20260929').resolve()
+          manifest = json.loads((root / 'SOURCE_FILES.json').read_text())['files']
+          present = sorted(p.name for p in root.iterdir())
+          expected_names = sorted([e['path'] for e in manifest] + ['SOURCE_FILES.json'])
+          if present != expected_names:
+              raise ValueError('packet tree differs from manifest: ' + repr(present))
+          for entry in manifest:
+              path = root / entry['path']
+              if pathlib.PurePosixPath(entry['path']).name != entry['path'] or path.is_symlink():
+                  raise ValueError('flat regular source required: ' + entry['path'])
+              data = path.read_bytes()
+              if len(data) != entry['bytes'] or hashlib.sha256(data).hexdigest() != entry['sha256']:
+                  raise ValueError('source identity mismatch: ' + entry['path'])
+          script = str(root / 'cde_review_check.py')
+          expected = (root / 'RESULTS.json').read_bytes()
+          mutants = ['M1', 'M2', 'M3']
+          for flags in (['-B', '-S'], ['-B', '-O', '-S']):
+              out = subprocess.run([sys.executable, *flags, script],
+                                   check=True, capture_output=True, timeout=300).stdout
+              if out != expected:
+                  raise RuntimeError('output differs from RESULTS.json under ' + ' '.join(flags))
+              for m in mutants:
+                  rc = subprocess.run([sys.executable, *flags, script, '--mutant', m],
+                                      capture_output=True, timeout=300).returncode
+                  if rc != 1:
+                      raise RuntimeError('mutant ' + m + ' not rejected')
+          print(json.dumps({'scientific_effect': 'NONE', 'mathematical_acceptance': False}))
+          PY
+          git diff --exit-code

.github/workflows/d5-dimension-lift.yml

@@ -0,0 +1,61 @@
+name: D5 dimension-lift checks
+
+'on':
+  pull_request:
+    paths:
+      - 'frontiers/d5_dimension_lift_20260929/**'
+      - '.github/workflows/d5-dimension-lift.yml'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  exact-and-probe:
+    runs-on: ubuntu-latest
+    timeout-minutes: 15
+    steps:
+      - uses: actions/checkout@11d5960a326750d5838078e36cf38b85af677262
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@a26af69be951a213d495a4c3e4e4022e16d87065
+        with:
+          python-version: '3.11.16'
+      - name: Verify sources, replay both modes, reject mutants
+        env:
+          PYTHONDONTWRITEBYTECODE: '1'
+        run: |
+          set -euo pipefail
+          python -B -S - <<'PY'
+          import hashlib, json, pathlib, subprocess, sys
+          root = pathlib.Path('frontiers/d5_dimension_lift_20260929').resolve()
+          manifest = json.loads((root / 'SOURCE_FILES.json').read_text())['files']
+          present = sorted(p.name for p in root.iterdir())
+          expected_names = sorted([e['path'] for e in manifest] + ['SOURCE_FILES.json'])
+          if present != expected_names:
+              raise ValueError('packet tree differs from manifest: ' + repr(present))
+          for entry in manifest:
+              path = root / entry['path']
+              if pathlib.PurePosixPath(entry['path']).name != entry['path'] or path.is_symlink():
+                  raise ValueError('flat regular source required: ' + entry['path'])
+              data = path.read_bytes()
+              if len(data) != entry['bytes'] or hashlib.sha256(data).hexdigest() != entry['sha256']:
+                  raise ValueError('source identity mismatch: ' + entry['path'])
+          script = str(root / 'lift_exact_check.py')
+          expected = (root / 'RESULTS.json').read_bytes()
+          mutants = ['drop-frobenius-order', 'drop-s0-block', 'drop-a4-column', 'degree-four',
+                     'row-operation-third', 'euler-coefficient', 'adjugate-sign', 'one-soft-direction',
+                     'flat-shell', 'weight-one-less-power']
+          for flags in (['-B', '-S'], ['-B', '-O', '-S']):
+              out = subprocess.run([sys.executable, *flags, script],
+                                   check=True, capture_output=True, timeout=600).stdout
+              if out != expected:
+                  raise RuntimeError('output differs from RESULTS.json under ' + ' '.join(flags))
+              for m in mutants:
+                  rc = subprocess.run([sys.executable, *flags, script, '--mutant', m],
+                                      capture_output=True, timeout=600).returncode
+                  if rc != 1:
+                      raise RuntimeError('mutant ' + m + ' not rejected')
+          print(json.dumps({'scientific_effect': 'NONE', 'mathematical_acceptance': False}))
+          PY
+          git diff --exit-code

frontiers/d5_dimension_lift_20260929/CONTINUUM_CROSSWALK.md

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+# Continuum crosswalk: every held step, its planar line, and its `d`-dimensional replacement
+
+Review aid for the `d >= 3` continuum read of CL-D5-DIMENSION-LIFT-20260929-v1. Scientific effect NONE; this file
+asserts no verdict. It lists, for each continuum step that the xAI Slice A and Slice B records hold (Math-#141
+comments 5894274124 and 5894406926), the exact planar line it lifts, the place in `PROOF.md` where the
+`d`-dimensional argument is written, and the only things that change. Planar line numbers refer to the byte-pinned
+sources of `SOURCE_MAP.json`: [PP] blob `d8acf0bc`, [CP] blob `b5647907`, [IW] blob `f53a527c`.
