d6g8k5htny-coder · Sep 30, 2026 · Sep 30, 2026 · Sep 30, 2026 · Sep 30, 2026 · Sep 30, 2026
@@ -0,0 +1,40 @@
+name: Cluster exponential weight controls
+'on':
+  pull_request:
+    paths:
+      - 'frontiers/cluster_exponential_weight_20260930/**'
+      - '.github/workflows/cluster-exponential-weight.yml'
+  push:
+    branches: [main]
+    paths:
+      - 'frontiers/cluster_exponential_weight_20260930/**'
+      - '.github/workflows/cluster-exponential-weight.yml'
+  workflow_dispatch:
+permissions:
+  contents: read
+jobs:
+  exact-exponential:
+    runs-on: ubuntu-latest
+    timeout-minutes: 15
+    steps:
+      - uses: actions/checkout@11d5960a326750d5838078e36cf38b85af677262
+        with:
+          fetch-depth: 0
+          persist-credentials: false
+      - uses: actions/setup-python@a26af69be951a213d495a4c3e4e4022e16d87065
+        with:
+          python-version: '3.11.16'
+      - name: Finite controls and immutable source custody (not proof acceptance)
+        run: |
+          set -euo pipefail
+          packet=frontiers/cluster_exponential_weight_20260930
+          python -B -S "$packet/verify_packet.py"
+          python -B -O -S "$packet/verify_packet.py"
+          python -B -S "$packet/finite_checks.py" > /tmp/exponential-normal.json
+          python -B -O -S "$packet/finite_checks.py" > /tmp/exponential-optimized.json
+          cmp /tmp/exponential-normal.json /tmp/exponential-optimized.json
+          python -B -S -m unittest discover -s "$packet" -p 'test_*.py' -v
+          python -B -O -S -m unittest discover -s "$packet" -p 'test_*.py' -v
+          git fetch --no-tags origin cbb2f978f9b3e8e2eaca94f3b359b18d7c144f1b 7a44130b41b827577424a73c4feac4cde20b5568
+          python -B -S "$packet/verify_sources.py" --repo-root "$GITHUB_WORKSPACE"
+          git diff --exit-code
@@ -0,0 +1,141 @@
+# Review chronology and current scoped disposition
+
+The original author-side snapshot below is preserved verbatim as published at
+commit `0e70540b70e5e3183df5ed1a6bd70a212b734c9c` on 30 September 2026 UTC.
+Its pending-review wording describes that original snapshot. The appended
+current disposition records later actual native reviews of the same proof.
+
+## Original author-side snapshot (historical)
+
+# Internal challenges, exposure and unresolved review
+
+Target in both mathematical slices: PROOF.md, 12576 bytes, Git blob
+`bf1268b9c18ec05561fd9b14c645ef0b8e530484`, SHA256
+`3f32fdd744350a15359451bbbee6c6bcc71af47e4f57f6110d7afb4978e941ee`.
+The target was not amended after either mathematical review.
+
+Root authored the proof. The two OpenAI agents below made no proof edits and
+were noncontributors to this implication; both had the root's draft and source
+copies as exposure. Same-provider work supplies **zero organizational
+independence**. Exact model version was not independently verified. These are
+internal challenge results, not external organizational review or acceptance
+of either upstream theorem. Public nonauthor review of this packet remains
+required; its disposition is AUTHOR_SIDE / CONDITIONAL.
+
+## Slice A: endpoint tails and normalization (agent exp_weight_tail_review)
+
+**ACCEPT — §§1–3, conditional on MF1 and SC(3). No amendment required.**
+
+The declared input interfaces agree: original variance-one periodized field,
+endpoint regression, typed determinant weight, full endpoint-only normalizer,
+and all-index additional count in the open height window with both pins
+excluded. Setting T=L resolves the side-length notation. A fixed admissible
+positive gap lies inside a compact family with positive gap floor. No extra
+conditioning or size bias enters E1–E2.
+
+E1 gives sum n w(n)nu_r(n)<=C; retaining n yields the endpoint tail
+sum_(n>M)w(n)nu_r(n)<=C/(M+1). Fatou gives the same bound for the limit.
+Finite-coordinate convergence then proves EW1 at theta itself. Since w>=1,
+a_r->a>0. Centering at zero gives E4; positive conditioning correctly uses
+the denominator a_r. For q and theta'<theta, the factor
+n^(q-1)exp(-(theta-theta')n^alpha) tends to zero. This proves EW2 and the
+size-biased passage with the different denominator nu1+2nu2.
+
+E9 defines genuine probability laws for sufficiently small r, satisfies E1–E2,
+and has endpoint intensity error exactly 1/m. Its size-biased escaping mass
+has endpoint weighted value tending to 1/3. Thus the stronger endpoint
+size-bias conclusion is false. Dropping the retained n defeats the tail
+argument; changing the full tilt or count breaks interface compatibility.
