diff --git a/.github/workflows/register-alignment.yml b/.github/workflows/register-alignment.yml new file mode 100644 index 000000000..e8d30be7f --- /dev/null +++ b/.github/workflows/register-alignment.yml @@ -0,0 +1,75 @@ +name: Register alignment checks + +'on': + pull_request: + paths: + - 'reviews/register_alignment_20260930/**' + - '.github/workflows/register-alignment.yml' + - 'frontiers/three_fronts_20260924/LIFETIME_REMAINDER.md' + - 'frontiers/three_fronts_20260924/RN_COUNT_INTERFACE.md' + - 'coefficients/side24_v1/PROOF.md' + - 'frontiers/remote_window_20260924/PROOF.md' + - 'frontiers/rn_thin_tube_20260925/FIXED_ANNULUS_CANDIDATE.md' + - 'frontiers/full_price_20260924/PROOF.md' + - 'imports/lifetime_parent_20260925/UNIFORM_MATRIX_CAP_AND_LIFETIME.md' + - 'reviews/pr22_fixed_annulus_nonauthor_20260925/**' + - 'reviews/p15_full_price_nonauthor_20260926/**' + - 'reviews/side24_v1_coefficient_claude_20260929/**' + - 'frontiers/rn_thin_tube_20260925/TWO_SCALE_ADDENDUM.md' + - 'reviews/replacement_20260925_pr19_pr21/TWO_SCALE_REVIEW.md' + - 'frontiers/three_fronts_20260924/P15_REALIZED_COVERS.md' + - 'frontiers/downstream_gate_20260925/GRAPH.json' + - 'frontiers/downstream_gate_20260925/hard_gate.py' + - 'PROOF_INDEX.md' + 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/register_alignment_20260930').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 / 'alignment_check.py') + expected = (root / 'RESULTS.json').read_bytes() + mutants = ['allow-symlink', 'no-hash', 'stale-fingerprint', 'drop-review-source', 'controlling-true', 'executed-flag', 'skip-interface-premise', 'holder-reversed', 'baseline-drift', 'duplicate-drift', 'region-unlinked', 'review-metadata-only'] + 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 diff --git a/reviews/register_alignment_20260930/EXTERNAL_REVIEWS.md b/reviews/register_alignment_20260930/EXTERNAL_REVIEWS.md new file mode 100644 index 000000000..2be80e35b --- /dev/null +++ b/reviews/register_alignment_20260930/EXTERNAL_REVIEWS.md @@ -0,0 +1,265 @@ +# External review comments preserved for REGISTER-ALIGNMENT-20260930-v1 + +**Object:** REGISTER-ALIGNMENT-EXTERNAL-REVIEWS-20260930-v1 (component of the alignment record; source of the proposed +graph node `math.align-component.external-issue-reviews`). +**What this is.** The four nonauthor review comments and three owner reconciliation comments on GitHub issues of +`d6g8k5htny-coder/main` that the D2, D3, D4 and D6 rows of `RECONCILIATION.md` §2 cite, read back on 30 September 2026 +through the session's GitHub connector and transcribed here with their identity fields (comment id, URL, posting +account, provider and session named in the body, `created_at`, `updated_at`). The Cursor "Open in Web / Open in Cursor" +HTML footer appended to the four `cursor[bot]` comments is omitted; everything else is reproduced as returned. +**Status of this evidence.** An issue comment is a mutable external object: this file preserves what was read, it does +not make the comment immutable, and an offline check cannot re-authenticate it (the packet checker is stdlib-only and +has no network). What the checker binds is this file's bytes (the SHA256 fingerprint of the node) and the presence of +the quoted verdict lines in it (`VERDICTS`). OpenAI nonauthor review 5360327058 on Math-#167 reports having directly +authenticated comments 5841270276, 5841782206, 5841269490 and 5841783172 against GitHub. The canonical claim manifest +`claims/LANDING_CLAIMS.json` cites the same issues as the review objects of `lifetime-remainder` (main#67), +`side24-coefficient` (main#65), `rn-fixed-remote-window` (main#76) and `p15-full-price` (main#74). No Cursor agent was +contacted or restarted (owner stop of 27 September 2026); only published comments are cited. Same GitHub account +throughout; zero organizational-independence credit. + +## Index + +| # | Object | Issue | Comment | Posted by | Provider / session named | `created_at` | `updated_at` | Verdict line | +|---|---|---|---|---|---|---|---|---| +| 1 | D2 `frontiers/three_fronts_20260924/LIFETIME_REMAINDER.md` (blob `247b3ecf`, SHA256 `380b7d0a…`) | main#67 | 5841270276 | `cursor[bot]` | xAI, Grok 4.7 (`grok-4.7-high-fast`), Cursor cloud session `bc-81faa729-b944-48d7-991e-0411ea4e3f90` | 2026-09-25T23:59:05Z | 2026-09-26T00:07:25Z | R1–R3 ACCEPT, R4 ACCEPT for (R12), R5–R6 IMPORTED-OPEN | +| 2 | D2, same blob | main#67 | 5841782206 | `cursor[bot]` | xAI, Grok 4.7, Cursor cloud session `bc-dfbce246-8a04-471f-8d9b-8909a2e4eaa0` | 2026-09-26T01:04:21Z | 2026-09-26T01:07:56Z | "R5 and R6 are **ACCEPT**. Theorem R is accepted at its stated O(1) remainder scope." | +| 3 | D3 `coefficients/side24_v1/PROOF.md` (SHA256 `c06daccc…`, commit `e329fba1`) | main#65 | 5841269490 | `cursor[bot]` | Cursor cloud agent, Grok 4.7 (`grok-4.7-high-fast`), run `bc-be5dc8d9-8a69-4ca9-983b-af79d710c1c1` | 2026-09-25T23:58:59Z | 2026-09-26T00:09:32Z | "All six coefficient interfaces check out. The disposition is **COEFFICIENT-CALC-REVIEWED / PARENT-IMPORTED-OPEN**." | +| 4 | D3 reconciliation | main#65 | 5841779222 | `d6g8k5htny-coder` (owner) | — | 2026-09-26T01:03:54Z | 2026-09-26T01:03:54Z | "Closing #65 as the coefficient-review work package." | +| 5 | D4 `frontiers/remote_window_20260924/PROOF.md` (SHA256 `a332bae9…`, commit `191ea7d5`) | main#76 | 5841783172 | `cursor[bot]` | Cursor cloud session `bc-593a8246-91d3-4d99-90bc-7448dff875dc`; identified as the xAI/Grok review by the owner's reconciliation 5841861362 | 2026-09-26T01:04:29Z | 2026-09-26T01:12:36Z | "This accepts only the fixed-ρ and fixed-η interfaces below. It does not accept a full RN or 24-jet theorem." Items 1–7 ACCEPT | +| 6 | D4 reconciliation | main#76 | 5841861362 | `d6g8k5htny-coder` (owner) | — | 2026-09-26T01:15:52Z | 2026-09-26T01:15:52Z | "returns ACCEPT on all seven fixed-rho/fixed-eta interfaces … Closing #76 as the fixed-remote REVIEW work package only." | +| 7 | D6 reconciliation (the analytic review itself is the in-repo file `reviews/p15_full_price_nonauthor_20260926/REVIEW.md`) | main#74 | 5842112010 | `d6g8k5htny-coder` (owner) | — | 2026-09-26T01:48:31Z | 2026-09-26T01:48:31Z | "D6 ANALYTIC REVIEW COMPLETE … Closing #74 as the D6 review work package" | + +## 1. main#67 comment 5841270276 (D2, xAI review, R1–R6) + +URL: https://github.com/d6g8k5htny-coder/main/issues/67#issuecomment-5841270276 · posted by `cursor[bot]` · created 2026-09-25T23:59:05Z · updated 2026-09-26T00:07:25Z + +`````text +R1, R2, R3, and the cap-loss bound in R4 check. R5 and R6 stay IMPORTED-OPEN: their density and count conclusions still require open #63 interfaces. No counterexample turned up in the new estimates. Nothing here accepts issue #63 or promotes a status. + +**Reviewer.** xAI, Grok 4.7 (`grok-4.7-high-fast`), Cursor cloud session `bc-81faa729-b944-48d7-991e-0411ea4e3f90`. This is not an OpenAI session. Finite tests were not run and are not used as evidence. + +**Sources read.** Successor `LIFETIME-BOUNDED-REMAINDER-20260924-v1`: Math- `frontiers/three_fronts_20260924/LIFETIME_REMAINDER.md`, blob `247b3ecf80bfbe896948d5d489b2d5842a81c481`, 17734 bytes, SHA256 `380b7d0abdb0fe2de5a6564565af9560d3f1b1ce22fd5538927db0c52f4f3a4a`. That blob is unchanged from commit `8a13ee977530` through Math- `232a182fee316d2bb428b7351b5c5caae3b8cc2e`, and it is the file at `9b5fb7fa0ce3271afb4168dbada4893a53eaf307`. Parent #63: Drive `1foDgiDi4XIKOfbrZEE8dWKV_BkZU8LIb`, 40261 bytes, SHA256 `9350ad6eaba6626b93c3dedeef9e2ff816e5cdf1c8318e85fb27499141c84bc7`. Cap statement read for the event shape only: Drive `1BnPods7Lf-ECdD34noQihZcEfcqpy7R5`, 15160 bytes. + +## Dependency crosswalk + +| New step | Uses from #63 / cap | Disposition of that import | +|---|---|---| +| R1 coupling | §2 Fourier summability; §3 uniform positive-definiteness of the contact covariance on a fixed band | Read and used. This is not an acceptance of Theorems A–C. | +| R2 determinant lemmas | None beyond symmetric-matrix algebra | No parent probability. | +| R3 densities | §3 joint nonsingularity of `(U_r, A_M)`, target-independent | Same limited import as R1. | +| R4 bound `(R12)` | Parent (6.2), re-derived here; cap event `λ > (4/(3k)) r M_3^2`, `r M_4 ≤ 3k/10` | Integral bound stands on its own. | +| `A_r(1-p_r) ≤ B_r` | Cap global-elder conclusion; parent §8 Morse/Borel | **IMPORTED-OPEN** | +| R5–R6 densities `ν` | §9 Borel marked Kac–Rice; §10 radial ledger; §14 far `O(1)`; `c` named as (15.2) via §15 | **IMPORTED-OPEN** | + +## Verdicts + +**R1 — ACCEPT.** Centered rules meet the contact jet at order `r^2`. The fourth axial row is `f_xxx + (r^2/40) f^{(5)} + O(r^4)`. With `|v_r − v_0| ≤ C k r^2` and `Σ_r − Σ_0 = O(r^2)`, the common regression coupling satisfies `‖F_r − F_0‖_{L^p(C^q)} ≤ C_{p,q} r^2 (1+|b|+k)`. + +**R2 — ACCEPT.** For `K_t = [[α, √t βᵀ], [√t β, A]]`, `det K_t = α det A − t βᵀ adj(A) β` holds on singular `A`. If the indices differ, the affine determinant vanishes in between, so `|F_j(K_r) − F_j(K_0)| ≤ r |βᵀ adj(A) β|`. A direct Lipschitz bound on the `√r` entries would lose a square root; this cancellation keeps the later intensity error `O(r(k+r))`. Endpoint comparison with `diag(±6k, A_0)` then gives `(R10)` and `(R11)`. + +**R3 — ACCEPT.** Along the linear path in covariance and target, `Σ` stays uniformly positive and `|v(θ)|^2` stays coercive in `b^2+k^2`. Differentiating the Gaussian density produces a trace `O(r^2)`, a quadratic `O(r^2 P^2)`, and a target term `O(r^2 k P)`. Integrating `|dπ/dθ|` gives `(R5)` without a small-log restriction. The joint bound `(R13)` is the same uniformly nondegenerate Gaussian density at `(v_r, A)`. + +**R4 — ACCEPT for `(R12)`.** Both soft factors in parent (6.2) were re-derived, including the saddle factor `λ_1 + (3/2) r h`. Depth failure has width `O((r/k) U^2)`. The `λ_1` integral is `(D^3/3) δ^3 U^6 + (E D^2/2) r δ^2 U^5`, and `r δ^2 = k δ^3`. For `m=1`, failure sits in `{λ ≤ 4 D δ T^2} ∪ {λ > 1/(4 D δ)}`; the far piece and the `M_4` piece are fourth-moment Markov bounds, and `δ ≤ 1` turns `δ^4` into `δ^3`. The comparison `A_r(1−p_r) ≤ B_r` stays **IMPORTED-OPEN**. + +**R5 — IMPORTED-OPEN.** Conditional on `(R11)` and the parent intensity `r A_r dr db dk dσ`, the cutoff arithmetic is right. The missing mass `k < a = ℓ/r_0^3` is `O(a^{7/3})`. The two error monomials are `k^{−2/3} r k = ℓ^{1/3}` and `k^{−2/3} r^2 = ℓ^{2/3} k^{−4/3}`; the second, cut at `a`, is `O(ℓ^{1/3})`. Replacing `a` by `0` makes `∫ k^{−4/3} dk` diverge. The split `η = ℓ^{1/6}` makes `δ ≤ ℓ^{1/9}` on `k ≥ η`, and both loss pieces are `O(ℓ^{7/18})` inside the scaled density. Passage from these Gaussian integrals to `ν_cand` and `ν_eld` still requires open §8, §9, and §10. + +**R6 — IMPORTED-OPEN.** Given the `O(1)` density bound on `0 < ℓ ≤ ℓ_*`, `∫_0^t ν = (3/2) c t^{2/3} + O(t)` and the nonselected count is `O(t)`. For `q > −2/3` one also has `q > −1`, so `∫_0^t ℓ^q O(1) dℓ = O(t^{q+1})` and `(R20)` is the correct integration of that bound. The far `O(1)` that puts the unrestricted densities on the whole torus is parent §14 and remains open. The individual threshold `p < 2/3` and the nonselected range `p < 1` match these exponents. +````` + +## 2. main#67 comment 5841782206 (D2, xAI delta review, R5–R6 ACCEPT) + +URL: https://github.com/d6g8k5htny-coder/main/issues/67#issuecomment-5841782206 · posted by `cursor[bot]` · created 2026-09-26T01:04:21Z · updated 2026-09-26T01:07:56Z + +`````text +R5 and R6 are **ACCEPT**. Theorem R is accepted at its stated O(1) remainder scope. The parent imports left open in comment 5841270276 are the five interfaces accepted in #63 comment 5841570965. No successor-specific gap turned up. I did not replay R1–R4 and I did not edit the proof. + +**Reviewer.** xAI, Grok 4.7 (`grok-4.7-high-fast`), Cursor cloud session `bc-dfbce246-8a04-471f-8d9b-8909a2e4eaa0`. This delta uses the arithmetic already recorded in comment 5841270276 (session `bc-81faa729`) and the parent acceptance in comment 5841570965 (session `bc-ce4bf0bc`). Same provider family as those two reviews. This is not an OpenAI session. Finite tests were not run. + +**Immutable D2 source, re-read and hashed.** Math- `frontiers/three_fronts_20260924/LIFETIME_REMAINDER.md`, blob `247b3ecf80bfbe896948d5d489b2d5842a81c481`, 17734 bytes, SHA256 `380b7d0abdb0fe2de5a6564565af9560d3f1b1ce22fd5538927db0c52f4f3a4a`. Parent bytes checked against that citation: Math- blob `dfed3b8d318a3ab1950957f393307733a4bef3f2`, 40261 bytes, SHA256 `9350ad6eaba6626b93c3dedeef9e2ff816e5cdf1c8318e85fb27499141c84bc7`. + +## Import mapping + +| Prior open import | Where #63 comment 5841570965 accepts it | What R5/R6 use it for | +|---|---|---| +| `1-p_r ≤ Q^W(G_r^c)`, hence `A_r(1-p_r) ≤ B_r` | D1-A §8, lines 215–217 and 276–296. The cap event is the same pair `λ_min(-A_M) > (4/(3k)) r M_3^2` and `r M_4 ≤ 3k/10`. D1-A concludes `1-p_r ≤ Q^W(G_r^c)` for the embedded small-`r` cylinder, with `0 < Z_r < ∞`. | With D1-C’s `A_r = 12 π_r (Z_r/r^2)` and `B_r = 12 π_r E_Q[(W/r^2) 1_{G_r^c}]`, this is the comparison in successor §5. The quantitative bound on `B_r` remains the already checked `(R12)`. | +| §9 Borel marked Kac–Rice | D1-B, lines 298–308. Intensity equals the full-pin density times `E_Q[W]`; the selected intensity is that quantity times `p_r`. | Passage from the Gaussian integrands to `ν_cand` and `ν_eld`. | +| §10 radial ledger | D1-C, lines 88–94 and 310–335. `r A_r dr db dk dσ` with ordinary sphere area and no role-order `1/2`, and `A_r = 12 π_r (Z_r/r^2)`. | Successor §6. The lifetime Jacobian `r (dr/dℓ) = (1/3) k^{-2/3} ℓ^{-1/3}` turns that measure into `ℓ^{1/3} ν = ∫ A/(3 k^{2/3})`. | +| §14 far `O(1)` | D1-D, lines 386–445, equation (14.1): `0 ≤ ν_eld^far(ℓ) ≤ ν_cand^far(ℓ) ≤ C` for `0 < ℓ ≤ 1`. | Successor §7, added to `(R16)`–`(R18)` to reach `(R1)` on `0 < ℓ ≤ ℓ_*`. | +| `c` as (15.2) | D1-E, lines 447–480. | Successor §1 and §6. `A_0 = 12 π_0 z_0`, so `∫ A_0/(3 k^{2/3}) = 4 ∫ k^{-2/3} π_0 z_0`, which is parent (13.6). D1-E reduces that integral to (15.2). | + +The cutoff arithmetic recorded in comment 5841270276 still stands: missing mass `k < ℓ/r_0^3` is `O(a^{7/3})`; the monomials `k^{-2/3} r k` and `k^{-2/3} r^2` are both `O(ℓ^{1/3})` once the lower cutoff is kept; the split `η = ℓ^{1/6}` makes both pairing-loss pieces `O(ℓ^{7/18})` inside the scaled density. Given the resulting `O(1)` density bound, `∫_0^t ν = (3/2) c t^{2/3} + O(t)`, the nonselected count is `O(t)`, and `(R20)` is the same integration for `q > -2/3`. + +R5 and R6 take the elder comparison and the integral definition of `c`. They do not take the parent’s uniform `C r^3` selection bound (1.1), and they do not take