+
+Verdict columns record what is already on file; they are not claims. "xAI planar" refers to the planar (P2)
+continuum record 5894512272 (Grok: (P10), (P11), (P12), (P18), region II ACCEPT for the planar source, no `d > 2`
+transfer) and to #111; "xAI lift" refers to Slice A/B on this packet. Identities and rank claims accepted by Slice A/B
+are listed only where a continuum step depends on them. "OpenAI A+B" refers to the OpenAI nonauthor review 5357858391
+(bound to `c709854`): ACCEPT of every pending row of tables A and B at fixed `d`, fixed torus, compact marks and small
+`r`, subject to the accepted algebraic lemmas, hence Theorems P_d and C_d analytically discharged at that source;
+source-exposed (the reviewer authored the planar [PP]/[CP] inputs), with the xAI planar record as the independent base.
+"OpenAI C" refers to the follow-up OpenAI nonauthor review 5357882570 (same binding `c709854`): ACCEPT of every pending
+row of table C and of the analytic G_d composition at that source, same scope; with it the crosswalk A+B+C is complete.
+Its one wording clarification (the §6.5 "axis bound" is the axis-safe endpoint-short-column/Hadamard bound valid
+throughout the small strip) is written into `PROOF.md` §6.4–§6.5.
+
+## A. Pin ball, Theorem P_d (§4), planar source [PP]
+
+| Step | [PP] line | `PROOF.md` | What changes in `d` dimensions | Verdicts on file |
+|---|---|---|---|---|
+| (P4) axial Hermite expansion of `g'(rp)` | 115 | §4.2, first bullet | Nothing: `g(x) = f(x, 0)` is scalar in every `d`. | planar ACCEPT (#111 (P4)) |
+| (P7) remainders `ε_1`, `ε_2` | 143 | §4.2, (4.1') with the four-bullet derivation | Vector-valued: `h = grad_y f(·, 0) ∈ R^m` handled componentwise; transverse Taylor remainders `R_3`, `R_2` written with `|y|^3`, `|y|^2`; same powers, constants carry `sqrt(m)` and tensor norms. | lift: derived in this packet (answers the Slice A flag) |
+| (P8) error ratios `‖R‖_{L^s} ≤ C_s r` | 162 | §4.2 last paragraph, §4.3 remark after (4.3) | Nothing: the six ratios use only `Δ ≥ |q|`, `Δ ≥ r|p|`. | planar ACCEPT (continuum record n2) |
+| (P9) frame floor `det ≥ 9/131072` | 187 | (4.4), block-Schur | `det(BB^T) ≥ (9/64)^{d-1}/2048` via Lemma D3; equals the planar constant at `d = 2`. | lift ACCEPT (Slice A identity) |
+| (P10) Schur/compactness floor `c_0 I ≤ Σ ≤ C_0 I` | 193 | (4.5) and the sentence before it | `J` has `2 + 2m + m(m+1)` entries (orders 4, 3, 2, 3), none in `E_0`; positivity by distinct one-site monomials ([LP] §2); compactness over `O(d) × {|p| ≤ 1/4} × S^{d-1}`; `λ_min(BB^T) ≥ det(BB^T)/λ_max^{d-1}` from (4.4); the centered `L^2` triangle inequality with (P8) is unchanged. | xAI planar ACCEPT (P10); lift ACCEPT (OpenAI A+B, item 1) |
+| (P11) density `≤ C r^{-3} Δ^{-2} e^{-cχ^2}` | 210 | (4.6) | Jacobian `r^{d+1} Δ^d` in place of `r^3 Δ^2` (the map `grad f ↦ Y` is `diag(r^2Δ, rΔ I_m)`); the mean `dvec` is axial and unchanged; `|dvec + z|^2 ≥ |dvec|^2/2 - |z|^2` in `R^d`. | xAI planar ACCEPT (P11); lift ACCEPT (OpenAI A+B, item 2) |
