d6g8k5htny-coder · Oct 3, 2026 · Oct 3, 2026 · Oct 3, 2026 · Oct 3, 2026
@@ -0,0 +1,32 @@
+name: Planar soft-layer chain C91-C98 replay
+
+'on':
+  pull_request:
+    paths:
+      - 'frontiers/planar_soft_layer_chain_20261003/**'
+      - '.github/workflows/planar-soft-layer-chain.yml'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  chain-replay:
+    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 stored identities and replay every published checker, both modes
+        env:
+          PYTHONDONTWRITEBYTECODE: '1'
+        run: |
+          set -euo pipefail
+          python -B -S frontiers/planar_soft_layer_chain_20261003/replay.py
+          python -B -O -S frontiers/planar_soft_layer_chain_20261003/replay.py
+          git diff --exit-code
+          test -z "$(git status --porcelain)"
@@ -0,0 +1,312 @@
+# C101 independent reviewer checker and original stdout
+
+Dylan Roy — delegated AI reproducibility record. Actual performer: OpenAI/Codex agent `/root/c100_nonauthor_review`; exact runtime model variant/build UNKNOWN. This publishes the independently written finite controls supporting the [full frozen nonauthor review](https://github.com/d6g8k5htny-coder/main/issues/229#issuecomment-5967219096) of [C101 proof5967063473](https://github.com/d6g8k5htny-coder/main/issues/229#issuecomment-5967063473). It adds no new mathematical review vote, source acceptance, human review or organizational-independence credit. Same-provider independence credit: **0**.
+
+The bound proof is the entire native UTF-8 body, **36333 bytes**, SHA-256 `300d0d18abb74332e593e389485c817a3c0ea7c31345194e3cfdd4039ac3b5c4`. The full native review body is **29516 bytes**, SHA-256 `23a5b82cc4be6cbd9febd3eb5dd237fe0882ed59fef48d728a5687cd22208792`.
+
+## Exact extraction and execution
+
+There are exactly two payload blocks below. For each, start after the opening fence line immediately following its BEGIN marker, and stop immediately before the closing fence line immediately preceding its END marker. The payload includes its original final LF and excludes the fences and markers. Do not trim whitespace, normalize newlines, prepend a newline or append a second newline. Encode as UTF-8.
+
+- `reviewer_controls.py`: **10231 bytes**, SHA-256 `d358da75bf73442e9e97647657f9654ed13d2956d3d8aa7b7611420424d3a33b`.
+- `reviewer_controls.normal.txt`: **2304 bytes**, SHA-256 `51802ef2dd7f30466c2f110934d9a15ed412714026a7406fc28924db63e683e9`.
+
+The original reviewer executions used **Python 3.9.6**:
+
+```text
+python3 -B reviewer_controls.py
+python3 -B -O reviewer_controls.py
+python3 -B -S reviewer_controls.py
+```
+
+All three exited 0. Their stdout files were byte-identical, reporting **235 positive exact controls** and **17 rejected false shortcuts**. The stdout payload below is the exact original normal-run output; the optimized and no-site outputs have that same identity. A subsequent run with another Python version changes the runtime line and therefore the stdout digest. This record does not relabel such a replay as the original output.
+
+The checker was written after substantive proof reading without inspecting or running the author's checker or arithmetic outputs. It imports only Python standard-library modules and reads no source files, author modules, network resources or random samples. Its exact finite controls support transcription and falsification. Gaussian uniformity, continuum estimates, global topology, event identification and variation convergence require the written analytic review and its retained premises.
+
+## Independent checker payload
+
+<!-- C101_REVIEWER_CHECKER_BEGIN -->
+```python
+"""Independent exact controls for C101; no source, author code or network reads.
+
+These controls falsify algebraic shortcuts. They do not prove the Gaussian,
+topological, measurability or uniform-constant statements in the written review.
+All checks remain active under Python -O. Stdout is deterministic per runtime.