the dominated-convergence route to `p_r → 1`. Successor §1 and §6 already replace that route by `(R11)` and `(R12)`. The §§2–§7 chain is outside this delta. + +## Scope of the acceptance + +Theorem R is the existential statement: some `ℓ_* > 0` and some finite `C` give + +`|ν_cand(ℓ) - c ℓ^{-1/3}| ≤ C`, `0 ≤ ν_cand(ℓ) - ν_eld(ℓ) ≤ C`, and `|ν_eld(ℓ) - c ℓ^{-1/3}| ≤ C` + +for `0 < ℓ ≤ ℓ_*`, with `c` equal to parent (15.2). That includes `(R16)`, `(R18)`, `(R19)`, and `(R20)`. + +A numerical value of `C` or `ℓ_*`, convergence of the bounded remainder, a second coefficient, an RN expected-critical-count estimate, and a 24-jet certificate are outside this verdict. Scientific status of those separate items is unchanged. +````` + +## 3. main#65 comment 5841269490 (D3, xAI coefficient review, C1–C6) + +URL: https://github.com/d6g8k5htny-coder/main/issues/65#issuecomment-5841269490 · posted by `cursor[bot]` · created 2026-09-25T23:58:59Z · updated 2026-09-26T00:09:32Z + +`````text +All six coefficient interfaces check out. The disposition is **COEFFICIENT-CALC-REVIEWED / PARENT-IMPORTED-OPEN**. This is a same-session nonauthor check of the stated expression, and parent issue #63 is still open. + +Provider/model/session: Cursor cloud agent, Grok 4.7 (`grok-4.7-high-fast`), run `bc-be5dc8d9-8a69-4ca9-983b-af79d710c1c1`, https://cursor.com/agents/bc-be5dc8d9-8a69-4ca9-983b-af79d710c1c1. Source exposure: public `Math-` commit `e329fba1e927a12dbb4f0d1556f85f39284d17a9`, directory `coefficients/side24_v1/`; parent Drive proof `UNIFORM_MATRIX_CAP_AND_LIFETIME.md` (40,261 bytes, SHA256 `9350ad6eaba6626b93c3dedeef9e2ff816e5cdf1c8318e85fb27499141c84bc7`) only to transcribe (15.2) and recheck its scalar integral; NIST DLMF 5.11; issue #63’s displayed formula. No Vault99 reading, no source edits, no child agents. Local interpreter: CPython 3.12.3. + +## Interfaces + +| Interface | Result | +|---|---| +| C1 negative-cone moment \(D_1=4/3\) | **VERIFIED** | +| C2 \(D_2=29/6-\sqrt{6}\), negative-definite cone retained | **VERIFIED** | +| C3 angular / all-direction reduction | **VERIFIED** | +| C4 SIDE24 image / periodization bound | **VERIFIED** | +| C5 covariance / Schur transfer | **VERIFIED** | +| C6 outward Gamma / Stirling arithmetic | **VERIFIED** | + +**C1.** For the reference \(K_\infty(z)=\exp(-|z|^2/2)\), \(\mathrm{Cov}(H_{ij},H_{kl})=\delta_{ij}\delta_{kl}+\delta_{ik}\delta_{jl}+\delta_{il}\delta_{jk}\) and \(\mathrm{Cov}(V)=\mathrm{diag}(3,1,\ldots,1)\). Conditioning the transverse entry on \(V=0\) gives variance \(8/3\). The \(1\times1\) negative cone is \(A<0\), and \(A^2\) is even, so \(D_1=\tfrac12\cdot\tfrac83=\tfrac43\). + +**C2.** For \(m=2\), \(A=\begin{pmatrix}s+x&y\\y&s-x\end{pmatrix}\) with independent \(s,x,y\), \(\mathrm{Var}(s)=5/3\), \(\mathrm{Var}(x)=\mathrm{Var}(y)=1\). Both eigenvalues are negative exactly on \(s<-R\), \(R=\sqrt{x^2+y^2}\). With \(R^2\) of density \(e^{-z/2}/2\), +\[ +\int_0^a(a-z)^2 e^{-z/2}\,dz/2=a^2-4a+8-8e^{-a/2}. +\] +Symmetry then gives +\[ +D_2=\tfrac12\bigl(\tfrac{25}3-\tfrac{20}3+8-8\sqrt{3/8}\bigr)=\tfrac{29}6-\sqrt6, +\] +using \(E[s^4]=25/3\) and \(E[e^{-s^2/2}]=\sqrt{3/8}\). The identity \(4\sqrt{3/8}=\sqrt6\) is the square check \(16\cdot(3/8)=6\). Half the untruncated determinant-square moment is exactly \(29/6\); the cone cutoff is the \(-\sqrt6\) term. + +**C3.** Parent (15.2) is +\[ +c_{d,L}=\frac{\Gamma(7/6)}{24^{1/3}\sqrt\pi}\int_{S^{d-1}}p_G(0)\,p_{V_u}(0)\,\tau_u^{4/3}D_u\,d\sigma(u). +\] +The scalar identity was recomputed from the parent’s intermediate factors: \(4\cdot(6\kappa)^2=144\) and \(k^{-2/3}\cdot k^2=k^{4/3}\), then +\[ +144\int_0^\infty k^{4/3}\varphi_\tau(12k)\,dk=\Gamma(7/6)\,\tau^{4/3}/(24^{1/3}\sqrt\pi). +\] +For the isotropic reference, \(\tau^2=6\), \(p_G(0)p_V(0)=(2\pi)^{-d}/\sqrt3\), and \(|S^1|=2\pi\), \(|S^2|=4\pi\). Those areas equal \(2^{d-1}\pi\) for \(d=2,3\), and \(6^{2/3}/24^{1/3}=(3/2)^{1/3}\), which is formula (1). The same multiplicative bound holds in every orthonormal frame, so the sphere integral keeps it. + +**C4.** Coordinate partials of \(\varphi(x)=\exp(-|x|^2/2)\) factor as Hermite products. For every multi-index of order at most 6 and every \(|y|\ge24\), +\[ +\prod_i|He_{\alpha_i}(y_i)|\le76\,|y|^6. +\] +The check covered all 84 multi-indices in \(d\le3\); the worst ratio to \(76\cdot24^6\) is about \(0.0135\), on the pure sixth derivative. At the origin the same partials are at most 15. The lattice estimate +\[ +\sum_{n\neq0}|n|^6 e^{-288|n|^2}\le1458\,e^{-288} +\] +holds, and the degree-20 Taylor sum for \(e^{288/125}\) is greater than 10, so \(e^{-288}<10^{-125}\). Therefore +\[ +E=1458(76\cdot24^6+15)\cdot10^{-125}=21175738586478\cdot10^{-125}, +\] +and \(60E<10^{-108}\). + +**C5.** Entrywise differences are at most \(2E\) after the \(\sqrt2\) duplication on off-diagonal Hessian coordinates. In dimension at most 10 the spectral norm is at most \(20E\). The reference odd block \(\begin{pmatrix}1&-3\\-3&15\end{pmatrix}\) shifted by \(I/3\) has leading minor \(2/3\) and determinant \(7/9\), and \((23/3)^2-58=7/9>0\), so its smaller eigenvalue exceeds \(1/3\). Hessian eigenvalues are \(2\) and \(d+2\). Thus \(C_{\mathrm{ref}}\ge I/3\) and \((1-\varepsilon)C_{\mathrm{ref}}\le C_{24}\le(1+\varepsilon)C_{\mathrm{ref}}\) at \(\varepsilon=10^{-108}\). Schur complements are infima of the quadratic form, so the sandwich passes to \(\tau^2\) and to \(A\mid V=0\). The Gaussian density comparison and the degree-\(2m\) cone scaling then give integrand powers \(a=m+2/3+n/2\), \(b=d+n/2\). For \(d=3\), \(a+2b=79/6<14\) and \(2a+b=77/6<13\), and \(32\varepsilon<10^{-106}\). + +**C6.** Bernoulli numbers \(B_2,\ldots,B_{22}\) match the \(B_1=-1/2\) recurrence, including \(B_{22}=854513/138>0\). DLMF 5.11(ii) puts the positive-real remainder after the \(B_{20}\) term between 0 and the first omitted \(B_{22}\) term; the code encloses that way, then removes 32 logarithms from \(z=199/6\) by DLMF 5.5(i). An independent Stirling shift by 48, with a separate Machin/atan log/exp implementation, landed inside the package interval for \(\Gamma(7/6)\), width about \(1.4\cdot10^{-31}\), midpoint \(0.9277193336300392\). The \(10^{-106}\) allowance is applied to an already valid enclosure of \(c_{d,\mathrm{ref}}\). Author tests: `python3 -m unittest test_coefficient.py` in that directory, **30 runs, 0 failures**. The 20-digit outward endpoints are the published ones: +\[ +0.073406919306034271030`, because the conditional law of the transverse Hessian has full support on an open negative-definite ball. Remote conditioning changes the law inside the numerator expectation and leaves this denominator in place. The height split uses Lebesgue `dt` on the window. The factor `12` that appears in the unconditional pin intensity is absent from this conditional count. + +4. **Contact kernel and `O(k r^4 |E|)` remainder — ACCEPT.** `Λ_j` in (13) is continuous on the stated compact sets, finite, and bounded above and below by positive constants. Positivity uses the joint conditional support of `(A_0,H_x)` and keeps their dependence inside the expectation. The density error is `O(r^2)` and the endpoint-weight error is `O(r)`, so the Kac–Rice integrand differs from `Λ_j` by `O(r)`. Integration over a window of length `k r^3` gives the `O(k r^4 |E|)` count remainder, which is (2). The matching lower bound is for the expectation on a fixed positive-volume set. Markov is applied only from that expectation to the probability upper bound. + +5. **Fixed-separation factorial moments — ACCEPT.** For each fixed `m≥2` and `η>0`, one endpoint weight and one normalizer are used. There are `m+2` determinant factors. The ordered mean is `(k r^3)^m C_m+O(r^{3m+1})`, with a joint contact kernel. Each unordered `η`-separated `m`-set contributes `m!` ordered tuples, so its probability is at most `E[T]/m! = O(r^{3m})`. A separated pair is `O(r^6)`. + +6. **Selector and height-window mapping — ACCEPT for the implication in §7 only.** A `0/1` selector is dominated by `N_{r,j}(E)` when its type, location, and value conditions imply (1): index `j`, location in a Borel subset of the fixed `D_ρ`, and height strictly between the pinned heights. Boundary heights have expected count zero. No historical RN witness predicate, inner-wedge cell, whitened-jet cell, or all-cell partition is shown to imply (1). Those objects stay outside this acceptance. Ambient Lebesgue measure `dx` is the coordinate system of (14); a polar or scaled chart has to carry its own Jacobian. + +7. **Uncovered complement — ACCEPT as stated in §7.** The regions that remain open are exactly the ones listed in the crosswalk below. `ρ` and `η` stay fixed. + +## Region crosswalk + +| Region | This note | +|---|---| +| Fixed `D_ρ`, height in `(b-k r^3,b)`, index `j` | Theorem A and numerator (14) | +| Fixed `η>0`, ordered `m`-tuples of index `j` in that window | (15); probability ≤ `E[T]/m!` | +| Mesoscopic neighborhood `x=ry` | Open. Distance to the pins tends to zero | +| Pin collision, witness within `O(r)` of `M` or `S` | Open. Same distance restriction | +| Intermediate annulus, a multiple of `r` out to a shrinking cutoff, including `r≪\|x‖≪ρ` | Open. Compactness constants are not claimed there | +| Witness collision, mutual separation tending to zero | Open. (15) stops at fixed `η` | +| Remote critical points with no shrinking height window | Open. The factor `r^3` is the window length | +| Legacy all-cell, 24-jet, `ENV-RESCOV` through `CH-LIFT`, fixed-`r` inner wedge | Open. §7 requires a separate proof that the legacy selector implies (1). `STATUS_RN_UNIF` still records those carriers as absent | +| Probability lower bound, Poisson law, numerical `C` or `r_*`, elder selection | Not conclusions of this argument | + +## Checks and one citation correction + +I recomputed the pin Jacobian, the target `v_r`, the axial coefficient `r^2/40` on `s^5`, and the Hermite values `α_M=-6k`, `α_S=6k`, `f_xxx=12k`. The local exact suite, 28 tests, passed under Python 3. Those tests check finite algebra. They do not evaluate `Λ_j`. + +The operative Kac–Rice input is Theorem 6.1, Remark 8, and §7.1 of arXiv:2304.07424v3: the weight may depend on an extra field, the critical-point Jacobian is `|det Hess|` once, and the height split is the joint density in `dt`. In that HTML, Theorem 7.1 is the i.i.d. sum model, and the critical-point discussion is §7.1 rather than §8.1. The formula in (12) matches Theorem 6.1 and §7.1. A later bibliographic edit can retarget the sentence in §8; that mismatch is not a false step in the count. +````` + +## 6. main#76 comment 5841861362 (D4, owner reconciliation) + +URL: https://github.com/d6g8k5htny-coder/main/issues/76#issuecomment-5841861362 · posted by `d6g8k5htny-coder` (owner) · created 2026-09-26T01:15:52Z · updated 2026-09-26T01:15:52Z + +`````text +D4 REVIEW DELIVERY RECONCILED. The complete proof is in Math at `frontiers/remote_window_20260924/PROOF.md`, and the fresh xAI/Grok review on this issue returns ACCEPT on all seven fixed-rho/fixed-eta interfaces: conditioned covariance, all three determinant factors and O(k r^5) numerator, original endpoint normalizer, contact-kernel remainder, fixed-separation factorial moments, selector/window mapping, and the explicit uncovered complement. Closing #76 as the fixed-remote REVIEW work package only. This does not shrink rho or eta and does not close mesoscopic, pin, intermediate, or shrinking witness-collision regions. +````` + +## 7. main#74 comment 5842112010 (D6, owner reconciliation of the in-repo review) + +URL: https://github.com/d6g8k5htny-coder/main/issues/74#issuecomment-5842112010 · posted by `d6g8k5htny-coder` (owner) · created 2026-09-26T01:48:31Z · updated 2026-09-26T01:48:31Z + +`````text +D6 ANALYTIC REVIEW COMPLETE. The full proof is in Math at `frontiers/full_price_20260924/PROOF.md`, and merged Math PR63 records a cross-provider nonauthor ACCEPT on all six requested slices: hazard/separate concavity, odd-majority worst case, global independence/hazard direction, realized-family cover, sharpness, and demand-one boundary. Exact accepted scope is the realized disjoint capacity/clutter family with d_i>=2, every independent probability, prices c_v<=phi(p_v), same palette K>=K_H(d), and rho*=1/(3-log(3e-2)). The p=1 strictness sentence is corrected to interior 1/2=rho and between-pin height" + }, + "proposed": { + "classification": "PROVED_REVIEWED", + "controlling": false, + "fingerprint": "dist>=rho and between-pin height", + "source": null, + "scope": "the fixed-remote region at the D4 scope: dist >= rho from the pins, between-pin height window", + "explicit_limits": "as the covering node", + "review_disposition": "ACCEPT", + "review_sources": [ + { + "ref": "main#76 comment 5841783172", + "provider": "xAI/Grok 4.7 via Cursor", + "verdict": "covering theorem accepted at this exact region scope; region crosswalk table" + } + ], + "coverage_source": "math.rn-fixed-remote-window", + "notes": "PROVED_REVIEWED region: covered by math.rn-fixed-remote-window (required covered_by edge; coverage_source retained). Register alignment v1.3." + }, + "required_premises_after": [ + "math.rn-fixed-remote-window" + ], + "notes": "Covered by a PROVED_REVIEWED node after the previous transition; coverage_source retained and a required covered_by edge added so that a change to the covering proof reaches the region (Codex 4139807558; OpenAI 5360327058 item 1). The current hard gate reports PROVED_REVIEWED regions in its own proved_reviewed_regions bucket since ec6db8c (Math-#151), so the earlier region-reporting complaint (Codex 4139807545) is superseded." + }, + { + "node": "math.rn-fixed-annulus-window", + "kind": "candidate", + "current": { + "classification": "AUTHOR_SIDE_CANDIDATE", + "fingerprint": "081abc13c5e66342c13df2af2bd6b114f320486f" + }, + "proposed": { + "classification": "PROVED_REVIEWED", + "controlling": false, + "fingerprint": "1fd9fe7141e464fd1c09ebf0318d8a701729c9c61ea24f73f7e20a9cf10c552b", + "source": "frontiers/rn_thin_tube_20260925/FIXED_ANNULUS_CANDIDATE.md", + "scope": "d = 2; fixed L; fixed scaled annulus 1 < A0 <= |y| <= B0 < infinity; compact positive gaps k_- > 0; all frames; between-pin height window (live node scope)", + "explicit_limits": "no global D5/RN/JETMOD, k -> 0, d >= 3, pin-neighborhood, intermediate-scale, collision, or elder-selection closure; excludes PR28 and later blobs", + "review_disposition": "ACCEPT", + "review_sources": [ + { + "ref": "reviews/pr22_fixed_annulus_nonauthor_20260925/REVIEW.md", + "provider": "xAI/Grok 4.7 via Cursor", + "verdict": "ACCEPT at the exact scoped theorem (covariance floor, cutoff