+
+## Slice B: weighted convolution and replica bound (agent exp_weight_replica_review)
+
+**ACCEPT — §§4–5 with §6 scope limits, conditional on the inputs.**
+
+For 0<alpha<=1, w(n+k)<=w(n)w(k). Absolute summation proves E11;
+weighted l1 is a complete unital commutative convolution algebra. E5 implies
+||nu_r||_w<=C and a_r<=C, hence ||H_r||_w<=B=2C; the same holds for H.
+The exponential remainder is at most delta² B² exp(delta B)/2.
+Telescoping m factors contributes at most
+m delta² B² exp(m delta B)/2 <= t delta B² exp(tB)/2.
+The exponential derivative identity E15 is valid in the algebra and gives
+the stated Lipschitz constant. Flooring costs at most delta B exp(tB), and
+replacing H_r by H costs at most 2t epsilon_r exp(tB). These give E12.
+
+For s>=0, exp(-s a_r) sum_j s^j nu_r^{*j}/j! is nonnegative with mass one;
+the comparisons therefore use genuine compound-Poisson laws. Independence
+supplies the convolution power of the one-copy law. m=0, t=0 and T=0 are
+handled. For alpha=1, absolute weighted convergence controls PGFs uniformly
+on the closed disk of radius exp(theta), with analyticity in the interior
+and continuity at the boundary. For alpha<1, the proposed
+n^-3 exp(-2theta n^alpha) contamination obeys the premise but yields
+prelimit radius exactly one. No larger disk follows.
+
+Excluded stronger claims have concrete falsifiers: all replicas equal to
+the same N_r defeats the compound-Poisson limit; a coefficient perturbation
+1/|log r| defeats an automatic O(r³) replica rate and O(r6) one-copy
+limiting-mark error; alpha>1 defeats E11 using two unit atoms.
+
+Custody caveat at the first read: SOURCES.json was not yet present and the
+historical Git objects were unavailable locally. The root later supplied
+SOURCES.json and separately verified the source identities through the
+public GitHub connector. This is not attributed to the first reviewer as
+a historical-tree replay.
+
+## Custody challenge, repair and separate re-review (agent exp_weight_tail_review)
+
+Initial verifier SHA256 `45bddfbdd3e4c8b9cf5dd7311f46db870856f28c93c3d6a2bbbf9d4a3ecc78bb`:
+**AMEND**. Eight controls passed, but a tree could masquerade as a commit,
+and local Git replacement refs could make absent paths pass under an empty
+commit's identity. A boolean JSON schema also passed as integer 1.
+
+Root reproduced all three defects with failing tests before repair. Every
+Git read now uses --no-replace-objects; cat-file requires object type commit;
+schema requires an actual integer. Repaired verifier SHA256
+`0bc355e6b5bc4459d5395f1730456bca8bb26aa6220f94e657f6dd57f93d7784`:
+**PASS — bounded custody re-review**, 11 controls in each Python mode.
+The real manifest correctly fails locally when historical objects are absent.
+This repair concerns custody code only, not a proof amendment or parent verdict.
+
+---
+
+## Current disposition after actual native reviews (30 September 2026 UTC)
+
+The unchanged PROOF.md now has **scoped nonauthor ACCEPT, CONDITIONAL** for
+Slice A (§§1–3) and Slice B (§§4–5). This supersedes the historical pending-review
+status above; it does not rewrite the author-side challenges or make them
+independent reviews. The complete actual bodies are retained in
+[REVIEW_RECORD.json](REVIEW_RECORD.json):
+
+- [Anthropic/Claude A+B, review5360109371](https://github.com/d6g8k5htny-coder/Math-/pull/164#pullrequestreview-5360109371):
+  actual analytic acceptance of the elementary implications of E1–E2, at fixed
+  parameters with existential constants, independent copies and no rate.
+- [OpenAI/Codex A, review5360144037](https://github.com/d6g8k5htny-coder/Math-/pull/164#pullrequestreview-5360144037):
+  §§1–3, E1–E10, conditional on the exact MF1 and SC(3) interfaces; Slice B
+  outside that individual verdict.
+- [OpenAI/Codex B, review5360159070](https://github.com/d6g8k5htny-coder/Math-/pull/164#pullrequestreview-5360159070):
+  §§4–5, EW3/EW4, E11–E15 and dimension/independence/rate qualifications,
+  retaining E1–E2 and Slice A's endpoint consequence as dependencies.
+
+All three native objects identify original commit
+`0e70540b70e5e3183df5ed1a6bd70a212b734c9c`, PROOF.md's 12,576 bytes,
+Git blob `bf1268b9c18ec05561fd9b14c645ef0b8e530484`, and SHA256
+`3f32fdd744350a15359451bbbee6c6bcc71af47e4f57f6110d7afb4978e941ee`.
+Their source exposure is preserved in their complete native bodies, not
+replaced by this summary. Claude identifies provider distinction from the
+author and reviewer exposure to SC; both Codex reviewers disclose their earlier
+source reviews and challenges. All use the same GitHub account and carry
+**zero organizational-independence credit**.