+"""
+from fractions import Fraction as F
+from collections import Counter
+import sys
+
+counts = Counter()
+rejected = []
+
+
+def check(ok, group):
+    if not ok:
+        raise ValueError(group)
+    counts[group] += 1
+
+
+def reject(false_claim, label):
+    if false_claim:
+        raise ValueError("False shortcut survived: " + label)
+    rejected.append(label)
+
+
+def rank(rows):
+    a = [[F(x) for x in row] for row in rows]
+    pivot = 0
+    for col in range(len(a[0])):
+        found = next((i for i in range(pivot, len(a)) if a[i][col]), None)
+        if found is None:
+            continue
+        a[pivot], a[found] = a[found], a[pivot]
+        scale = a[pivot][col]
+        a[pivot] = [x / scale for x in a[pivot]]
+        for i in range(len(a)):
+            if i != pivot:
+                scale = a[i][col]
+                a[i] = [x - scale * y for x, y in zip(a[i], a[pivot])]
+        pivot += 1
+    return pivot
+
+
+monomials = [(i, degree - i) for degree in range(4) for i in range(degree + 1)]
+for cosine, sine, reflection in [(F(1), F(0), 1), (F(3, 5), F(4, 5), 1),
+                                  (F(5, 13), F(12, 13), -1)]:
+    rows = []
+    for x in range(-3, 4):
+        for y in range(-3, 4):
+            u = cosine * x + sine * y
+            z = reflection * (-sine * x + cosine * y)
+            rows.append([u**i * z**j for i, j in monomials])
+    check(rank(rows) == 10, "exact finite jet evaluation rank")
+reject(rank([[F(x)**i * F(0)**j for i, j in monomials]
+             for x in range(-3, 4)]) == 10, "line samples certify all planar jets")
+duplicate = [row[:-1] + [row[0]] for row in rows]
+reject(rank(duplicate) == 10, "duplicated observation preserves full jet rank")
+
+
+def positive(x):
+    return max(F(0), x)
+
+
+for lam in map(F, [-2, -1, 0, 1, 3]):
+    for gamma in map(F, [-2, 0, 1, 3]):
+        for b1 in map(F, [-2, 0, 2]):
+            dm = 6 * lam + 3 * b1 - gamma**2 / 4
+            ds = -6 * lam + 3 * b1 - gamma**2 / 4
+            actual_typed_model = (dm if dm > 0 else 0) * (-ds if ds < 0 else 0)
+            am, ass = 24 * lam - gamma**2 + 12 * b1, 24 * lam + gamma**2 - 12 * b1
+            weight = positive(am) * positive(ass) / 16
+            check(actual_typed_model == weight, "typed determinant including boundaries")
+            check(weight <= 36 * positive(lam)**2, "typed weight quadratic envelope")
+reject(abs(F(-6) * F(6)) == 0, "absolute determinants replace endpoint typing")
+
+
+for lam, gamma, b1, c3 in [(F(2), F(1), F(1, 3), F(-2)),
+                          (F(3), F(-2), F(-1, 2), F(7, 3)),
+                          (F(1, 3), F(3, 2), F(5, 7), F(-1, 5))]:
+    d = gamma**2 - 12 * b1
+    j = 8 * gamma**3 - 144 * b1 * gamma + 576 * c3
+    bsh = b1 - gamma**2 / 12
+    dsh = (c3 - gamma * b1 / 4 + gamma**3 / 72) / 2
+    check(bsh == -d / 12 and dsh == j / 1152, "raw to CUB parameter map")
+    check(9 * (4 * lam**2 - bsh**2) ==
+          (24 * lam - d) * (24 * lam + d) / 16, "model weight identity")
+    psi, c, rr = 24 * lam / gamma**2, d / gamma**2, j / gamma**3
+    for x, zeta in [(F(0), F(1)), (F(-1, 2), F(2, 3)),
+                    (F(3, 2), F(-4, 5)), (F(2, 7), F(5, 3))]:
+        u, z = x + gamma * zeta / 12, gamma * zeta
+        raw = 2*x**3-3*x/2-F(1, 2)+(gamma/2)*(x*x-F(1, 4))*zeta-lam*zeta*zeta/2+b1*x*zeta*zeta/2+c3*zeta**3/6
+        qs = 2*u**3-3*u/2-F(1, 2)-(psi+2*c*u)*z*z/48+rr*z**3/3456
+        check(raw == qs, "raw cubic shear including negative gamma")
+    check(gamma**6 * abs(c)**3 == abs(d)**3 and gamma**6 * rr**2 == j**2,
+          "decision band chart pole cancellation")
+reject(F(1, 16) * F(1, 24) == F(1, 384) / 12,
+       "decision band Jacobian acquires extra factor twelve")
+
+
+for upper in [F(1, 3), F(2), F(7, 2)]:
+    # Integrate s(48 lambda-s)/16 first in s, then in lambda.