r^(1/24), rare target density, conditioned C^3 sixth moment, ...)", + "binds": "commit 2804dc1, blob 081abc13, SHA256 1fd9fe71" + } + ], + "notes": "PROVED_REVIEWED at the fixed d = 2 scaled-annulus window scope; see explicit_limits. Evidence: pr22 review record; consumed S6-S21 stitching input with its review. Single nonauthor provider. Register alignment v1.3." + }, + "required_premises_after": [ + "math.rn-count-interface", + "math.align-component.pr22-annulus-review", + "math.align-component.two-scale-addendum" + ], + "notes": "Fingerprint kind changes from git blob 081abc13 (current) to SHA256, matching the other component nodes; same bytes. Single nonauthor provider. Its consumed S6-S21 stitching input (TWO_SCALE_ADDENDUM.md) and that input's review are component nodes since v1.3 (Codex 4139807567; OpenAI 5360327058 item 2)." + }, + { + "node": "math.rn-region.fixed-annulus-window", + "kind": "region", + "current": { + "classification": "COVERED_BY_CANDIDATE", + "fingerprint": "fixed-d2-annulus-between-pin-window-reviewed" + }, + "proposed": { + "classification": "PROVED_REVIEWED", + "controlling": false, + "fingerprint": "fixed-d2-annulus-between-pin-window-reviewed", + "source": null, + "scope": "the fixed d = 2 scaled annulus at the covering node's exact declared scope", + "explicit_limits": "as the covering node", + "review_disposition": "ACCEPT", + "review_sources": [ + { + "ref": "reviews/pr22_fixed_annulus_nonauthor_20260925/REVIEW.md", + "provider": "xAI/Grok 4.7 via Cursor", + "verdict": "covering theorem accepted at this exact scope" + } + ], + "coverage_source": "math.rn-fixed-annulus-window", + "notes": "PROVED_REVIEWED region: covered by math.rn-fixed-annulus-window (required covered_by edge; coverage_source retained). Register alignment v1.3." + }, + "required_premises_after": [ + "math.rn-fixed-annulus-window" + ], + "notes": "Covered by a PROVED_REVIEWED node after the previous transition; coverage_source retained and a required covered_by edge added (as for the fixed-remote region)." + }, + { + "node": "math.p15-full-price", + "kind": "candidate", + "current": { + "classification": "AUTHOR_SIDE_CANDIDATE", + "fingerprint": "full-price-20260924" + }, + "proposed": { + "classification": "PROVED_REVIEWED", + "controlling": false, + "fingerprint": "87521901ca8e5405b4d1e47f1deb1cd0326affbd6f5967b53c4178590da993f9", + "source": "frontiers/full_price_20260924/PROOF.md", + "scope": "realized disjoint capacity/clutter family with d_i >= 2, all independent probabilities, c_v <= phi(p_v), same palette K >= K_H(d), sharp rho* = 1/(3 - log(3e-2)) (STATUS D6 row)", + "explicit_limits": "demand one remains an obstruction; no arbitrary-downset or unrestricted prize-problem extension", + "review_disposition": "ACCEPT", + "review_sources": [ + { + "ref": "reviews/p15_full_price_nonauthor_20260926/REVIEW.md", + "provider": "xAI/Grok 4.7 via Cursor (Math- issue 57, merged Math-#63)", + "verdict": "ACCEPT on all six slices", + "binds": "blob 582180e4, SHA256 87521901" + }, + { + "ref": "main#74 comment 5842112010", + "provider": "owner", + "verdict": "D6 analytic review complete; #74 closed as the D6 review work package" + } + ], + "notes": "PROVED_REVIEWED on the realized family with d_i >= 2; see explicit_limits. Evidence: p15 review record, consumed setwise interfaces of P15_REALIZED_COVERS.md, main#74 reconciliation (external record node). Single nonauthor provider. Register alignment v1.3." + }, + "required_premises_after": [ + "math.align-component.external-issue-reviews", + "math.align-component.p15-review", + "math.align-component.p15-realized-covers-setwise" + ], + "notes": "Fingerprint changes from the label full-price-20260924 to SHA256; the live note 'review open' is stale against the merged review record. Single nonauthor provider. The consumed setwise interfaces (P1), (P2), Theorem P2 of P15_REALIZED_COVERS.md are a component node since v1.3, at the D6 review's scope only." + } + ], + "execution_order": [ + "0. create the component nodes and edges of proposed_graph_nodes / proposed_graph_edges (review records, consumed sources, covered_by, the interface's two live premises); they are evidence records and change no classification of an existing node", + "1. math.rn-count-interface -> PROVED_REVIEWED (premise of 4 and 6)", + "2. math.lifetime-remainder and math.side24-coefficient -> PROVED_REVIEWED (premise D1 is live PROVED_REVIEWED)", + "3. Math-#151 is on main (ec6db8c): the D4 bytes are carried by two live nodes (math.rn-fixed-remote-window AUTHOR_SIDE_CANDIDATE; math.d5-component.remote-window-proof PROVED_REVIEWED; same fingerprint, same main#76 review); execute math.rn-fixed-remote-window -> PROVED_REVIEWED, then math.rn-region.fixed-remote; collapsing the component node onto the live node is an optional one-edge follow-up", + "4. math.rn-fixed-annulus-window -> PROVED_REVIEWED (fingerprint to SHA256), then math.rn-region.fixed-annulus-window", + "5. math.p15-full-price -> PROVED_REVIEWED (fingerprint to SHA256)", + "6. regenerate the hard gate's manifest/results per frontiers/downstream_gate_20260925/README.md; run git_transition_audit base->head; expect promotion_permission false and no controlling node", + "executing lane: non-Claude; this record executes nothing; a lane that wants a second provider on the single-provider rows (D2, D4, D5-annulus, D6) asks for it before step 2-5" + ], + "not_proposed": [ + "math.rn-region.mesoscopic-scaled-annulus, pin-collision, intermediate-r-to-rho: Math-#151 (D5 fold)", + "math.rn-region.witness-collision and its residual: Math-#160", + "math.rn-mesoscopic-reduction (legacy PR7 route), eng.* controls, hist.* predicates: unchanged", + "any controlling flag, STATUS, PROOF_INDEX, SELECTOR_REGION or catalog edit" + ], + "independence_caveat": "All cited nonauthor reviews except D3's second read and the interface review are xAI/Grok via Cursor cloud sessions on the shared account; no organizational independence. The D1 precedent for PROVED_REVIEWED used xAI plus Anthropic reads. No Cursor agent is restarted or contacted (owner stop 2026-09-27); only published comments are cited.", + "declarative": true, + "executed": false, + "review_record": [ + { + "lane": "xAI", + "id": 5901912476, + "kind": "inventory read", + "at": "670e4ae", + "verdict": "ACCEPT as declarative inventory; HOLD execution until Math-#151 Cut A is on current tip; execute #151 first, then this alignment", + "hold_precondition_math_151": "satisfied: Math-#151 merged at ec6db8c (2026-09-30T00:56:58Z)" + }, + { + "lane": "xAI/Grok (Lucas)", + "id": 5360240245, + "kind": "review", + "at": "670e4ae", + "verdict": "ACCEPT at classification-lag scope; HOLD execution until #151 on main and single-provider rows recorded as such; interface flip conditional on this packet's Anthropic note, not an xAI re-read", + "hold_precondition_math_151": "satisfied: Math-#151 merged at ec6db8c (2026-09-30T00:56:58Z)" + }, + { + "lane": "OpenAI/ChatGPT", + "id": 5360320845, + "kind": "source-custody and RN-interface review", + "at": "f2250bf", + "verdict": "historical lag and logical-interface inequalities sound at stated scopes; AMEND REQUIRED before the proposal is represented as a complete executable evidence-bound fold: (1) review bytes not carried by the graph, production read_snapshot reads node.source only; (2) N4/N5 checks are floating, relabel; (3) the interface is not a quantitative rate; N6 may be recorded via the canonical-kernel interface", + "answered_by": "v1.3: review records and consumed sources as fingerprinted component nodes with required edges; external comments preserved in EXTERNAL_REVIEWS.md and labelled mutable; PROPAGATION two-commit cases; INTERFACE exact/numerical labels; interface scope narrowed with its premises as edges" + }, + { + "lane": "OpenAI/Codex (delegated)", + "id": 5360327058, + "kind": "engineering/interface review", + "at": "f2250bf", + "verdict": "ACCEPT the bounded historical inventory; AMEND the executable proposal; HOLD execution: (1) covering-proof loss does not reach the promoted regions; (2) TWO_SCALE_ADDENDUM, P15_REALIZED_COVERS, the interface's consumed C6-Palm/cap items are not tracked; (3) apply() drops explicit_limits and keeps stale notes; region-reporting complaint superseded on main; D2/D3/D4 comments directly authenticated", + "answered_by": "v1.3: covered_by edges; consumed-source component nodes; interface premises as edges to the live D1 node and cap component (Lemma 5.1 cited, not consumed); apply() carries explicit_limits, replacement notes and review_basis; PROPAGATION regressions; the superseded complaint recorded, not replayed" + }, + { + "lane": "OpenAI/Codex (bot review 5360253242)", + "id": "4139807545/4139807551/4139807558/4139807562/4139807567", + "kind": "review threads", + "at": "670e4ae", + "verdict": "region reporting (superseded on main); stale notes on apply; region-to-covering-proof dependency; authenticate external verdicts; track consumed source dependencies", + "answered_by": "v1.3 (all five); 4139807545 by Math-#151's hard_gate.py proved_reviewed_regions bucket, recorded in the region transition notes" + } + ], + "revision": { + "version": "v1.3", + "applies": [ + "xAI 5901912476 and 5360240245 recorded; #151-first ordering of the D4 flips made explicit", + "re-verified at ec6db8c (Math-#151 merged); live D4 duplicate bound (D4_DUPLICATE check, duplicate-drift mutant); HOLD precondition on Math-#151 recorded as met", + "OpenAI 5360320845 and 5360327058 and Codex threads 4139807545-67: eight review-record / consumed-source component nodes and sixteen required edges (edges_unchanged false); covered_by edges from regions; interface premises as edges to the live D1 node and cap component and its scope narrowed; apply() carries explicit_limits, replacement notes, review_basis; PROPAGATION check with nine two-commit cases and mutants region-unlinked / review-metadata-only; INTERFACE exact versus numerical labels; RN_COUNT_INTERFACE_REVIEW.md evidence labels; EXTERNAL_REVIEWS.md preserved and labelled mutable" + ], + "unchanged": "the eight classifications and every scope exclusion; the ten original inventory identities" + }, + "reverified_at": "ec6db8c (Math- main after Math-#151 merged 2026-09-30T00:56:58Z; the ten inventoried sources and the eight live nodes unchanged; math.d5-component.remote-window-proof live as PROVED_REVIEWED with fingerprint a332bae9bdc0106ce17047f7e0409cc3d94eb610a0c7b74ba5ba2d01a1620cb7 beside math.rn-fixed-remote-window at AUTHOR_SIDE_CANDIDATE)", + "live_duplicate": { + "node": "math.d5-component.remote-window-proof", + "since": "ec6db8c (Math-#151)", + "classification": "PROVED_REVIEWED", + "controlling": false, + "fingerprint": "a332bae9bdc0106ce17047f7e0409cc3d94eb610a0c7b74ba5ba2d01a1620cb7", + "source": "frontiers/remote_window_20260924/PROOF.md", + "component_of": "math.d5-pin-neighborhood-first-moment", + "review_basis": "STATUS D4 (main#76, external), nonauthor, ACCEPT, full", + "relation_to_this_record": "same bytes and same review as the math.rn-fixed-remote-window transition; the flip aligns the older node with it; collapsing the pair is a one-edge follow-up for the executing lane, not proposed here", + "check": "D4_DUPLICATE; mutant duplicate-drift" + }, + "proposed_graph_nodes": [ + { + "id": "math.align-component.rn-interface-review", + "layer": "D4", + "kind": "reading_rule_component", + "classification": "PROVED_REVIEWED", + "controlling": false, + "component_of": "math.rn-count-interface", + "component_role": "review_record", + "author_provider": "Anthropic (nonauthor; session 017Mi3hx)", + "fingerprint": "52d9038a3f27335d3c219babec785984e00b77f28d7cd7b390477c0bc6a749d1", + "source": "reviews/register_alignment_20260930/RN_COUNT_INTERFACE_REVIEW.md", + "scope": "ACCEPT at the logical-interface scope: (N1)-(N5) and the section 3 counterexamples self-contained; (N6)-(N7) and section 5 as formula-level implications conditional on the parent regression law / section 9 convention and the cap support source", + "review_basis": [ + { + "review": "reviews/register_alignment_20260930/RN_COUNT_INTERFACE_REVIEW.md", + "provider": "Anthropic", + "verdict": "ACCEPT at the logical-interface scope", + "depth": "full at that scope; exact rational checks plus labelled floating-point corroborations in alignment_check.py" + } + ], + "notes": "This packet's own review record; a nonauthor read by a second provider was not available at v1.3 (xAI 5360240245 did not re-read the note)." + }, + { + "id": "math.align-component.external-issue-reviews", + "layer": "D2", + "kind": "reading_rule_component", + "classification": "PROVED_REVIEWED", + "controlling": false, + "component_of": null, + "components_of": [ + "math.lifetime-remainder", + "math.side24-coefficient", + "math.rn-fixed-remote-window", + "math.p15-full-price" + ], + "component_role": "review_record_external", + "author_provider": "xAI/Grok 4.7 via Cursor (posted by cursor[bot]) and owner reconciliations; transcribed by Anthropic from the GitHub API read-back of 2026-09-30", + "fingerprint": "fa6677f16f688352f3fc9b1703d39324fe57a3b2bf61960591f524f858e99c9d", + "source": "reviews/register_alignment_20260930/EXTERNAL_REVIEWS.md", + "scope": "seven main-repository issue comments: main#67 5841270276 and 5841782206 (D2), main#65 5841269490 and 5841779222 (D3), main#76 5841783172 and 5841861362 (D4), main#74 5842112010 (D6), with comment id, URL, posting account, created_at, updated_at and body", + "review_basis": [ + { + "review": "main#67 comment 5841270276", + "provider": "xAI/Grok 4.7 via Cursor (session bc-81faa729)", + "verdict": "R1-R3 ACCEPT, R4 ACCEPT for (R12), R5-R6 IMPORTED-OPEN", + "created_at": "2026-09-25T23:59:05Z", + "updated_at": "2026-09-26T00:07:25Z" + }, + { + "review": "main#67 comment 5841782206", + "provider": "xAI/Grok 4.7 via Cursor (session bc-dfbce246)", + "verdict": "R5 and R6 ACCEPT; Theorem R accepted at its stated O(1) remainder scope", + "created_at": "2026-09-26T01:04:21Z", + "updated_at": "2026-09-26T01:07:56Z" + }, + { + "review": "main#65 comment 5841269490", + "provider": "xAI/Grok 4.7 via Cursor (run bc-be5dc8d9)", + "verdict": "C1-C6 VERIFIED; COEFFICIENT-CALC-REVIEWED / PARENT-IMPORTED-OPEN", + "created_at": "2026-09-25T23:58:59Z", + "updated_at": "2026-09-26T00:09:32Z" + }, + { + "review": "main#65 comment 5841779222", + "provider": "owner", + "verdict": "reconciliation; #65 closed as the coefficient-review work package", + "created_at": "2026-09-26T01:03:54Z" + }, + { + "review": "main#76 comment 5841783172", + "provider": "xAI/Grok via Cursor (session bc-593a8246; provider named by the owner's