+| (P12) conditional moment `E[K^6 | grad f(X) = 0] ≤ C(1 + χ^6)` | 217 | (4.7) | Same regression on `Y`; stated for every `n` (used at `n = 3d`); cross-covariances through order three bounded by Cauchy–Schwarz and (4.5). | xAI planar ACCEPT (P12); lift ACCEPT (OpenAI A+B, item 2) |
+| (P13)–(P14) normalizer `Z_r ≥ c_Z r^2` | 241, 249 | §4.5 | Replaced by [LP] (5.5), which holds in every fixed `d` (accepted as A1–A4 in the D1 reconciliation, Math-#106). | consumed at its accepted row |
+| (P15)–(P16) angle-sensitive product | 261, 289 | (4.8) | Lemma D1 replaces the `2 × 2` two-column bound at each Hessian; new factor `K^{3(d-2)}`; segment identity (P15) is one-dimensional. | lift ACCEPT (Slice A, Lemma D1) |
+| (P17) angle-free product | 308 | (4.9) | Lemma D2 (Hadamard) in place of the planar two-column bound. | lift ACCEPT (Slice A, Lemma D2 is Hadamard) |
+| (P18) weighted Kac–Rice at the zero level | 323 | §4.7, (4.10) | Field `grad f : X → R^d`, parameter and value dimensions agree; same mark `W_r 1{H_X ∈ O_j}`; same framework citation. | xAI planar ACCEPT (P18); lift ACCEPT (OpenAI A+B, item 3) |
+| (P19) region I | 341 | (4.11) | `|q|^2 Δ^{-d} ≤ |q|^{2-d}` supplies the weight `ω_d`; `χ^2 ∈ [t^2/2, t^2]` unchanged; `n = 3d` in (4.7). | lift ACCEPT (OpenAI A+B, item 4; ledger identity Slice A) |
+| (P20) region II | 361 | (4.12) | Pointwise `r^{-2-4d}` and absorption `2n ≥ 5 + 3d` in place of the planar sixth term; axis included; no division by `q`. | xAI planar ACCEPT (region II); lift ACCEPT (OpenAI A+B, item 4) |
+| Integration and Lemma D5 | 367 | §4.8 "Integration", Lemma D5 | Weight `ω_d` integrable: radial exponent `(2-d) + (m-1) = 0`; nested ball `O(r^5)`. | lift ACCEPT (Slice A, weight only) |
+| §10.1 reflection to `S` | 377–386 | §4.9 | Any orthogonal transverse map; `b̃ = b - kr^3`, `k̃ = -k`; the original `Z_r` retained. | lift ACCEPT (OpenAI A+B, item 5) |
+
+## B. Collar, Theorem C_d (§5), planar source [CP]
+
+| Step | [CP] line | `PROOF.md` | What changes in `d` dimensions | Verdicts on file |
+|---|---|---|---|---|
+| §3 degree-five interpolation, three sites | 61–85 | §5.1 | Explicit families `h_i, d_i, e_{i,j}` in `d` variables; generic projection direction. | lift ACCEPT (Slice B, rank) |
+| (C4)–(C6) coarse floor `Cov(V_r) ≥ c r^{10} I` | 95, 109, 116 | (5.1) | `3(d+1)` observations; `dim P_5 = C(d+5, 5)`; same `r^5` floor versus `r^6` remainder; principal submatrix and Schur complement unchanged. | lift ACCEPT (OpenAI A+B, item 6) |
+| (C7) midpoint expansion `G_1, G_2` | 133 | (5.2) with the sentence after it, and §6.3 (6.2)–(6.3) at `s = r`, `ε = 1` | Vector form: `u v·T_3`, `v^T C_3 v`, `S_0 v`; derived from the vector-valued endpoint identities (6.2), written componentwise in §6.3. | lift: derived in this packet |