+    weight_integral = (48**3 * (F(1, 2)-F(1, 3)) / 16) * upper**4 / 4
+    error_integral = 48 * upper**2 / 2
+    check(weight_integral == 288 * upper**4 and error_integral == 24 * upper**2,
+          "radius integral and finite radius correction")
+    check(weight_integral/12 == 24*upper**4 and error_integral/12 == 2*upper**2,
+          "radius B1 Jacobian")
+reject(-2 * 4 == -6, "actual radius leading term has rho minus six power")
+
+
+h, r, delta, upper = F(3), F(1, 16), F(1, 1024), F(96)
+strip = h*h*delta*delta/2+r*h**4*delta
+check(strip > h*h*delta*delta/2, "actual strip retains finite radius mass")
+reject(strip == h*h*delta*delta/2, "model strip substitutes for actual strip")
+for v in [3, 4, 6]:
+    exact = h*h*(delta**(2-v)-upper**(2-v))/(v-2) + r*h**4*(delta**(1-v)-upper**(1-v))/(v-1)
+    bound = h*h*delta**(2-v)/(v-2)+r*h**4*delta**(1-v)/(v-1)
+    check(0 < exact < bound, "truncated actual inverse powers")
+    reject(exact <= h*h*delta**(2-v)/(v-2), "omit actual inverse correction v="+str(v))
+check(F(1, 2)*(1*1+3*3) != (F(1, 2)*(1+3))**2,
+      "correlated weight and norm are not independent")
+reject(F(1, 2)*(1*1+3*3) == (F(1, 2)*(1+3))**2,
+       "factor a correlated weighted moment")
+
+
+d_cap, c_scalar, r_scalar, j_res = F(2, 3), F(5, 7), F(1, 4), F(3)
+limit = 4*d_cap*r_scalar*j_res*j_res
+scalar_integral = r_scalar**2*j_res**4*(limit**3/3+c_scalar*r_scalar*j_res**2*limit**2/2)
+coefficient = (4*d_cap)**3/3+c_scalar*(4*d_cap)**2/2
+check(scalar_integral == coefficient*r_scalar**5*j_res**10,
+      "actual near scalar numerator r5 J10")
+check(F(1)+4-2 == 3, "physical Jacobian soft determinant full normalizer")
+reject(F(1)+4-2-2 == 3, "divide by full normalizer twice")
+check(4-3 == 1, "scaled far and derivative exceptions")
+reject(4-3 > 1, "discard finite radius cap exceptions")
+for m in [1, 3, 7]:
+    for a, jvalue in [(F(1), F(2)), (F(3), F(5)), (F(3), F(2))]:
+        left = jvalue**10 if jvalue > a else 0
+        check(left <= a**(-2*m)*jvalue**(10+2*m), "fixed residual tail moment")
+
+
+for selected in [False, True]:
+    for model_selected in [False, True]:
+        model_rejected = not model_selected
+        check(((not selected) != model_rejected) == (selected != model_selected),
+              "Boolean complement agreement on typed partition")
+reject(((not False) != False) == (False != False),
+       "Boolean complements agree outside the typed partition")
+mu = F(15, 16)
+death_depth = 1-mu
+endpoint_error = F(-3, 8)
+check(abs(endpoint_error) < mu and 4*death_depth+endpoint_error < 0,
+      "saddle clearance alone loses older endpoint")
+reject(4*death_depth+endpoint_error > 0, "one margin certifies rejected chord")
+budget = min(mu, 4*death_depth)/2
+check(-death_depth-budget > -1 and 4*death_depth-budget > 0,
+      "two margins certify chord and older endpoint")
+
+
+# Affine expressions below represent a + b*beta, with alpha=(1-2 beta)/6.
+def add(*pairs):
+    return tuple(sum(p[i] for p in pairs) for i in [0, 1])
+
+
+def scale(pair, amount):
+    return tuple(x*amount for x in pair)
+
+
+one, beta = (F(1), F(0)), (F(0), F(1))
+alpha = (F(1, 6), F(-1, 3))
+e = add(one, scale(beta, F(-1, 2)))
+derived = [beta, add(one, scale(alpha,-3), scale(beta,F(1,2))),
+           add(scale(alpha,-4),e), add(one,scale(alpha,-5),scale(e,F(1,2))),
+           add(scale(alpha,-4),scale(e,F(2,3))), add(one,scale(alpha,-5),scale(e,F(1,3))),
+           beta, add(one,scale(alpha,-4)), add(scale(alpha,-3),scale(add(e,scale(beta,-1)),2)),
+           add(scale(one,2),scale(alpha,-5),scale(beta,F(-1,2))),
+           add(scale(one,2),scale(alpha,-7),scale(beta,F(-1,4))), beta, one]
+claimed = [(0,1),(F(1,2),F(3,2)),(F(1,3),F(5,6)),(F(2,3),F(17,12)),
+           (0,1),(F(1,2),F(3,2)),(0,1),(F(1,3),F(4,3)),(F(3,2),-2),
+           (F(7,6),F(7,6)),(F(5,6),F(25,12)),(0,1),(1,0)]
+for actual, expected in zip(derived, claimed):
+    check(actual == expected, "all thirteen cutoff exponents")
+    # Affine nonnegativity at both endpoints proves it throughout [0,1/2].