reconciliation)", + "verdict": "items 1-7 ACCEPT at fixed-rho/fixed-eta scope; not a full RN or 24-jet theorem", + "created_at": "2026-09-26T01:04:29Z", + "updated_at": "2026-09-26T01:12:36Z" + }, + { + "review": "main#76 comment 5841861362", + "provider": "owner", + "verdict": "reconciliation; ACCEPT on all seven interfaces; #76 closed as the fixed-remote REVIEW work package only", + "created_at": "2026-09-26T01:15:52Z" + }, + { + "review": "main#74 comment 5842112010", + "provider": "owner", + "verdict": "D6 ANALYTIC REVIEW COMPLETE; cross-provider nonauthor ACCEPT on all six slices (the review itself is reviews/p15_full_price_nonauthor_20260926/REVIEW.md); #74 closed", + "created_at": "2026-09-26T01:48:31Z" + } + ], + "authentication": "mutable external evidence, read back through the session's GitHub connector and transcribed; not byte-authenticated offline (stdlib checker, no network); OpenAI 5360327058 reports direct authentication of 5841270276, 5841782206, 5841269490 and 5841783172; claims/LANDING_CLAIMS.json cites the same issues as review objects", + "notes": "One node for one byte object (this file); loss-only: any edit to the record revalidates D2, D3, D4 and D6." + }, + { + "id": "math.align-component.side24-review-claude", + "layer": "D3", + "kind": "reading_rule_component", + "classification": "PROVED_REVIEWED", + "controlling": false, + "component_of": "math.side24-coefficient", + "component_role": "review_record", + "author_provider": "Anthropic (session 01NMeKE)", + "fingerprint": "258c414c46be93142ee552cfa4c32c03dd89b6bf7b0b470334f152e1e0a57eef", + "source": "reviews/side24_v1_coefficient_claude_20260929/REVIEW.md", + "scope": "second-provider read of coefficients/side24_v1/PROOF.md: ACCEPT at the arithmetic-enclosure scope", + "review_basis": [ + { + "review": "reviews/side24_v1_coefficient_claude_20260929/REVIEW.md", + "provider": "Anthropic", + "verdict": "ACCEPT at the arithmetic-enclosure scope", + "depth": "full at that scope" + } + ], + "notes": "Makes D3 the two-provider row (with main#65 5841269490)." + }, + { + "id": "math.align-component.pr22-annulus-review", + "layer": "D5", + "kind": "reading_rule_component", + "classification": "PROVED_REVIEWED", + "controlling": false, + "component_of": "math.rn-fixed-annulus-window", + "component_role": "review_record", + "author_provider": "xAI/Grok 4.7 via Cursor", + "fingerprint": "29a0c6d00ce739baf1d29a3163977d8e707e2079e216fba4fee3669cebec127d", + "source": "reviews/pr22_fixed_annulus_nonauthor_20260925/REVIEW.md", + "scope": "ACCEPT of FIXED_ANNULUS_CANDIDATE.md (blob 081abc13, SHA256 1fd9fe71) at the exact scoped theorem: covariance floor, cutoff r^{1/24}, rare target, conditioned C^3 sixth moment, inner two-scale stitching; PR28 and later blobs excluded", + "review_basis": [ + { + "review": "reviews/pr22_fixed_annulus_nonauthor_20260925/REVIEW.md", + "provider": "xAI/Grok 4.7 via Cursor", + "verdict": "ACCEPT at the exact scoped theorem", + "depth": "full" + } + ], + "notes": "Single nonauthor provider." + }, + { + "id": "math.align-component.two-scale-addendum", + "layer": "D5", + "kind": "reading_rule_component", + "classification": "PROVED_REVIEWED", + "controlling": false, + "component_of": "math.rn-fixed-annulus-window", + "component_role": "consumed_proof", + "author_provider": "OpenAI", + "fingerprint": "079f9399aef401d58749b3684f3acbb7f49ffdcbcac9f501b79e06c28a7f4e7d", + "source": "frontiers/rn_thin_tube_20260925/TWO_SCALE_ADDENDUM.md", + "scope": "S6-S21 and (S3)-(S5): the inner two-scale stitching input (S4) consumed by FIXED_ANNULUS_CANDIDATE.md for |t| < h_r on A <= |u| <= B (claims/LANDING_CLAIMS.json dependency two-scale-s6-s21)", + "review_basis": [ + { + "review": "reviews/replacement_20260925_pr19_pr21/TWO_SCALE_REVIEW.md", + "provider": "xAI/Grok 4.7 via Cursor", + "verdict": "ACCEPT S6-S21 and (S3)-(S5) at blob 89cae3a9", + "depth": "full" + }, + { + "review": "reviews/pr22_fixed_annulus_nonauthor_20260925/REVIEW.md", + "provider": "xAI/Grok 4.7 via Cursor", + "verdict": "inner two-scale stitching ACCEPT; the addendum read as the imported inner bound, not re-derived", + "depth": "gluing step" + } + ], + "notes": "The addendum's own review record is the next node; the addendum requires it." + }, + { + "id": "math.align-component.two-scale-review", + "layer": "D5", + "kind": "reading_rule_component", + "classification": "PROVED_REVIEWED", + "controlling": false, + "component_of": "math.align-component.two-scale-addendum", + "component_role": "review_record", + "author_provider": "xAI/Grok 4.7 via Cursor (session bc-ff620630)", + "fingerprint": "04cf4c986f29ac7ac33b3cc87feac23f3cf494e0c1b3bf4476e4e6666de46574", + "source": "reviews/replacement_20260925_pr19_pr21/TWO_SCALE_REVIEW.md", + "scope": "ACCEPT of TWO_SCALE_ADDENDUM.md S6-S21 and (S3)-(S5) at blob 89cae3a9 (Math- PR34, commit bc7d7545)", + "review_basis": [ + { + "review": "reviews/replacement_20260925_pr19_pr21/TWO_SCALE_REVIEW.md", + "provider": "xAI/Grok 4.7 via Cursor", + "verdict": "ACCEPT", + "depth": "full" + } + ], + "notes": "Single nonauthor provider." + }, + { + "id": "math.align-component.p15-review", + "layer": "D6", + "kind": "reading_rule_component", + "classification": "PROVED_REVIEWED", + "controlling": false, + "component_of": "math.p15-full-price", + "component_role": "review_record", + "author_provider": "xAI/Grok 4.7 via Cursor (Math- issue 57 lane)", + "fingerprint": "691ea0db5c0f073326c9f7208c9804c6f5d0daf92ba7467529c9d57e08b15eb7", + "source": "reviews/p15_full_price_nonauthor_20260926/REVIEW.md", + "scope": "ACCEPT of Theorem F on the realized disjoint capacity/clutter family (six slices) at blob 582180e4, SHA256 87521901; checked the setwise (P1), (P2), Theorem P2 dependency of P15_REALIZED_COVERS.md", + "review_basis": [ + { + "review": "reviews/p15_full_price_nonauthor_20260926/REVIEW.md", + "provider": "xAI/Grok 4.7 via Cursor", + "verdict": "ACCEPT Theorem F on the realized family", + "depth": "full" + } + ], + "notes": "Single nonauthor provider; owner reconciliation main#74 5842112010 is in the external record." + }, + { + "id": "math.align-component.p15-realized-covers-setwise", + "layer": "D6", + "kind": "reading_rule_component", + "classification": "PROVED_REVIEWED", + "controlling": false, + "component_of": "math.p15-full-price", + "component_role": "consumed_interface", + "author_provider": "OpenAI", + "fingerprint": "c0dbb821fb57b685a20cc321e4074456f39a9697f3104afd1f728e4732179bb9", + "source": "frontiers/three_fronts_20260924/P15_REALIZED_COVERS.md", + "scope": "setwise interfaces only: realized-family definition (P1), actual local restrictions (P2) and Theorem P2 full-block cover at K >= K_H(d), as consumed by Theorem F with d_i >= 2 (claims/LANDING_CLAIMS.json dependency p15-realized-covers:setwise-interfaces); the note's c_v <= p_v price theorem and any broader P15 statement are not included", + "review_basis": [ + { + "review": "reviews/p15_full_price_nonauthor_20260926/REVIEW.md", + "provider": "xAI/Grok 4.7 via Cursor", + "verdict": "read as the cited setwise dependency and checked for the local restriction and the full-block cover; the c_v <= p_v price theorem not accepted", + "depth": "setwise interfaces" + } + ], + "notes": "The realized-covers claim itself stays HOLD_WITH_DOMAIN in the claim manifest; only the consumed setwise interfaces are represented here, at the D6 review's scope." + } + ], + "proposed_graph_edges": [ + { + "from": "math.rn-count-interface", + "to": "math.align-component.rn-interface-review", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.rn-count-interface", + "to": "math.uniform-matrix-cap-lifetime", + "required": true, + "relation": "uses_parent_regression_law_and_section9_convention" + }, + { + "from": "math.rn-count-interface", + "to": "math.d1-component.marked-cylinder-cap", + "required": true, + "relation": "consumes_cap_support_scope_section5" + }, + { + "from": "math.lifetime-remainder", + "to": "math.align-component.external-issue-reviews", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.side24-coefficient", + "to": "math.align-component.external-issue-reviews", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.side24-coefficient", + "to": "math.align-component.side24-review-claude", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.rn-fixed-remote-window", + "to": "math.align-component.external-issue-reviews", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.rn-region.fixed-remote", + "to": "math.rn-fixed-remote-window", + "required": true, + "relation": "covered_by" + }, + { + "from": "math.rn-fixed-annulus-window", + "to": "math.align-component.pr22-annulus-review", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.rn-fixed-annulus-window", + "to": "math.align-component.two-scale-addendum", + "required": true, + "relation": "consumes_s6_s21_stitching_input" + }, + { + "from": "math.align-component.two-scale-addendum", + "to": "math.align-component.two-scale-review", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.rn-region.fixed-annulus-window", + "to": "math.rn-fixed-annulus-window", + "required": true, + "relation": "covered_by" + }, + { + "from": "math.p15-full-price", + "to": "math.align-component.external-issue-reviews", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.p15-full-price", + "to": "math.align-component.p15-review", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.p15-full-price", + "to": "math.align-component.p15-realized-covers-setwise", + "required": true, + "relation": "consumes_setwise_interfaces_P1_P2_TheoremP2" + }, + { + "from": "math.align-component.p15-realized-covers-setwise", + "to": "math.align-component.p15-review", + "required": true, + "relation": "requires_evidence" + } + ], + "nodes_added": 8, + "edges_added": 16, + "edges_removed": 0, + "external_evidence": { + "file": "reviews/register_alignment_20260930/EXTERNAL_REVIEWS.md", + "sha256": "fa6677f16f688352f3fc9b1703d39324fe57a3b2bf61960591f524f858e99c9d", + "node": "math.align-component.external-issue-reviews", + "status": "mutable external evidence, read back on 2026-09-30 through the session's GitHub connector and transcribed with comment id, URL, posting account, created_at, updated_at and body (Cursor footer HTML omitted); not byte-authenticated offline; OpenAI 5360327058 reports direct authentication of 5841270276, 5841782206, 5841269490 and 5841783172; this is not an additional review and not an additional provider" + } +} diff --git a/reviews/register_alignment_20260930/RECONCILIATION.md b/reviews/register_alignment_20260930/RECONCILIATION.md new file mode 100644 index 000000000..ece9655fd --- /dev/null +++ b/reviews/register_alignment_20260930/RECONCILIATION.md @@ -0,0 +1,270 @@ +# Register alignment — graph nodes for the accepted STATUS rows D2, D3, D4, D5-annulus and D6 + +**Object:** REGISTER-ALIGNMENT-20260930-v1. +**Reconciler:** Anthropic Claude, Claude Code session `session_017Mi3hxjaxV45x6zo6o1ee3`. +**Read at:** Math- `main` `aa288385af9392c509233c25a0f4012c9ba023e5` (30 September 2026); main `STATUS.md` at `7bbbdc9`. +Re-verified at `ec6db8c` (Math-#151 merged, 30 September 00:56Z): the ten inventoried sources and the eight live nodes of +§4 are unchanged; the live graph now also carries `math.d5-component.remote-window-proof` (`PROVED_REVIEWED`, fingerprint +`a332bae9…`, `review_basis` "STATUS D4 (main#76, external)") beside the still-`AUTHOR_SIDE_CANDIDATE` +`math.rn-fixed-remote-window`: the D4 dual-node inconsistency is now live, and the `D4_DUPLICATE` check binds it. +**Revision:** v1.1 records the two xAI reads of `670e4ae` and makes the Math-#151-first ordering of the D4 flips +explicit; transitions unchanged. v1.2 re-verifies at `ec6db8c` after Math-#151 merged, binds the now-live duplicate D4 +node (`D4_DUPLICATE` check, `duplicate-drift` mutant) and records that the HOLD's Math-#151 precondition is met; +transitions unchanged. v1.3 answers the two OpenAI AMEND reviews (5360320845, 5360327058) and the five Codex threads +(4139807545–67): review records and consumed sources become fingerprinted component nodes with required edges, regions +gain `covered_by` edges, `apply()` carries scope exclusions and replacement notes, a nine-case `PROPAGATION` check replays +two-commit source mutations through the production reverse-impact rule, the interface's promoted scope is narrowed to +self-contained inequalities plus conditional implications with its consumed premises as edges, the interface evidence +labels separate exact from floating-point checks, and the external issue comments are preserved in `EXTERNAL_REVIEWS.md` +and labelled as mutable evidence; the eight classifications are unchanged. +**Effect:** register reconciliation, **declarative only**. This record introduces **no new mathematical claim**. It binds +five objects that the register already lists as accepted to their exact bytes, quotes the nonauthor verdicts that +accepted them, records that their live graph nodes still carry the pre-review classification, and proposes the node +transitions in machine-readable form (`PROPOSED_TRANSITIONS.json`, `"executed": false`). It carries one bounded +nonauthor review (`RN_COUNT_INTERFACE_REVIEW.md`) of the RN count-interface note, the only unreviewed required premise +in these chains. Execution of any `GRAPH.json` change is a separate act for a **non-Claude lane**. `lemma_closed`, +prizes and premises are untouched. Scientific effect: NONE. + +## 0. Exposure, stated first + +- Every lane shares one GitHub account; no organizational independence is claimed anywhere below. +- I authored none of the six sources inventoried in §2 (all six are OpenAI / ChatGPT notes). I authored + `reviews/d1_chain_reconciliation_20260928/` (Math-#126), the record that moved the D1 parent node + `math.uniform-matrix-cap-lifetime` to `PROVED_REVIEWED`; the D2 and D3 nodes require that node. I authored + `reviews/d5_reconciliation_20260929/` (Math-#138), executed by Math-#151, which handles the mesoscopic, pin-collision + and intermediate regions; none of those is re-proposed here. +- Reviews cited: D2, D4, the D5 fixed annulus and D6 each rest on **one** nonauthor provider, xAI / Grok 4.7 running in + Cursor cloud sessions on 25–26 September. D3 has two providers (xAI; Anthropic, session `01NMeKE…`, in-repo record). + The count-interface review in §3 is by this session. No Cursor agent is restarted or contacted (owner stop of + 27 September); only their published comments are cited, with the byte identities they state. +- **Precedent and caveat.