+| (C8)–(C10) drift, variance, Mahalanobis | 138, 142, 148 | §5.3 | First physical coordinate only; `(C10)` is Cauchy–Schwarz in the covariance inner product in any dimension. | lift ACCEPT (OpenAI A+B, item 7) |
+| (C11)–(C13) near-axis strip | 157, 161, 167 | §5.4 | Prefactor `r^{-5d}` (from `det Σ_X ≥ c r^{10d}`), moment `r^{-30d}` (for `K^{3d}`), pointwise `r^{-2-35d}`, absorption `2n/3 ≥ 5 + 34d`. | lift ACCEPT (OpenAI A+B, item 7) |
+| (C14)–(C15) frame `B` and `c v^4 ≤ Cov(G) ≤ C v^2` | 180, 193 | §5.5, (5.3) | `BB^T ≥ diag(|v|^4/4, (|v|^2/2) I_m)` by Lemma D3 in place of the explicit `2 × 3` rows; the same `r/|v|^2 ≤ r^{1/3}` perturbation. | Lemma D3 ACCEPT (Slice A); floor use ACCEPT (OpenAI A+B, item 8) |
+| (C16)–(C17) density and moment | 198, 202 | (5.4), (5.5) | Jacobian `r^{d+1}`; prefactor `|v|^{-2d}`; moment `|v|^{-12d}`. | lift ACCEPT (OpenAI A+B, item 8) |
+| (C18) three soft Hessians | 208 | (5.6) | Lemma D1 with `σ = 1` on the orthonormal pair `(e_x, v̂)`; factor `K^{3(d-2)}`. | lift ACCEPT (Slice B, D1 use) |
+| (C19) ledger | 214 | (5.7) | `r^{3-d}` per unit scaled volume; `|v|^{-(14d+6)}` absorbed by `e^{-c/|v|^2}`. | ledger identity accepted; count ACCEPT (OpenAI A+B, items 8–9) |
+| §8 compact remainder | 218–223 | §5.6 | Fixed singular-value floor of `B` for `|v| ≥ v_0`; unchanged. | lift ACCEPT (OpenAI A+B, item 8) |
+| (C20) Kac–Rice and gluing | 231, 235–242 | §5.7 | `dX = r^d du dv`; the two punctured balls and the collar with `η = 1/4`. | lift ACCEPT (Slice B, tiling bookkeeping) |
+
+## C. Shells, Theorem I_d (§6), planar source [IW]
+
+| Step | [IW] line | `PROOF.md` | What changes in `d` dimensions | Verdicts on file |
+|---|---|---|---|---|
+| (I6)–(I8) endpoint inputs and shell | 73, 88, 94 | §6 preamble | [LP] (4.1), (5.5) in every `d`; `U_r` extended by the `2m` transverse rows. | consumed at accepted rows |
+| §3.1 rank through confluence | 96–147 | §6.1 | Explicit confluent families with determinants `-|v|^{2d+2}` and `u^{2d+6}`; degree-four negative control. | lift ACCEPT (Slice B, rank) |
+| (I9)–(I11) remainder and floors `c s^{10}` | 124, 149, 153 | (6.1) | `(d+1)`-dimensional `Σ_X`; the divided-difference argument is one-dimensional along the axis and is applied to each transverse component. | lift ACCEPT (OpenAI C, item 1) |
+| (I12) endpoint identities at the midpoint | 167 | (6.2), now with the componentwise derivation in §6.3 | Vector-valued: `grad_y f(0) = -r^2 T_3/8 + O(r^4 K)` and `grad_y f_x(0) = O(r^2 K)` componentwise from the symmetric Taylor formulas; axial identities unchanged. | lift: derived in this packet |
+| (I13)–(I16) expansions, row operation, target | 179, 185, 192, 197 | (6.3), (6.4), the Jacobian `s^{d+4}` | Vector form; the row operation subtracts `(s/2) v·grad_y f`; target `τ_{d+1}` bounded through `ε → 0`; exact finite control `RO` in `d = 3`. | lift: derived; `RO` exact |
+| (I17)–(I18) Euler identity and `|S_0|` | 208, 212 | (6.5), (6.6) | Euler degree three in every `d`; controls the quadratic form `v̂^T S_0 v̂` only (one entry, not the matrix). | lift ACCEPT (OpenAI C, item 2; finite control `EU` in `d = 3`) |