+    gap = add(actual,scale(beta,-1))
+    check(gap[0] >= 0 and gap[0]+gap[1]/2 >= 0,
+          "error exponents dominate target over entire beta interval")
+conditions = [add(one,scale(alpha,-1)),add(one,scale(beta,F(-1,8))),e,
+              add(e,scale(alpha,-2)),add(e,scale(alpha,-3)),
+              add(one,scale(beta,F(-1,4))),beta]
+for a,b in conditions:
+    check(a >= 0 and a+b/2 > 0, "all admissibility powers positive in open interval")
+for m in range(1, 21):
+    aa, bb = F(1,2*(m+3)), F(m,2*(m+3))
+    check(bb == m*aa and aa > 0 and 0 < bb < F(1,2), "fixed integer cutoff family")
+check(F(3,12) == F(1,4) and F(1,4)/8 == F(1,32) and 1-F(1,4)/2 == F(7,8),
+      "m3 displayed specialization")
+check(10+2*3 == 16 and 6+2*3 == 12, "m3 actual and model moment orders")
+for requested in [F(1,10),F(1,4),F(2,5),F(49,100)]:
+    needed = 6*requested/(1-2*requested)
+    m = max(1,(needed.numerator+needed.denominator-1)//needed.denominator)
+    check(F(m,2*(m+3)) >= requested, "requested beta finite moment selection")
+reject(F(1,6)-F(1,2)/3 > 0, "endpoint beta one half has an exhausting cutoff")
+reject(F(3,2)-2*F(51,100) >= F(51,100), "beta beyond half satisfies Taylor balance")
+reject(derived[4] == add(derived[4],scale(alpha,4)), "omit growing H4 endpoint loss")
+
+
+for left,right in [([F(1,3),F(2,3)],[F(1,2),F(1,2)]),
+                   ([F(1),F(2)],[F(2),F(4)]),
+                   ([F(1,8),F(3,8)],[F(1,3),F(1,3)])]:
+    a,b = sum(left),sum(right)
+    variation = sum(abs(x-y) for x,y in zip(left,right))
+    normalized = sum(abs(x/a-y/b) for x,y in zip(left,right))
+    check(abs(a-b) <= variation and normalized <= 2*variation/a,
+          "mass consumer and positive mass normalization")
+
+print("C101 independent reviewer exact controls")
+print("Runtime: Python " + sys.version.split()[0])
+for group,count in sorted(counts.items()):
+    print(str(count) + " PASS: " + group)
+print("Positive exact controls: " + str(sum(counts.values())))
+for label in rejected:
+    print("REJECTED: " + label)
+print("Rejected false shortcuts: " + str(len(rejected)))
+print("Analytic Gaussian, topology and continuum conclusions require the written review.")