+
+The original MF1/SC(3) statements remain imported hypotheses; these reviews
+do not prove their Gaussian, spectral or regional parents, supply rates or
+moving-mark uniformity, identify a spatial event, or justify spatial
+independence. Scientific effect remains NONE. The later engineering repair
+preserves every mathematical source byte. Its implementer previously reviewed
+Slice B; that does not self-accept the engineering repair. A separate engineering
+review, current-base CI and authorized integration remain distinct gates.
+
+VALIDATION.json is retained unchanged as the original author execution/history
+record. The new packet guard binds its proof hash and REVIEW_RECORD.json's
+proof identity to actual PROOF.md and checks MANIFEST.json membership and hashes.
+Passing that guard establishes local custody only, not GitHub authenticity or
+mathematical acceptance.
@@ -0,0 +1,85 @@
+{
+  "files": [
+    {
+      "path": "INTERNAL_REVIEWS.md",
+      "bytes": 8160,
+      "sha256": "3df02b032e97e735a3a52973312d6459aa103e069fde38359e250741e11b0f5d",
+      "git_blob": "a2f77a2d8e5516e1a851e6db06266edac7489cc3"
+    },
+    {
+      "path": "PROOF.md",
+      "bytes": 12576,
+      "sha256": "3f32fdd744350a15359451bbbee6c6bcc71af47e4f57f6110d7afb4978e941ee",
+      "git_blob": "bf1268b9c18ec05561fd9b14c645ef0b8e530484"
+    },
+    {
+      "path": "README.md",
+      "bytes": 4224,
+      "sha256": "c4fe795143c4b922bea2f215e73b97ca30cd697f3aca2eabbd58f26ebea8f894",
+      "git_blob": "31bfd56bce487a695a46b257e95ef57a9af75689"
+    },
+    {
+      "path": "RECONNAISSANCE.md",
+      "bytes": 1440,
+      "sha256": "fb0ecd7559e5d451c567896fcc8e5a614ad4f6cb010fdc9699b138ac4c62d847",
+      "git_blob": "e0b3d9ea52aff5b1abc4b808f96be416289adcb1"
+    },
+    {
+      "path": "REVIEW_RECORD.json",
+      "bytes": 42755,
+      "sha256": "0d9239543a0c23eb476843f6c122884f2b6258c2bf371adad598266b2fa5b56e",
+      "git_blob": "ee34321999980716e320b8c25eb0f12a7abd3e15"
+    },
+    {
+      "path": "SOURCES.json",
+      "bytes": 1650,
+      "sha256": "478bd0ad93200b0993562d1a7ea3a6f96c7e15620781df469df1e5c127a1b4a1",
+      "git_blob": "4b3eeb938bca54aa28ce4746028a2f152a94dac6"
+    },
+    {
+      "path": "VALIDATION.json",
+      "bytes": 1932,
+      "sha256": "b1e6b78b10c61820e3ee25db4602348690a2f20dd63348de37f5aa0dec0e1347",
+      "git_blob": "ab9e91fce0c8b8dba5c69a3538ed6dad826794b2"
+    },
+    {
+      "path": "finite_checks.py",
+      "bytes": 7409,
+      "sha256": "143e3a64f7f07d2d2e0c29bb5dae5cc1ad59b06d50650ff72dc1daf4e1be8ad2",
+      "git_blob": "86d7f2482acf9326f47b9e39ebe3d56a92fce8f1"
+    },
+    {
+      "path": "test_finite_checks.py",
+      "bytes": 11876,
+      "sha256": "134f7e3074afa8b5fa2e5fbc67fd7867b246434469e00d96575e51a3df477787",
+      "git_blob": "d350286f0b1291813d6c0dcbb9c3b849e1b0e2f3"
+    },
+    {
+      "path": "test_verify_packet.py",
+      "bytes": 9862,
+      "sha256": "6409627e94f41358d880aacb25f90fc58b693c641c5c9251d54424c4188243e4",
+      "git_blob": "e597b179f3d116ae79e15c616f3b17b4f13630ea"
+    },
+    {
+      "path": "test_verify_sources.py",
+      "bytes": 4863,
+      "sha256": "ac8a0ae72e3f1982ea722992ae3c9af2684454301a7fc7d407ea3e23e5b3186f",
+      "git_blob": "0cde3642d6fff16223e94003978d9a00e1de9383"
+    },
+    {
+      "path": "verify_packet.py",
+      "bytes": 5441,
+      "sha256": "a505f52939e10eff494aab7ae81f7dce96f5ea8f78a94a34e49d689fa15aceab",
+      "git_blob": "70b540e53f9921885c62a2a09724d022fdadcadf"
+    },
+    {
+      "path": "verify_sources.py",
+      "bytes": 3410,
+      "sha256": "0bc355e6b5bc4459d5395f1730456bca8bb26aa6220f94e657f6dd57f93d7784",
+      "git_blob": "a8ac3636c011337d9d4a12f4cd052d666572afb8"
+    }
+  ],
+  "manifest_self_excluded": true,
+  "schema": 1,
+  "scientific_effect": "NONE"
+}