+| (I19) endpoint determinants | 218 | (6.7), (6.8) | Lemma D4 with the gradient equation `|S_0 v̂| ≤ C s K/|v|` supplying the transverse column; same shape `(r + s^2)/|v|^2`. | Lemma D4 and the shape ACCEPT (Slice B); constants ACCEPT (OpenAI C, item 3) |
+| (I20) witness determinant | 223 | (6.9) | Lemma D1 on `(e_x, v̂)`. | lift ACCEPT (OpenAI C, item 3) |
+| (I21)–(I22) combined product, axis bound | 230, 236 | (6.10) and the sentence after it | `K^{3d}`; on the axis Lemma D2 with `e_x`. | lift ACCEPT (OpenAI C, item 3; axis-safe reading written into §6.4) |
+| (I23)–(I26) small axial strip | 245, 258, 264, 270 | §6.5 | Prefactor `s^{-5(d+1)}`, moment `s^{-30d}`, strip volume `O(s^d) ≤ O(s^2)`. | lift ACCEPT (OpenAI C, item 4) |
+| (I27)–(I30) transverse floor, density, moment | 279, 290, 297, 301 | (6.11), (6.12), (6.13) | `BB^T ≥ diag(|v|^4/4, (|v|^2/2) I_m, |v|^6/144)` by Lemma D3; `det ≥ c|v|^{2d+8}`; `σ_min(B) ≥ c|v|^3`; prefactor `|v|^{-(d+4)}`; moment `|v|^{-18d}`. | Lemma D3 ACCEPT; floor use ACCEPT (OpenAI C, item 5) |
+| (I31)–(I32) shell ledger | 311, 319 | (6.14), (6.15) | `s^{-(d+2)}` in place of `s^{-4}`; `r` powers `-2 + 2 + 3 = 3`, `s` powers `-(d+4) + 2 + d = -2`. | ledger arithmetic ACCEPT (Slice B); count ACCEPT (OpenAI C, item 6) |
+| (I33) marked Kac–Rice with height disintegration | 334 | §6.8 | Same framework; `(grad f(X), f(X))` nondegenerate on the closed shell by (6.1). | lift ACCEPT (OpenAI C, item 7) |
+| (I34) dyadic sum | 347 | §6.8 | Unchanged. | lift ACCEPT (Slice B) |
+
+## D. What "pending" means here
+
+After OpenAI reviews 5357858391 (tables A, B) and 5357882570 (table C) no row of this crosswalk is pending; the
+verdict columns record the item of the review that covers each row. Before those reviews, every pending row is a `d`-dimensional instance of a planar step whose planar version now carries a nonauthor
+ACCEPT (xAI 5894512272 for the pin ball; `reviews/d5_collar_count_20260928/` for the collar; `reviews/d5_i5_planar_f_20260928/`
+for the shells), with the change listed in the fourth column. A reader can therefore check each row by (i) confirming
+the planar step at the cited line, (ii) confirming that the fourth column is the complete list of changes, and (iii)
+confirming the exponent arithmetic in `RESULTS.json` (groups `L`, `W`) where it applies.
+
+The three clarifications of reviews 5357858391 and 5357882570 are written into `PROOF.md`: the unscaling step of §5.2 is the
+congruence and the Schur variational identity, not an eigenvalue-monotonicity claim under entrywise scaling; and the
+collar constants depend on the fixed `d`, `R`, `eta` and the mark compacts (§5.7), with nothing uniform as `d` grows;
+and the axis bound of §6.4 is stated as the axis-safe endpoint-short-column/Hadamard bound `W_r |det H_X| / Z_r <= C K^(3d)`
+valid throughout `|v| <= s^(1/8)`, which is what §6.5 uses.