+```
+<!-- C101_REVIEWER_CHECKER_END -->
+
+## Original Python 3.9.6 stdout payload
+
+<!-- C101_REVIEWER_STDOUT_BEGIN -->
+```text
+C101 independent reviewer exact controls
+Runtime: Python 3.9.6
+4 PASS: Boolean complement agreement on typed partition
+1 PASS: actual near scalar numerator r5 J10
+1 PASS: actual strip retains finite radius mass
+7 PASS: all admissibility powers positive in open interval
+13 PASS: all thirteen cutoff exponents
+1 PASS: correlated weight and norm are not independent
+3 PASS: decision band chart pole cancellation
+13 PASS: error exponents dominate target over entire beta interval
+3 PASS: exact finite jet evaluation rank
+20 PASS: fixed integer cutoff family
+9 PASS: fixed residual tail moment
+1 PASS: m3 actual and model moment orders
+1 PASS: m3 displayed specialization
+3 PASS: mass consumer and positive mass normalization
+3 PASS: model weight identity
+1 PASS: physical Jacobian soft determinant full normalizer
+3 PASS: radius B1 Jacobian
+3 PASS: radius integral and finite radius correction
+12 PASS: raw cubic shear including negative gamma
+3 PASS: raw to CUB parameter map
+4 PASS: requested beta finite moment selection
+1 PASS: saddle clearance alone loses older endpoint
+1 PASS: scaled far and derivative exceptions
+3 PASS: truncated actual inverse powers
+1 PASS: two margins certify chord and older endpoint
+60 PASS: typed determinant including boundaries
+60 PASS: typed weight quadratic envelope
+Positive exact controls: 235
+REJECTED: line samples certify all planar jets
+REJECTED: duplicated observation preserves full jet rank
+REJECTED: absolute determinants replace endpoint typing
+REJECTED: decision band Jacobian acquires extra factor twelve
+REJECTED: actual radius leading term has rho minus six power
+REJECTED: model strip substitutes for actual strip
+REJECTED: omit actual inverse correction v=3
+REJECTED: omit actual inverse correction v=4
+REJECTED: omit actual inverse correction v=6
+REJECTED: factor a correlated weighted moment
+REJECTED: divide by full normalizer twice
+REJECTED: discard finite radius cap exceptions
+REJECTED: Boolean complements agree outside the typed partition
+REJECTED: one margin certifies rejected chord
+REJECTED: endpoint beta one half has an exhausting cutoff
+REJECTED: beta beyond half satisfies Taylor balance
+REJECTED: omit growing H4 endpoint loss
+Rejected false shortcuts: 17
+Analytic Gaussian, topology and continuum conclusions require the written review.
+```
+<!-- C101_REVIEWER_STDOUT_END -->
@@ -0,0 +1,21 @@
+## C101 delivered: a quantitative rate for the actual pairing-failure law
+
+The [full proof](https://github.com/d6g8k5htny-coder/main/issues/229#issuecomment-5967063473) now has a [whole-proof nonauthor PASS at its stated conditional scope](https://github.com/d6g8k5htny-coder/main/issues/229#issuecomment-5967219096), with no required amendment.
+
+For the stated fixed planar Gaussian torus, compact birth heights, all frames and gap parameter (k=1), it gives
+
+```text
+1 - p_r = r^3 (alpha_1 + alpha_2) + O(r^(13/4)).
+```
+
+More generally, the remainder is (O_beta(r^{3+beta})) for each fixed (0<beta<1/2). The full raw-jet measure on actual pairing failure, divided by (r^3), converges in variation at rate (O_beta(r^beta)). The proof tracks growing cutoff constants and bounds the actual and model failure tails separately. Constants and the small-radius cutoff remain analytic/existential.
+
+This counts each designated candidate's failure once. It does not sum extra saddles, count replacement bars once, identify all small bars, or close regional shrinking-witness, small-gap/intermediate or Conjecture7 obligations. The original correlated weight, full normalizer and exact retained analytic/geometric interfaces remain required.
+
+**Verification and custody.** The [author controls](https://github.com/d6g8k5htny-coder/main/issues/229#issuecomment-5967085160) and [independent reviewer controls](https://github.com/d6g8k5htny-coder/main/issues/229#issuecomment-5967229472) replayed in the final Python3.11.16 normal/optimized no-site run: 6,859 author controls with23 rejected false inferences;235 reviewer controls with17 rejected shortcuts. Only the explicit runtime-version lines differ from the originally published stdout. These finite controls support the written review; they do not prove its analytic premises.
+
+One private immutable delivery,52 payloads and646482 bytes, was downloaded back and verified exactly: SHA256 `d6fceb739b5b1b29b08e1d685340fff1002d0f02ffd907b65c6ebd0b457a154d`. Registered once at Artifact Index897, Evidence Lineage619, Review Queue166 and Work Events652; claim `5c1dc0ee-7ca9-4a65-8016-d41b59d8f6b2` released at Work Events653 with exact full CellData readback. The frozen author header is preserved and its later review is a separate record.
+
+Next, [C102](https://github.com/d6g8k5htny-coder/main/issues/229#issuecomment-5967094705) is a separately claimed compact-positive-gap Gaussian estimate, now frozen for fresh review. It does not itself extend the actual pairing event, and it does not consume C101 as a premise.
+
+Dylan Roy — delegated AI work/review. Actual proof author OpenAI/Codex root01a0adb2, author-side contributor c93_edge_integral_audit; fresh full reviewer c100_nonauthor_review, with source exposure disclosed and no author-checker use; root01a0bbb5 custody/source-author, c99_custody_audit author-controls replay. Same-provider independence0, human review NONE, personal reading PENDING, scientific effect NONE. No repository commit, hosted CI, merge or site deployment is claimed. Existing integration owners and publication/metadata holds are unchanged.