** The D1 node moved to `PROVED_REVIEWED` on xAI plus Anthropic reads. Four of the five flips + proposed here rest on a single provider. The executing lane may ask for a second read before flipping any of them; + this record binds what exists and says so per row. STATUS already records all five as accepted at scope. + +**Verdicts on this record.** xAI inventory read 5901912476 and xAI/Grok (Lucas) review 5360240245, both at `670e4ae`: +**ACCEPT as a declarative inventory of already-accepted STATUS scopes** (classification lag, not new mathematics; no +edge, node, controlling, prize or `lemma_closed` change; single-provider caveat correctly stated; the D3 row is the +two-provider one), with **HOLD on execution** until Math-#151 is on main so that the D4 dual-node inconsistency is +resolved in one direction, and with the single-provider rows recorded as such by the executing lane. Neither read +re-read the count-interface note: that flip rests on this packet's Anthropic review alone. Both say: do not touch +witness-collision here, do not enlarge any scope, do not treat this as a prize or Boolean fold. This record agrees +on every point; v1.1 makes the #151-first ordering explicit in §4 and `execution_order`. Math-#151 merged at `ec6db8c` +(30 September 00:56Z; main#207 closed at 00:57Z), so the first HOLD condition is met; the second, that the executing +lane record the single-provider rows as such, is already stated per row in §4 and in `PROPOSED_TRANSITIONS.json` and is +that lane's to carry out. + +OpenAI source-custody / RN-interface review 5360320845 and OpenAI-Codex engineering review 5360327058 (both at `f2250bf`, +with Codex threads 4139807545/51/58/62/67 at `670e4ae`): **the historical classification lag and the logical-interface +inequalities are sound at their stated scopes; AMEND the executable proposal; HOLD execution.** Their findings: the +acceptance evidence lived only in `review_sources` metadata, which the production loss-only audit +(`git_transition_audit.read_snapshot`, `node.source` only) never sees; a covering-proof change did not reach the promoted +regions; the annulus's `TWO_SCALE_ADDENDUM.md`, D6's `P15_REALIZED_COVERS.md` and the interface's consumed cap / parent +items were not tracked; `apply()` dropped `explicit_limits` and kept stale notes; the (N4)/(N5) checks were floating +point while labelled exact; external issue-comment verdicts were quoted, not preserved. v1.3 answers each (§4, §6; the +eight classifications and scope exclusions unchanged). The region-reporting complaint (4139807545) is superseded on main +since `ec6db8c` (`hard_gate.d4_region_complement` has a `proved_reviewed_regions` bucket) and is not replayed. Neither +OpenAI read is a new mathematical acceptance of the six sources; both keep the single-provider caveat. + +## 1. The lag + +The main `STATUS.md` accepted-scope table (rows D1–D4, D6) and `PROOF_INDEX.md` "Reviewed scoped results" list these +objects as reviewed. The downstream graph does not: + +| Object | STATUS / PROOF_INDEX | Live node | Live classification | Live fingerprint | +|---|---|---|---|---| +| D2 Theorem R | accepted, `O(1)` remainder scope | `math.lifetime-remainder` | `AUTHOR_SIDE_CANDIDATE` (in-node `review_disposition: ACCEPT`) | SHA256 `380b7d0a…` = current | +| D3 SIDE24 coefficient | accepted, `d = 2, 3` arithmetic | `math.side24-coefficient` | `AUTHOR_SIDE_CANDIDATE` (in-node `ACCEPT`) | SHA256 `c06daccc…` = current | +| D4 fixed-remote theorem | accepted, fixed `ρ`, `η` | `math.rn-fixed-remote-window` | `AUTHOR_SIDE_CANDIDATE`; region `math.rn-region.fixed-remote` `COVERED_BY_CANDIDATE` | SHA256 `a332bae9…` = current | +| D5 fixed-annulus window | PROOF_INDEX reviewed row | `math.rn-fixed-annulus-window` | `AUTHOR_SIDE_CANDIDATE` (in-node `ACCEPT`); region `math.rn-region.fixed-annulus-window` `COVERED_BY_CANDIDATE` | git blob `081abc13…` = current | +| D6 P15 full price | accepted, realized family | `math.p15-full-price` | `AUTHOR_SIDE_CANDIDATE`, note "review open" | label `full-price-20260924` | +| (premise) RN count interface | — | `math.rn-count-interface` | `AUTHOR_SIDE_CANDIDATE`, unreviewed | SHA256 `aa993f52…` = current | + +Why it matters: the hard gate's rule is "Only `PROVED_REVIEWED` satisfies a still-required positive premise" +(`frontiers/downstream_gate_20260925/README.md`). As long as these nodes stay author-side, the fixed-remote region is +"covered by candidate" only, and D2, D3, D4 and D6 satisfy no downstream premise, although their STATUS rows are +accepted. The register is also internally inconsistent on D4: since `ec6db8c` the live graph carries +`math.d5-component.remote-window-proof` (Math-#151, executing the D5 proposal of Math-#138) for the same bytes as +`PROVED_REVIEWED`, with `review_basis` "STATUS D4 (main#76, external), nonauthor, ACCEPT, full", beside +`math.rn-fixed-remote-window` at `AUTHOR_SIDE_CANDIDATE`. The same review either suffices for those bytes or it does +not; this record proposes that it does, on the older live node, so that the two agree; collapsing the pair is a +separate one-edge follow-up for the executing lane (§7). The `D4_DUPLICATE` check binds the duplicate's classification, +fingerprint, source and review basis to the D4 transition. + +## 2. Bindings: what each review bound, and what the bytes are now + +All six sources, and the two consumed sources and the addendum's review added in v1.3, are unchanged since their landing +commits. Identities of all fifteen inventoried files (six sources, the D1 parent, four in-repo reviews, two consumed +sources, this packet's two review records) are checked by `alignment_check.py` (`IDENTITIES`); the quoted verdict lines +are checked as substrings where the review is in this repository (`VERDICTS`). The issue-comment reviews are preserved +as a transcribed read-back in `EXTERNAL_REVIEWS.md` (comment id, URL, posting account, timestamps, body) and are +labelled there as mutable external evidence that an offline check cannot re-authenticate; OpenAI 5360327058 reports +having directly authenticated the D2, D3 and D4 comments. + +| Object | Source now | Review binding (quoted) | Verdict (quoted) | +|---|---|---|---| +| D2 | `frontiers/three_fronts_20260924/LIFETIME_REMAINDER.md`, 17734 B, SHA256 `380b7d0abdb0fe2de5a6564565af9560d3f1b1ce22fd5538927db0c52f4f3a4a`, blob `247b3ecf80bfbe896948d5d489b2d5842a81c481` | main#67 5841270276: "blob `247b3ecf80bfbe896948d5d489b2d5842a81c481`, 17734 bytes, SHA256 `380b7d0a…`"; 5841782206 re-read "and hashed" the same blob | 5841270276: "R1 — ACCEPT … R2 — ACCEPT … R3 — ACCEPT … R4 — ACCEPT for (R12) … R5 — IMPORTED-OPEN … R6 — IMPORTED-OPEN"; 5841782206: "R5 and R6 are **ACCEPT**. Theorem R is accepted at its stated O(1) remainder scope." The imports are mapped to #63 comment 5841570965 (D1-A…E), the review that the D1 reconciliation binds. | +| D3 | `coefficients/side24_v1/PROOF.md`, 10272 B, SHA256 `c06daccc4ba4b9168522b9888b76a7d599934fc3b91bd753ee5d492262917769`, blob `44b66f04f89fcd87383b3603fa69f1feb64cdddd` | main#65 5841269490: "commit `e329fba1…`, directory `coefficients/side24_v1/`", "`PROOF.md` 10272 bytes, SHA256 `c06daccc…`" | "All six coefficient interfaces check out. The disposition is **COEFFICIENT-CALC-REVIEWED / PARENT-IMPORTED-OPEN**." Second provider: `reviews/side24_v1_coefficient_claude_20260929/REVIEW.md` (blob `665d1683f33a7180957923c3cb2abce8ade235d1`): "Overall: **ACCEPT at the arithmetic-enclosure scope**". Owner reconciliation 5841779222 closed the package. The parent import is now the live `PROVED_REVIEWED` D1 node. | +| D4 | `frontiers/remote_window_20260924/PROOF.md`, 18355 B, SHA256 `a332bae9bdc0106ce17047f7e0409cc3d94eb610a0c7b74ba5ba2d01a1620cb7`, blob `b383bfcc88ec4ad497dff01fb6640e429ba24a84` | main#76 5841783172: "at commit `191ea7d541a486736ba7bbddfd4eac25a6c4567b` … 18355 bytes, SHA256 `a332bae9…`" | "This accepts only the fixed-ρ and fixed-η interfaces below. It does not accept a full RN or 24-jet theorem." Items 1–7: conditional covariance ACCEPT; three determinant factors and `O(k r⁵)` numerator ACCEPT; original endpoint normalizer ACCEPT; contact kernel and `O(k r⁴ ‖E‖)` remainder ACCEPT; fixed-separation factorial moments ACCEPT; selector/window mapping ACCEPT for the §7 implication only; uncovered complement ACCEPT as stated. Owner 5841861362: "returns ACCEPT on all seven fixed-rho/fixed-eta interfaces … Closing #76 as the fixed-remote REVIEW work package only." | +| D5 annulus | `frontiers/rn_thin_tube_20260925/FIXED_ANNULUS_CANDIDATE.md`, 17646 B, SHA256 `1fd9fe7141e464fd1c09ebf0318d8a701729c9c61ea24f73f7e20a9cf10c552b`, blob `081abc13c5e66342c13df2af2bd6b114f320486f` | `reviews/pr22_fixed_annulus_nonauthor_20260925/REVIEW.md` (blob `1f153966dae48d10574db0d272f75d08ca3a8b23`): "Immutable commit `2804dc1d…`", "Blob `081abc13…`", "SHA256 `1fd9fe71…`" | rows "Covariance floor … **ACCEPT**", "Cutoff `r^{1/24}` **ACCEPT**", "Rare target in the full joint gradient/height density **ACCEPT**", "Conditioned `C^3` sixth moment **ACCEPT**", at the exact scoped theorem; PR28 and later blobs excluded. | +| D6 | `frontiers/full_price_20260924/PROOF.md`, 11352 B, SHA256 `87521901ca8e5405b4d1e47f1deb1cd0326affbd6f5967b53c4178590da993f9`, blob `582180e41dca0ad815ad0f18574df42040912149` | `reviews/p15_full_price_nonauthor_20260926/REVIEW.md` (blob `07db19f826763b8faa7414ba2e403d9c45bc0b6e`): "Blob `582180e4…`", "SHA256 `87521901…`" | six rows **ACCEPT** (hazard transform and separate concavity; odd-majority worst case; global hazard direction and independence; full-block cover; sharpness; demand-one boundary). Owner 5842112010: "D6 ANALYTIC REVIEW COMPLETE … Closing #74 as the D6 review work package". | +| premise | `frontiers/three_fronts_20260924/RN_COUNT_INTERFACE.md`, 8938 B, SHA256 `aa993f5217bd70e6d1060402d121ab659f6582a098e29042c67585a345a8e3ab`, blob `371fd6d17920f2eb3b1c5ec30297acf6daf1d385` | this packet, `RN_COUNT_INTERFACE_REVIEW.md` | ACCEPT at the logical-interface scope (§3); its consumed formulation was reconstructed inside the D4 review (items 2–3). | +| D1 parent (premise of D2, D3) | `imports/lifetime_parent_20260925/UNIFORM_MATRIX_CAP_AND_LIFETIME.md`, 40261 B, SHA256 `9350ad6eaba6626b93c3dedeef9e2ff816e5cdf1c8318e85fb27499141c84bc7` | live node `math.uniform-matrix-cap-lifetime`, `PROVED_REVIEWED`, four required reading-rule components (Math-#126) | not re-reviewed; checked live (`BASELINE`). | +| consumed by D5 annulus | `frontiers/rn_thin_tube_20260925/TWO_SCALE_ADDENDUM.md`, 15902 B, SHA256 `079f9399aef401d58749b3684f3acbb7f49ffdcbcac9f501b79e06c28a7f4e7d`, blob `89cae3a9734f2ec7172cd0b6b0b3af3ddd355d73` | `reviews/replacement_20260925_pr19_pr21/TWO_SCALE_REVIEW.md` (10073 B, SHA256 `04cf4c98…`, blob `89882516`): "blob `89cae3a9…`, 15902 bytes, SHA256 `079f9399…`"; the pr22 review: "Read as the imported inner bound, not re-derived: `TWO_SCALE_ADDENDUM.md` blob `89cae3a9…`" | S6–S21 and (S3)–(S5) **ACCEPT** (xAI, Math- PR34); pr22 row "Inner two-scale stitching **ACCEPT**". Component nodes `…two-scale-addendum`, `…two-scale-review` (§4). | +| consumed by D6 | `frontiers/three_fronts_20260924/P15_REALIZED_COVERS.md`, 11467 B, SHA256 `c0dbb821fb57b685a20cc321e4074456f39a9697f3104afd1f728e4732179bb9`, blob `173881916ccd0e738bdb41279e835e78e520fcbc` | the p15 review: "Read as the cited setwise dependency, and checked for the local restriction and the full-block cover: … SHA256 `c0dbb821…`. That is the digest named in the proof. The check uses (P1), (P2), and Theorem P2 there. It does not accept that note's `c_v<=p_v` price theorem" | setwise interfaces only, at the D6 review's scope. Component node `…p15-realized-covers-setwise` (§4). | +| external comments (D2, D3, D4, D6) | `reviews/register_alignment_20260930/EXTERNAL_REVIEWS.md` (this packet) | seven comments with id, account, `created_at`, `updated_at`, body; the four `cursor[bot]` reviews and three owner reconciliations | preserved read-back; mutable external evidence, labelled. Component node `…external-issue-reviews` (§4). | + +## 3. The count-interface note + +`RN_COUNT_INTERFACE_REVIEW.md` reviews `RN-COUNT-INTERFACE-20260924-v1` at the scope the note itself states: the Hölder +implications (N1)–(N3), the two counterexamples of its §3 and the layer-cake bound (N5), the marked Kac–Rice formula +(N6)–(N7) as a formula, and the support statement of §5. Verdict: **ACCEPT at the logical-interface scope**; it is not +an expected-count rate and is not treated as one. The finite parts are checked in `INTERFACE` in two labelled parts: exact rational arithmetic (Hölder on finite rational +distributions for `p = 2, 3`; the exponent identity of (N2); the (N3) identity; the single-`p` sharp example at +`r = 2^(−pm)`, where `E N^p = 1` and `E N = r^(3−3/p)` exactly) and floating-point numerical corroborations of arguments +proved in the review (the (N4) example's moments and the located maximum of `(t+1)^p e^(−3t)`; the identity +`∫ min(q, A e^(−t/B)) dt = B q [1 + log(A/q)]` by Simpson quadrature; the uniform tail `P(N_r > t) ≤ e³ e^(−3t)` of the +(N4) example on a grid); OpenAI 5360320845 item 2 asked for exactly this separation. The note's consumed premises are the +parent's regression law and §9 Borel-mark convention (live node `math.uniform-matrix-cap-lifetime`, with its four +reading-rule components) and the cap support source of §5 (live node `math.d1-component.marked-cylinder-cap`, SHA256 +`0bf922b9…`, the digest the note quotes); both are required edges of the proposal, and the promoted scope is narrowed to +(N1)–(N5) with the counterexamples as self-contained statements and (N6)–(N7), §5 as conditional implications at formula +level. A later rigorous statement of (N6) is Lemma 5.1 of `frontiers/c6_palm_route_20260929/PROOF.md` (Math-#145), +cited for the reader and not consumed. + +## 4. Proposed transitions + +Eight node transitions and, since v1.3, the evidence that carries them, represented in the graph itself: eight +fingerprinted review-record / consumed-source component nodes and sixteen required edges (`PROPOSED_TRANSITIONS.json`: +`transitions`, `proposed_graph_nodes`, `proposed_graph_edges`; `edges_unchanged: false`). The change of packaging answers +OpenAI 5360320845 item 1, OpenAI 5360327058 items 1–2 and Codex threads 4139807558/4139807562/4139807567: the production +loss-only audit (`git_transition_audit.read_snapshot`) reads `node.source` only, so acceptance evidence and consumed +sources that live only in `review_sources` metadata would never revalidate a promoted object when they change. The eight +classifications and every scope exclusion are unchanged from v1.0. + +| Node | Current | Proposed | Scope (STATUS row) | Review sources | Required premises after | +|---|---|---|---|---|---| +| `math.rn-count-interface` | `AUTHOR_SIDE_CANDIDATE` | `PROVED_REVIEWED` | (N1)–(N5) and the §3 counterexamples as self-contained probability statements; (N6)–(N7) and §5 as formula-level implications conditional on the parent's regression law / §9 convention and on the cap support source | this packet (`RN_COUNT_INTERFACE_REVIEW.md`, a component node); main#76 items 2–3 | `math.uniform-matrix-cap-lifetime` and `math.d1-component.marked-cylinder-cap` (both live `PROVED_REVIEWED`; the note's consumed premises); `math.align-component.rn-interface-review` | +| `math.lifetime-remainder` | `AUTHOR_SIDE_CANDIDATE` | `PROVED_REVIEWED` | Theorem R, existential `O(1)` remainder | main#67 5841270276, 5841782206 | D1 (live `PROVED_REVIEWED`); `math.align-component.external-issue-reviews` | +| `math.side24-coefficient` | `AUTHOR_SIDE_CANDIDATE` | `PROVED_REVIEWED` | coefficient arithmetic, `d = 2, 3` | main#65 5841269490; in-repo Anthropic record | D1; `…external-issue-reviews`; `…side24-review-claude` | +| `math.rn-fixed-remote-window` | `AUTHOR_SIDE_CANDIDATE` | `PROVED_REVIEWED` | fixed `ρ`, `η`, between-pin window | main#76 5841783172, 5841861362 | `math.rn-count-interface`; `…external-issue-reviews` | +| `math.rn-region.fixed-remote` | `COVERED_BY_CANDIDATE` | `PROVED_REVIEWED` | the D4 region | as the covering node | `math.rn-fixed-remote-window` (new required `covered_by` edge) | +| `math.rn-fixed-annulus-window` | `AUTHOR_SIDE_CANDIDATE` (blob fingerprint) | `PROVED_REVIEWED` (SHA256 fingerprint) | `d = 2` fixed scaled annulus, window | `reviews/pr22_…/REVIEW.md` | `math.rn-count-interface`; `…pr22-annulus-review`; `…two-scale-addendum` (the S6–S21 stitching input, which itself requires `…two-scale-review`) | +| `math.rn-region.fixed-annulus-window` | `COVERED_BY_CANDIDATE` | `PROVED_REVIEWED` | the covering node's scope | as the covering node | `math.rn-fixed-annulus-window` (new required `covered_by` edge) | +| `math.p15-full-price` | `AUTHOR_SIDE_CANDIDATE` (label fingerprint) | `PROVED_REVIEWED` (SHA256 fingerprint) | realized family, `d_i ≥ 2` | `reviews/p15_…/REVIEW.md`; main#74 5842112010 | `…external-issue-reviews`; `…p15-review`; `…p15-realized-covers-setwise` ((P1), (P2), Theorem P2 setwise only, which itself requires `…p15-review`) | + +Component nodes (`kind: reading_rule_component`, `PROVED_REVIEWED`, `controlling: false`, `fingerprint` = SHA256 of the +source; one node per byte identity; none duplicates a source the live graph already carries with a fingerprint): + +| Node | Source | Role | Provider | Consumed by | +|---|---|---|---|---| +| `math.align-component.rn-interface-review` | `reviews/register_alignment_20260930/RN_COUNT_INTERFACE_REVIEW.md` (this packet) | review record | Anthropic (nonauthor) | `math.rn-count-interface` | +| `math.align-component.external-issue-reviews` | `reviews/register_alignment_20260930/EXTERNAL_REVIEWS.md` (this packet: seven issue comments transcribed with id, account, timestamps and body; mutable external evidence, labelled) | external review record | xAI/Grok via Cursor (posted by `cursor[bot]`) and owner; recorded by Anthropic | D2, D3, D4, D6 | +| `math.align-component.side24-review-claude` | `reviews/side24_v1_coefficient_claude_20260929/REVIEW.md` | review record | Anthropic (other session) | D3 | +| `math.align-component.pr22-annulus-review` | `reviews/pr22_fixed_annulus_nonauthor_20260925/REVIEW.md` | review record | xAI | annulus | +| `math.align-component.two-scale-addendum` | `frontiers/rn_thin_tube_20260925/TWO_SCALE_ADDENDUM.md` (`079f9399…`, blob `89cae3a9`) | consumed proof: the S6–S21 stitching input ((S4) on `A ≤ |u| ≤ B`) | OpenAI | annulus | +| `math.align-component.two-scale-review` | `reviews/replacement_20260925_pr19_pr21/TWO_SCALE_REVIEW.md` (`04cf4c98…`, blob `89882516`) | review record of the addendum (S6–S21 and (S3)–(S5) ACCEPT) | xAI | `…two-scale-addendum` | +| `math.align-component.p15-review` | `reviews/p15_full_price_nonauthor_20260926/REVIEW.md` | review record | xAI | D6, `…p15-realized-covers-setwise` | +| `math.align-component.p15-realized-covers-setwise` | `frontiers/three_fronts_20260924/P15_REALIZED_COVERS.md` (`c0dbb821…`, blob `17388191`) | consumed interface: (P1), (P2), Theorem P2 setwise at `K ≥ K_H(d)` only, as the D6 review checked them; the note's `c_v ≤ p_v` price theorem is not included | OpenAI | D6 | + +These are exactly the support dependencies the canonical claim manifest records for the annulus (`two-scale-s6-s21`) +and for the full-price theorem (`p15-realized-covers:setwise-interfaces`). The interface's two consumed premises are +the live D1 node (regression law `Q`, §9 Borel-mark convention, read with its four reading-rule components) and the live +cap component (`0bf922b9…`, the SHA256 the note quotes for its §5 support statement); the (N6) cross-reference to the +C6 Palm route's Lemma 5.1 in the review is for the reader and is not consumed. + +Every proposed node keeps `controlling: false`; each candidate node's `fingerprint` becomes the SHA256 of its source in +§2, and `apply()` carries `scope`, `explicit_limits`, a replacement `notes`, `review_disposition`, `review_sources` and a +structured `review_basis` onto the node, so no promoted node keeps a "review open" or "covered by candidate only" note +(Codex 4139807551; OpenAI 5360327058 item 3). Region nodes keep `coverage_source` and gain a required `covered_by` edge +to their covering node, so that a change to the covering proof reaches the region in `reverse_impact_between` (Codex +4139807558; OpenAI 5360327058 item 1). No `hist.*`, `eng.*` or `regional.*` node moves; no live node other than the +eight changes; no live edge is removed; every added edge leaves one of this record's objects. The order in +`execution_order` creates the component nodes and edges first, then the premise, then each region after its covering +node; the D4 theorem node and its region are executed only after Math-#151 is on main (satisfied at `ec6db8c`): the D4 +bytes are now carried by two live nodes on the same review, and the flip aligns the older one with the newer one; the +executing lane may then collapse `math.d5-component.remote-window-proof` onto the live node or keep both (xAI +5901912476, 5360240245). STATUS, PROOF_INDEX, SELECTOR_REGION and the catalog need no edit for this record: they +already say what the graph is being aligned to. + +`alignment_check.py` applies the proposal to a copy of the live graph and replays it through the hard gate's own +validators (`validate_graph_fail_closed`, `closure_report`, `reverse_impact_between`, imported from +`frontiers/downstream_gate_20260925/hard_gate.py`): the proposed graph is well formed, no node is controlling, +`gate_ok` holds, and the loss-only reverse-impact proposal names exactly the changed nodes and their dependents. +`PROPAGATION` then runs nine two-commit mutations through `reverse_impact_between` with source snapshots in the shape of +`git_transition_audit.read_snapshot` (proof edits reach their regions and consumers; a deleted review record and an +edited external-review record reach the accepted objects and their dependents; consumed-source edits reach their +consumers; an unrelated edit and a no-op reach none of the eight), the guarantee OpenAI 5360320845 asked to be tested +rather than inferred from old-versus-new GRAPH metadata. + +## 5. What is not proposed + +- The mesoscopic, pin-collision and intermediate regions: Math-#151. The witness-collision region and its residual: + Math-#160. `math.rn-mesoscopic-reduction` (legacy PR7 route): unchanged, still `AUTHOR_SIDE_REDUCTION`. +- Any second-provider reads. Where a row rests on one provider the row says so; the lane executing the flip decides + whether that is enough, as it was not for D1. +- Any controlling flag, promotion, `lemma_closed`, prize, STATUS, PROOF_INDEX, catalog or selector edit. + +## 6. Checks + +`alignment_check.py` (stdlib only, run from the repository root): +- **IDENTITIES.** All fifteen inventoried files (the six sources, the D1 parent, the four in-repo reviews, the two + consumed sources, and this packet's two review records) exist as regular files, no symlink on their paths, stated + SHA256 and blob. +- **VERDICTS.** The quoted verdict rows and binding lines of the in-repo reviews (pr22, p15, side24, two-scale), the + object headers of the sources, the D4 sentence that consumes the interface, the interface note's (N1)/(N4)/(N5) + displays, the five PROOF_INDEX rows, the interface review's overall verdict and evidence labels, and the seven comment + ids with their verdict lines and the mutability label in `EXTERNAL_REVIEWS.md` are present as substrings. +- **BASELINE.** Each transition's live node exists with exactly the recorded current classification, fingerprint, + kind and source; the D1 node is `PROVED_REVIEWED` with its four reading-rule components `PROVED_REVIEWED`. +- **TRANSITIONS.** `declarative` true, `executed` false, `edges_unchanged` false; every proposed classification is + `PROVED_REVIEWED` with `controlling: false`, a non-empty scope, explicit limits, replacement notes and at least one + review source; every candidate node's fingerprint equals the SHA256 of its inventoried source; every component node + is a `reading_rule_component`, `PROVED_REVIEWED`, non-controlling, fingerprinted to its inventoried source, with a + role, a provider, a review basis and a consumer, one node per byte identity and none for bytes the live graph already + carries; every added edge is well formed, new, and leaves one of this record's objects; applied to a copy of the live + graph, no live node other than the eight changes, no live edge is removed, every flipped node's required premises (the + live D1 node and cap component, the interface, the component nodes) are `PROVED_REVIEWED`, every region requires its + covering node, and every applied node carries its `explicit_limits`, its replacement `notes` and a `review_basis`. +- **GATE.** The proposed graph passes the hard gate's `validate_graph_fail_closed`; `closure_report` gives `gate_ok` + with no illegal controlling node; `reverse_impact_between(live, proposed)` runs and its impacted set (the eight nodes, + the eight component nodes and their dependents) is recorded. +- **PROPAGATION.** Nine two-commit cases on the proposed graph with source snapshots in the shape of + `git_transition_audit.read_snapshot`: a D4 proof edit reaches the fixed-remote region and the mesoscopic consumer; an + annulus proof edit reaches its region; deleting the interface review record reaches the interface, D4, the annulus and + both regions; editing the external-review record reaches D2, D3, D4, D6 and the fixed-remote region; editing the + two-scale addendum reaches the annulus and its region; editing the realized-covers source reaches D6; a D4 fingerprint + edit reaches the region; an unrelated edit reaches none of the eight; a no-op impacts nothing. +- **INTERFACE.** The finite content of §3, in two labelled parts: exact rational checks (Hölder for `p = 2, 3` on + finite spaces, the (N2) exponent identity, the (N3) identity, the sharp-`p` example at `r = 2^(−pm)`, the integer + monotonicity in (N4)) and floating-point numerical corroborations (the (N4) grid maximum, the (N5) Simpson quadrature + at three parameter points, the (N4) example's uniform tail on a grid). The analytic arguments are in the review; the + numerical part corroborates, it does not prove. +- **NEGATIVES.** Real filesystem faults on a temporary copy of the inventory (delete, change one byte, symlink, symlink + parent of the D4 proof) are rejected. +- **D4_DUPLICATE.** The live graph carries `math.d5-component.remote-window-proof` as `PROVED_REVIEWED`, + non-controlling, with the same SHA256 fingerprint and source as the D4 transition and as the inventory, a `review_basis` + citing main#76 with verdict ACCEPT, `component_of` `math.d5-pin-neighborhood-first-moment`; and the older live node + `math.rn-fixed-remote-window` still carries that fingerprint at `AUTHOR_SIDE_CANDIDATE`, the lag this record aligns. + +Twelve mutants must fail: `allow-symlink`, `no-hash`, `stale-fingerprint`, `drop-review-source`, `controlling-true`, +`executed-flag`, `skip-interface-premise`, `holder-reversed`, `baseline-drift`, `duplicate-drift`, `region-unlinked` +(the `covered_by` edges removed before the propagation replay: proof edits no longer reach the regions) and +`review-metadata-only` (the review-record nodes and their edges removed before the replay, leaving the citations as +metadata only: a deleted or edited review record no longer reaches its accepted object). + +## 7. Relation to other lanes + +- **Math-#151 (Codex, D5 fold; merged at `ec6db8c`, 30 September 00:56Z, final head `609e559`):** landed as proposed, + so the live graph carries `math.d5-component.remote-window-proof` (`PROVED_REVIEWED`, `component_of` + `math.d5-pin-neighborhood-first-moment`, `review_basis` main#76) for the D4 bytes beside `math.rn-fixed-remote-window` + (`AUTHOR_SIDE_CANDIDATE`); the coordination note (comment 5901742635) was not taken up before the merge. This record's + D4 flip aligns the two; collapsing the component node to a `required` edge onto the live node is a one-edge follow-up + for the executing lane, not proposed here. +- **Math-#160 (this session, C6 reconciliation):** already references the live D4 node with supporting edges; nothing + there changes. +- **OpenAI reviews 5360320845 and 5360327058; Codex review 5360253242 (threads 4139807545–67):** answered by v1.3 (§0, + §4, §6); the region-reporting thread is superseded on main since `ec6db8c` and not replayed. The single-provider caveat + and the HOLD on execution stand until the executing lane decides. +- **Math-#163 (navigation refresh):** availability index only; disjoint. +- **main#207 (closed 30 September 00:57Z, after Math-#151 merged):** the delivery note for this record is comment + 5901889845. The executing lane for this record remains non-Claude; any new coordination thread is that lane's to open. diff --git a/reviews/register_alignment_20260930/RESULTS.json b/reviews/register_alignment_20260930/RESULTS.json new file mode 100644 index 000000000..6702db536 --- /dev/null +++ b/reviews/register_alignment_20260930/RESULTS.json @@ -0,0 +1,99 @@ +{ + "checks": { + "BASELINE": true, + "D4_DUPLICATE": true, + "GATE": true, + "IDENTITIES": true, + "INTERFACE": true, + "NEGATIVES": true, + "PROPAGATION": true, + "TRANSITIONS": true, + "VERDICTS": true + }, + "component_nodes": 8, + "edges_added": 16, + "gate": { + "changed_nodes": [ + "math.align-component.external-issue-reviews", + "math.align-component.p15-realized-covers-setwise", + "math.align-component.p15-review", + "math.align-component.pr22-annulus-review", + "math.align-component.rn-interface-review", + "math.align-component.side24-review-claude", + "math.align-component.two-scale-addendum", + "math.align-component.two-scale-review", + "math.lifetime-remainder", + "math.p15-full-price", + "math.rn-count-interface", + "math.rn-fixed-annulus-window", + "math.rn-fixed-remote-window", + "math.rn-region.fixed-annulus-window", + "math.rn-region.fixed-remote", + "math.side24-coefficient" + ], + "impacted": [ + "math.align-component.external-issue-reviews", + "math.align-component.p15-realized-covers-setwise", + "math.align-component.p15-review", + "math.align-component.pr22-annulus-review", + "math.align-component.rn-interface-review", + "math.align-component.side24-review-claude", + "math.align-component.two-scale-addendum", + "math.align-component.two-scale-review", + "math.lifetime-remainder", + "math.p15-full-price", + "math.rn-count-interface", + "math.rn-fixed-annulus-window", + "math.rn-fixed-remote-window", + "math.rn-mesoscopic-reduction", + "math.rn-region.fixed-annulus-window", + "math.rn-region.fixed-remote", + "math.rn-selector-region-crosswalk", + "math.side24-coefficient" + ], + "reverse_impact_keys": [ + "changed_nodes", + "context_changed", + "graph", + "impacted", + "meaning", + "promotion_permission", + "source_snapshots_supplied", + "traversal_edges" + ] + }, + "interface_evidence": { + "exact_rational": [ + "(N1) Holder p=2,3 on finite rational spaces", + "(N2) exponent identity", + "(N3) conditional-mean identity", + "sharp-p example at r=2^-pm", + "(N4) integer monotonicity of ceil(t)" + ], + "numerical_corroboration_floating_point": [ + "(N4) grid maximum of (t+1)^p e^-3t", + "(N5) Simpson quadrature at three parameter points", + "(N4) example uniform tail on a grid" + ], + "results": { + "exact": true, + "numerical_corroboration": true + } + }, + "inventory_files": 15, + "object": "REGISTER-ALIGNMENT-20260930-v1", + "passed": true, + "propagation": { + "annulus-proof-edit-reaches-region": true, + "d4-fingerprint-edit-reaches-region": true, + "d4-proof-edit-reaches-region-and-consumer": true, + "external-review-record-edit-reaches-d2-d3-d4-d6": true, + "interface-review-deleted-reaches-interface-consumers-regions": true, + "no-op-impacts-nothing": true, + "realized-covers-edit-reaches-d6": true, + "two-scale-addendum-edit-reaches-annulus-and-region": true, + "unrelated-edit-leaves-the-eight-untouched": true + }, + "scope": "identity, verdict-row, live-baseline, transition-shape, hard-gate replay, two-commit propagation, interface arithmetic (exact and numerical parts labelled), filesystem-negative and live D4-duplicate checks; no mathematics is re-proved; nothing is written", + "transitions": 8 +} diff --git a/reviews/register_alignment_20260930/RN_COUNT_INTERFACE_REVIEW.md b/reviews/register_alignment_20260930/RN_COUNT_INTERFACE_REVIEW.md new file mode 100644 index 000000000..7e7049e2b --- /dev/null +++ b/reviews/register_alignment_20260930/RN_COUNT_INTERFACE_REVIEW.md @@ -0,0 +1,56 @@ +# Nonauthor review — RN count interface note (D4 premise) + +**Object reviewed:** `frontiers/three_fronts_20260924/RN_COUNT_INTERFACE.md` (RN-COUNT-INTERFACE-20260924-v1), author +OpenAI / ChatGPT; on Math- `main` `aa288385af9392c509233c25a0f4012c9ba023e5`; 8938 bytes, SHA256 +`aa993f5217bd70e6d1060402d121ab659f6582a098e29042c67585a345a8e3ab`, git blob `371fd6d17920f2eb3b1c5ec30297acf6daf1d385`; unchanged since its landing commit `8a13ee9` +(24 September 2026). Live graph node `math.rn-count-interface` carries this SHA256 as fingerprint. +**Revision:** v1.3 (30 September 2026) corrects the evidence labels after OpenAI review 5360320845 item 2: the checks +that use floating point are now called numerical corroborations, the rational ones exact; and names the note's consumed +premises (item 3 there; OpenAI 5360327058 item 2). Verdicts unchanged. +**Reviewer:** Anthropic Claude, Claude Code session `session_017Mi3hxjaxV45x6zo6o1ee3`. Different provider from the +author. Same GitHub account as every lane; no organizational independence is claimed. +**Exposure:** I authored none of the three-fronts notes. I authored the remote-collision packet and the C6L packet, +both downstream of the fixed-remote theorem that consumes this note; neither is an input here. +**Scope:** the logical interface only, as the note itself states: the implications (N1)–(N3), the counterexamples of +§3 with (N4)–(N5), the marked Kac–Rice expression (N6)–(N7) as a formula, and the support statement of §5. No rate, +no RN numerical certificate and no evaluation of the Gaussian triple integral are claimed by the note or accepted +here. Scientific effect: NONE. +**Promoted scope (v1.3):** (N1)–(N5) and the §3 counterexamples as self-contained probability statements; (N6)–(N7) +and §5 as formula-level implications conditional on the note's two consumed premises, the parent's regression law `Q` +with its §9 Borel-mark convention (live node `math.uniform-matrix-cap-lifetime`, read with its four reading-rule +components) and the cap support source of §5 (live node `math.d1-component.marked-cylinder-cap`, SHA256 `0bf922b9…`, the +digest the note quotes); both are required edges in `PROPOSED_TRANSITIONS.json`. Nothing quantitative. + +## Verdicts + +| Item | Statement | Verdict | +|---|---|---| +| (N1) | `E[N 1_E] ≤ (E N^p)^(1/p) P(E)^(1−1/p)` for `p > 1` | **ACCEPT**: Hölder with exponents `p` and `p/(p−1)` applied to `N · 1_E`. Exact rational check for `p = 2` (Cauchy–Schwarz form `(E[N1_E])² ≤ E[N²] P(E)`) and `p = 3` (`(E[N1_E])³ ≤ E[N³] P(E)²`) on finite distributions in `alignment_check.py` (`INTERFACE`). | +| (N2) | `E N^p ≤ A r^(−β)` gives `E[N 1_E] ≤ A^(1/p) C^(1−1/p) r^([3(p−1)−β]/p)` | **ACCEPT**: substitution into (N1); the exponent `3 − 3/p − β/p` is the moment convention, as the note says. | +| (N3) | `E[N 1_E] = q E[N | E]`, `q = P(E) > 0` | **ACCEPT**: definition of conditional expectation; the two remarks (sufficiency of a bounded conditional mean; equivalence only under a lower comparison `q ≥ c r³`) follow. | +| §3 (N4) | `U` uniform, `E_r = {U ≤ r³}`, `N_r = ⌈log(1/r)⌉ 1_{E_r}`: `E N_r / r³ → ∞` while `sup_r E N_r^p < ∞` for every fixed `p` | **ACCEPT**: `P(E_r) = r³`; `E N_r^p = ⌈t⌉^p e^(−3t) ≤ (t+1)^p e^(−3t)` with `t = log(1/r) ≥ 1`, whose supremum over `t ≥ 1` is finite (the logarithmic derivative `−3 + p/(t+1)` is eventually negative). The argument is the log-derivative; `INTERFACE` corroborates it numerically, in floating point, on `r = e^(−t)`, `t = 1, …, 12`, and on a grid against the located maximum (labelled `numerical_corroboration`, not exact). | +| §3 sharp `p` | `N_r = ⌈r^(−3/p)⌉ 1_{E_r}`: `E N_r^p ≤ 2^p` for `r ≤ 1`, `E N_r ≍ r^(3−3/p)` | **ACCEPT**: `r^(−3/p) ≥ 1` gives `⌈r^(−3/p)⌉ ≤ 2 r^(−3/p)`. Checked exactly at `r = 2^(−pm)`, where `r^(−3/p) = 2^(3m)` is an integer, `E N_r^p = 1` and `E N_r = r^(3−3/p)` exactly. | +| (N5) | `P(N > t) ≤ A e^(−t/B)`, `A ≥ 1`, gives `E[N 1_E] ≤ ∫ min(q, A e^(−t/B)) dt = B q [1 + log(A/q)]` | **ACCEPT**: layer cake `E[N 1_E] = ∫_0^∞ P(N > t, E) dt ≤ ∫ min(q, P(N > t)) dt`; the crossover is `t_0 = B log(A/q)` and the two pieces are `q t_0` and `A B e^(−t_0/B) = B q`. The (N4) example has the uniform tail `P(N_r > t) ≤ e³ e^(−3t)` (`A = e³`, `B = 1/3`), so the logarithmic loss in (N5) is not removable from a tail hypothesis alone, as the note says. The identity is proved by the antiderivative; `INTERFACE` corroborates it by floating-point Simpson quadrature at three parameter points and checks the tail comparison on a floating-point grid (numerical corroboration, not exact). | +| §4 (N6) | marked Kac–Rice for `E_Q^W N_B` with the endpoint weight as a field mark and the event indicator inside the conditional expectation | **ACCEPT as a formula at the note's stated level of rigour** (bounded continuous cylinder marks, extension of finite measures, truncation of `W_r`, monotone convergence; compact `B` off the pins, exhaustion), conditional on the note's consumed premise: the parent's regression law `Q` and its §9 Borel-mark convention (live node `math.uniform-matrix-cap-lifetime`, read with its four reading-rule components; a required edge in the proposal). Its fixed-remote instance is the reviewed formula (12)–(14) of the D4 proof, accepted in main#76 comment 5841783172 items 2–3. A later rigorous statement of the same identity with the kernel convention fixed is Lemma 5.1 of `frontiers/c6_palm_route_20260929/PROOF.md` (Math-#145); it is cited for the reader and is not consumed here. Nothing quantitative is asserted by (N6) and nothing quantitative is accepted here. | +| §4 (N7) | an `A r⁵` enclosure of the numerator with `Z_r ≥ z_* r²` gives `E_Q^W N_B ≤ (A/z_*) r³` | **ACCEPT**: division; the note correctly separates this from the cap probability argument (`E_Q[W_r 1_{G^c}]`). | +| §5 | support on the rare event only inside the deterministic cap cylinder; remote regions need their own support statement or the count `N 1_{G^c}` | **ACCEPT as a scope statement**; it consumes the cap source `0bf922b9…` for the containment `{M, S}` on `G_r` (the live node `math.d1-component.marked-cylinder-cap` carries exactly that SHA256; a required edge in the proposal) and adds nothing to it. | +| §6 | completion test: (N7) or a uniform conditional mean with the support relation; finite moments give (N2), tails give (N5) | **ACCEPT** as the logical summary of the above. | + +**Overall: ACCEPT at the logical-interface scope.** The note proves exactly what it claims and no more: correct +inequalities and counterexamples, and the form of the full-pin Kac–Rice expression that the fixed-remote theorem later +evaluated. It is not an expected-count rate and is not treated as one. Evidence labels: the (N1)–(N3) and sharp-`p` +checks in `INTERFACE` are exact rational arithmetic; the (N4) grid, the (N5) quadrature and the tail grid are floating-point +numerical corroborations of arguments proved above, not exact checks. + +## Relation to its consumers +- `math.rn-fixed-remote-window` (D4) reads the interface as the formulation it completes: PROOF §1 "identified a + three-determinant integral whose unnormalized numerator must be O(r^5), but did not bound it. This note supplies + that bound"; §7 "Equation (14) now supplies it for every fixed remote region and the entire BETWEEN-PIN HEIGHT WINDOW". + The D4 review reconstructed the three determinant factors, the `O(k r⁵)` numerator and the original normalizer + (items 2–3), i.e. the consumed content of (N6)–(N7). +- `math.rn-fixed-annulus-window` (D5 fixed annulus) uses the same normalized three-determinant intensity with the + original normalizer (its (A8) and §5 ledger), reviewed in `reviews/pr22_fixed_annulus_nonauthor_20260925/REVIEW.md`. + +## Not established here +No rate, no RN or 24-jet certificate, no `ENV-RESCOV` or historical carrier, no register transition. This file is a +review record; the proposal that consumes it is `RECONCILIATION.md` in this directory. diff --git a/reviews/register_alignment_20260930/SOURCE_FILES.json b/reviews/register_alignment_20260930/SOURCE_FILES.json new file mode 100644 index 000000000..e49e54aee --- /dev/null +++ b/reviews/register_alignment_20260930/SOURCE_FILES.json @@ -0,0 +1,47 @@ +{ + "schema": 1, + "object": "REGISTER-ALIGNMENT-20260930-v1", + "scientific_effect": "NONE", + "disposition": "PROPOSAL_FOR_A_NON_CLAUDE_LANE", + "declarative": true, + "executed": false, + "base": "aa288385af9392c509233c25a0f4012c9ba023e5", + "files": [ + { + "path": "PROPOSED_TRANSITIONS.json", + "bytes": 40189, + "sha256": "dad87926726d8a86d5ff33d1d03eecafa9b05bf9e4c0eaeb08dd67104efc695d", + "git_blob": "1c1bea9ba98ca212159fa907e2bdeda1ff863d36" + }, + { + "path": "RECONCILIATION.md", + "bytes": 32725, + "sha256": "0baf1c4e3c48ca3e2bb4eaeb419ee8ba368f082447f38f638fd10ce023c5249f", + "git_blob": "ece9655fd80ea51c18d7b1b2410d4c073854db89" + }, + { + "path": "RN_COUNT_INTERFACE_REVIEW.md", + "bytes": 8115, + "sha256": "52d9038a3f27335d3c219babec785984e00b77f28d7cd7b390477c0bc6a749d1", + "git_blob": "7e7049e2b5e96e51394d44683d61c9d0e03b9323" + }, + { + "path": "RESULTS.json", + "bytes": 3452, + "sha256": "cbbff25994c22c55fd49c59bc2748af1c6ef128793a34880613cf7cb1d9162df", + "git_blob": "6702db536f00ec5689ab398c003f46a91b645d7b" + }, + { + "path": "alignment_check.py", + "bytes": 31556, + "sha256": "eb1888ea57416f87fbfa4692b6c07b20261c97bd08ce926aee7ec6fca5486502", + "git_blob": "cd110b0cfb2cfaf6f11e7405d99e0070c816a224" + }, + { + "path": "EXTERNAL_REVIEWS.md", + "bytes": 29877, + "sha256": "fa6677f16f688352f3fc9b1703d39324fe57a3b2bf61960591f524f858e99c9d", + "git_blob": "2be80e35bce1ffc90d1f7a0675ad5e8830ddbd28" + } + ] +} diff --git a/reviews/register_alignment_20260930/alignment_check.py b/reviews/register_alignment_20260930/alignment_check.py new file mode 100644 index 000000000..cd110b0cf --- /dev/null +++ b/reviews/register_alignment_20260930/alignment_check.py @@ -0,0 +1,585 @@ +"""Checks for REGISTER-ALIGNMENT-20260930-v1 (RECONCILIATION.md, PROPOSED_TRANSITIONS.json, RN_COUNT_INTERFACE_REVIEW.md). + +Standard library only. Run from the repository root: python -B -S reviews/register_alignment_20260930/alignment_check.py +Checks: IDENTITIES, VERDICTS, BASELINE, TRANSITIONS, GATE, PROPAGATION, INTERFACE, NEGATIVES, D4_DUPLICATE. No mathematics +is re-proved; the proposed graph is replayed through the downstream hard gate's own validators, and two-commit source +mutations through its reverse-impact rule. Nothing is written to the repository. +""" +import argparse +import copy +import hashlib +import importlib.util +import json +import math +import os +import pathlib +import shutil +import sys +import tempfile +from fractions import Fraction as F + +MUTANTS = ("allow-symlink", "no-hash", "stale-fingerprint", "drop-review-source", "controlling-true", "executed-flag", + "skip-interface-premise", "holder-reversed", "baseline-drift", "duplicate-drift", "region-unlinked", + "review-metadata-only") +MUT = None +HERE = "reviews/register_alignment_20260930" +GRAPH = "frontiers/downstream_gate_20260925/GRAPH.json" +HARD_GATE = "frontiers/downstream_gate_20260925/hard_gate.py" +D1 = "math.uniform-matrix-cap-lifetime" +D4_DUP = "math.d5-component.remote-window-proof" +D4_NODE = "math.rn-fixed-remote-window" +IFACE = "math.rn-count-interface" +D4 = "frontiers/remote_window_20260924/PROOF.md" +INVENTORY = { + "frontiers/three_fronts_20260924/LIFETIME_REMAINDER.md": [ + 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"04cf4c986f29ac7ac33b3cc87feac23f3cf494e0c1b3bf4476e4e6666de46574", + "8988251631cab8e65eb2b01a08f7fc593b018570" + ], + "frontiers/three_fronts_20260924/P15_REALIZED_COVERS.md": [ + "c0dbb821fb57b685a20cc321e4074456f39a9697f3104afd1f728e4732179bb9", + "173881916ccd0e738bdb41279e835e78e520fcbc" + ], + "reviews/register_alignment_20260930/RN_COUNT_INTERFACE_REVIEW.md": [ + "52d9038a3f27335d3c219babec785984e00b77f28d7cd7b390477c0bc6a749d1", + "7e7049e2b5e96e51394d44683d61c9d0e03b9323" + ], + "reviews/register_alignment_20260930/EXTERNAL_REVIEWS.md": [ + "fa6677f16f688352f3fc9b1703d39324fe57a3b2bf61960591f524f858e99c9d", + "2be80e35bce1ffc90d1f7a0675ad5e8830ddbd28" + ] +} +VERDICTS = { + "frontiers/three_fronts_20260924/LIFETIME_REMAINDER.md": ["**Object:** LIFETIME-BOUNDED-REMAINDER-20260924-v1."], + "frontiers/three_fronts_20260924/RN_COUNT_INTERFACE.md": [ + "**Object:** RN-COUNT-INTERFACE-20260924-v1.", + "E[N_r 1_Er] <= (E N_r^p)^(1/p) P(E_r)^(1-1/p).", + "N_r=ceil(log(1/r)) 1_Er.", + "= B q[1+log(A/q)]."], + "coefficients/side24_v1/PROOF.md": ["Object: SIDE24-COEFFICIENT-D23-20260924-v1."], + "frontiers/remote_window_20260924/PROOF.md": [ + "**Object:** RN-FIXED-REMOTE-WINDOW-20260924-v1.", + "Equation (14) now supplies it for every fixed remote region and the entire BETWEEN-PIN HEIGHT WINDOW."], + "frontiers/rn_thin_tube_20260925/FIXED_ANNULUS_CANDIDATE.md": ["**Object:** D5-FIXED-ANNULUS-STITCH-20260925-v1."], + "frontiers/full_price_20260924/PROOF.md": ["**Object:** P15-FULL-TRANSFORMED-PRICE-20260924-v1."], + "reviews/pr22_fixed_annulus_nonauthor_20260925/REVIEW.md": [ + "| Blob | `081abc13c5e66342c13df2af2bd6b114f320486f` |", + "| SHA256 | `1fd9fe7141e464fd1c09ebf0318d8a701729c9c61ea24f73f7e20a9cf10c552b` |", + "| Cutoff `r^{1/24}` | **ACCEPT** |", + "| Inner two-scale stitching | **ACCEPT** |", + "`TWO_SCALE_ADDENDUM.md` blob `89cae3a9734f2ec7172cd0b6b0b3af3ddd355d73`, 15902 bytes"], + "reviews/p15_full_price_nonauthor_20260926/REVIEW.md": [ + "| Blob | `582180e41dca0ad815ad0f18574df42040912149` |", + "| SHA256 | `87521901ca8e5405b4d1e47f1deb1cd0326affbd6f5967b53c4178590da993f9` |", + "| 1. Coordinatewise hazard transform, separate concavity, chord, `p=0,1` | **ACCEPT** |", + "SHA256 `c0dbb821fb57b685a20cc321e4074456f39a9697f3104afd1f728e4732179bb9`. That is the digest named in the proof.", + "| 4. Full-block cover, same palette, realized family | **ACCEPT** |"], + "reviews/side24_v1_coefficient_claude_20260929/REVIEW.md": [ + "c06daccc4ba4b9168522b9888b76a7d599934fc3b91bd753ee5d492262917769", + "Overall: **ACCEPT at the arithmetic-enclosure scope**"], + "PROOF_INDEX.md": [ + "- D2 lifetime remainder: proof [frontiers/three_fronts_20260924/LIFETIME_REMAINDER.md]", + "- D3 SIDE24 coefficient: proof [coefficients/side24_v1/PROOF.md]", + "- D4 fixed-remote RN theorem: proof [frontiers/remote_window_20260924/PROOF.md]", + "- D5 fixed-annulus height-window fallback: proof [frontiers/rn_thin_tube_20260925/FIXED_ANNULUS_CANDIDATE.md]", + "- D6 P15 full price theorem: proof [frontiers/full_price_20260924/PROOF.md]"], + "frontiers/rn_thin_tube_20260925/TWO_SCALE_ADDENDUM.md": ["**Object:** D5-TWO-SCALE-20260925-v1."], + "reviews/replacement_20260925_pr19_pr21/TWO_SCALE_REVIEW.md": [ + "blob `89cae3a9734f2ec7172cd0b6b0b3af3ddd355d73`, 15902 bytes, SHA256 `079f9399aef401d58749b3684f3acbb7f49ffdcbcac9f501b79e06c28a7f4e7d`", + "| S6 | **ACCEPT** |"], + "frontiers/three_fronts_20260924/P15_REALIZED_COVERS.md": ["**Object:** P15-REALIZED-COVERS-20260924-v1."], + HERE + "/RN_COUNT_INTERFACE_REVIEW.md": [ + "**Overall: ACCEPT at the logical-interface scope.**", + "numerical corroborations of arguments proved above, not exact checks"], + HERE + "/EXTERNAL_REVIEWS.md": [ + "issuecomment-5841270276", "issuecomment-5841782206", "issuecomment-5841269490", "issuecomment-5841779222", + "issuecomment-5841783172", "issuecomment-5841861362", "issuecomment-5842112010", + "R5 and R6 are **ACCEPT**. Theorem R is accepted at its stated O(1) remainder scope.", + "All six coefficient interfaces check out. The disposition is **COEFFICIENT-CALC-REVIEWED / PARENT-IMPORTED-OPEN**.", + "This accepts only the fixed-ρ and fixed-η interfaces below. It does not accept a full RN or 24-jet theorem.", + "D6 ANALYTIC REVIEW COMPLETE", + "An issue comment is a mutable external object"], +} + + +def git_blob(data): + return hashlib.sha1(b"blob %d\0" % len(data) + data).hexdigest() + + +def no_symlink_on_path(root, path): + parts = pathlib.PurePosixPath(path).parts + return not any((root / pathlib.PurePosixPath(*parts[:i])).is_symlink() for i in range(1, len(parts) + 1)) + + +def identities_ok(root): + for path, (sha, blob) in INVENTORY.items(): + p = root / path + if not os.path.lexists(p): + return False + if MUT != "allow-symlink" and not no_symlink_on_path(root, path): + return False + if not p.is_file(): + return False + data = p.read_bytes() + if MUT != "no-hash" and (hashlib.sha256(data).hexdigest() != sha or git_blob(data) != blob): + return False + return True + + +def check_verdicts(root): + for path, needles in VERDICTS.items(): + text = (root / path).read_text(encoding="utf-8") + if not all(n in text for n in needles): + return False + return True + + +def load_spec(root): + spec = json.loads((root / HERE / "PROPOSED_TRANSITIONS.json").read_text(encoding="utf-8")) + if MUT == "executed-flag": + spec["executed"] = True + if MUT == "skip-interface-premise": + spec["transitions"] = [t for t in spec["transitions"] if t["node"] != IFACE] + if MUT == "drop-review-source": + for t in spec["transitions"]: + if t["node"] == D4_NODE: + t["proposed"]["review_sources"] = [] + if MUT == "controlling-true": + for t in spec["transitions"]: + if t["node"] == D4_NODE: + t["proposed"]["controlling"] = True + if MUT == "stale-fingerprint": + for t in spec["transitions"]: + if t["node"] == D4_NODE: + t["proposed"]["fingerprint"] = "0" * 64 + if MUT == "baseline-drift": + for t in spec["transitions"]: + if t["node"] == D4_NODE: + t["current"]["classification"] = "PROVED_REVIEWED" + return spec + + +def check_baseline(root, spec): + live = json.loads((root / GRAPH).read_text(encoding="utf-8"))["nodes"] + ok = True + for t in spec["transitions"]: + n = live.get(t["node"]) + if not isinstance(n, dict): + return False + ok &= n.get("classification") == t["current"]["classification"] + ok &= n.get("fingerprint") == t["current"]["fingerprint"] + ok &= n.get("kind") == t["kind"] and n.get("controlling") is False + if t["kind"] == "candidate": + ok &= n.get("source") == t["proposed"]["source"] + d1 = live.get(D1, {}) + ok &= d1.get("classification") == "PROVED_REVIEWED" and d1.get("fingerprint") == INVENTORY[ + "imports/lifetime_parent_20260925/UNIFORM_MATRIX_CAP_AND_LIFETIME.md"][0] + rr = d1.get("reading_rule", []) + ok &= len(rr) == 4 and all(live.get(x, {}).get("classification") == "PROVED_REVIEWED" for x in rr) + return bool(ok) + + +def apply(spec, graph): + """The proposal applied to a copy of the live graph: the eight flips with their scope exclusions and replacement + notes, plus the review-record / consumed-source component nodes and the required edges that carry the evidence.""" + new = copy.deepcopy(graph) + for t in spec["transitions"]: + n = new["nodes"][t["node"]] + p = t["proposed"] + n["classification"] = p["classification"] + n["controlling"] = p["controlling"] + n["fingerprint"] = p["fingerprint"] + if p.get("source"): + n["source"] = p["source"] + n["scope"] = p["scope"] + n["explicit_limits"] = p["explicit_limits"] + n["notes"] = p["notes"] + n["review_disposition"] = p["review_disposition"] + n["review_sources"] = [r["ref"] for r in p["review_sources"]] + n["review_basis"] = [{"review": r["ref"], "provider": r.get("provider", "unstated"), "verdict": r.get("verdict", "")} + for r in p["review_sources"]] + if p.get("coverage_source"): + n["coverage_source"] = p["coverage_source"] + for c in spec["proposed_graph_nodes"]: + new["nodes"][c["id"]] = {k: v for k, v in c.items() if k != "id"} + new["edges"] = list(new["edges"]) + [dict(e) for e in spec["proposed_graph_edges"]] + return new + +def check_transitions(root, spec): + graph = json.loads((root / GRAPH).read_text(encoding="utf-8")) + ok = spec.get("declarative") is True and spec.get("executed") is False and spec.get("edges_unchanged") is False + ids = [t["node"] for t in spec["transitions"]] + ok &= len(ids) == len(set(ids)) and len(ids) >= 1 + for t in spec["transitions"]: + p = t["proposed"] + ok &= p["classification"] == "PROVED_REVIEWED" and p["controlling"] is False + ok &= bool(p.get("scope")) and bool(p.get("explicit_limits")) and bool(p.get("notes")) + ok &= len(p.get("review_sources", [])) >= 1 + if t["kind"] == "candidate": + ok &= p.get("source") in INVENTORY and p["fingerprint"] == INVENTORY[p["source"]][0] + else: + ok &= t["kind"] == "region" and p.get("coverage_source") in ids + ok &= not t["node"].startswith(("hist.", "eng.", "regional.")) + # component nodes: one per byte identity, fingerprinted to the inventory, PROVED_REVIEWED evidence records, + # none for bytes the live graph already carries with a fingerprint (Codex 4139312869 on Math-#160) + comps = spec["proposed_graph_nodes"] + cids = [c["id"] for c in comps] + live_fp_sources = {n.get("source") for n in graph["nodes"].values() + if isinstance(n, dict) and n.get("fingerprint") and n.get("source")} + ok &= len(cids) == len(set(cids)) and not (set(cids) & set(graph["nodes"])) and len(comps) == spec["nodes_added"] + ok &= len({c["source"] for c in comps}) == len(comps) + for c in comps: + ok &= c["kind"] == "reading_rule_component" and c["classification"] == "PROVED_REVIEWED" and c["controlling"] is False + ok &= c["source"] in INVENTORY and c["fingerprint"] == INVENTORY[c["source"]][0] + ok &= c["source"] not in live_fp_sources + ok &= bool(c.get("component_role")) and bool(c.get("author_provider")) and len(c.get("review_basis", [])) >= 1 + consumers = c.get("components_of") or [c.get("component_of")] + ok &= all(x in ids + cids for x in consumers) and len(consumers) >= 1 + edges_new = spec["proposed_graph_edges"] + known = set(graph["nodes"]) | set(cids) + live_keys = {(e["from"], e["to"], e["relation"]) for e in graph["edges"]} + seen = set() + for e in edges_new: + ok &= {"from", "to", "required", "relation"} <= set(e) and type(e["required"]) is bool + ok &= e["from"] in known and e["to"] in known and bool(e["relation"].strip()) + key = (e["from"], e["to"], e["relation"]) + ok &= key not in seen and key not in live_keys + seen.add(key) + ok &= e["from"] in ids or e["from"] in cids # every added edge leaves one of this record's objects + ok &= len(edges_new) == spec["edges_added"] + if not ok: + return False, None + new = apply(spec, graph) + nodes = new["nodes"] + edges = new["edges"] + ok &= edges[:len(graph["edges"])] == graph["edges"] and len(edges) == len(graph["edges"]) + len(edges_new) + ok &= all(graph["nodes"][k] == nodes[k] for k in graph["nodes"] if k not in ids) # only the eight live nodes change + for t in spec["transitions"]: + nid = t["node"] + req = [e["to"] for e in edges if e["from"] == nid and e["required"] is True] + ok &= all(nodes[d]["classification"] == "PROVED_REVIEWED" for d in req) + ok &= sorted(req) == sorted(t["required_premises_after"]) + if t["kind"] == "region": + ok &= t["proposed"]["coverage_source"] in req # a region depends on its covering node + ok &= nodes[t["proposed"]["coverage_source"]]["classification"] == "PROVED_REVIEWED" + n = nodes[nid] + ok &= n.get("explicit_limits") == t["proposed"]["explicit_limits"] and n.get("notes") == t["proposed"]["notes"] + ok &= "review open" not in n["notes"] and "candidate only" not in n["notes"] + ok &= isinstance(n.get("review_basis"), list) and len(n["review_basis"]) >= 1 + for c in comps: # component nodes' own required premises + req = [e["to"] for e in edges if e["from"] == c["id"] and e["required"] is True] + ok &= all(nodes[d]["classification"] == "PROVED_REVIEWED" for d in req) + return bool(ok), new + +def load_hard_gate(root): + hg_spec = importlib.util.spec_from_file_location("hard_gate", root / HARD_GATE) + hg = importlib.util.module_from_spec(hg_spec) + hg_spec.loader.exec_module(hg) + return hg + + +def check_gate(root, spec, new): + if new is None: + return False, {} + hg = load_hard_gate(root) + old = json.loads((root / GRAPH).read_text(encoding="utf-8")) + try: + hg.validate_graph_fail_closed(new) + rep_new = hg.closure_report(new) + rep_old = hg.closure_report(old) + ri = hg.reverse_impact_between(old, new) + except Exception: + return False, {} + ok = rep_new.get("gate_ok") is True and not rep_new.get("illegal_controlling") + ok &= rep_old.get("gate_ok") is True + ok &= not any(n.get("controlling") for n in new["nodes"].values()) + changed = sorted([t["node"] for t in spec["transitions"]] + [c["id"] for c in spec["proposed_graph_nodes"]]) + imp = ri.get("impacted") if isinstance(ri, dict) else None + names = [] + if isinstance(imp, list): + for x in imp: + names.append(x if isinstance(x, str) else str(x.get("node") or x.get("id") or x)) + # loss-only rule: every changed node is itself in the impacted set + ok &= isinstance(ri, dict) and set(changed) <= set(names) + return bool(ok), {"changed_nodes": changed, "impacted": sorted(set(names)), "reverse_impact_keys": sorted(ri.keys()) if isinstance(ri, dict) else []} + + +def check_interface(): + """Finite content of RN_COUNT_INTERFACE_REVIEW.md: exact rational checks, and floating-point corroborations + labelled as such (OpenAI 5360320845 item 2).""" + ok = True + num = True + le = (lambda a, b: a >= b) if MUT == "holder-reversed" else (lambda a, b: a <= b) + # (N1) on finite rational spaces, p = 2 and p = 3 (Cauchy-Schwarz / Holder in power form) + spaces = [([F(1, 4)] * 4, [0, 1, 3, 7], [1, 0, 1, 0]), ([F(1, 2), F(1, 3), F(1, 6)], [2, 5, 11], [1, 1, 0]), + ([F(1, 8), F(3, 8), F(1, 2)], [0, 0, 9], [0, 0, 1]), ([F(9, 10), F(1, 10)], [0, 13], [0, 1])] + for probs, N, E in spaces: + assert sum(probs) == 1 + ene = sum(p * n * e for p, n, e in zip(probs, N, E)) + pe = sum(p * e for p, e in zip(probs, E)) + m2 = sum(p * n * n for p, n in zip(probs, N)) + m3 = sum(p * n ** 3 for p, n in zip(probs, N)) + ok &= le(ene ** 2, m2 * pe) and le(ene ** 3, m3 * pe ** 2) + if pe > 0: # (N3) + ok &= ene == pe * (ene / pe) + # (N2) exponent: (3(p-1) - beta)/p == 3 - 3/p - beta/p + for p in (2, 3, 5): + for beta in (F(0), F(1, 2), F(3)): + ok &= F(3 * (p - 1), 1) / p - beta / p == 3 - F(3, p) - beta / p + # (N4), NUMERICAL (floating point): r = e^-t, t = 1..12: E N / r^3 = ceil(t) increases; ceil(t)^p e^-3t <= (t+1)^p e^-3t, + # and the grid maximum of (t+1)^p e^-3t stays below the located critical value. The proof is the log-derivative argument. + for p in (1, 2, 4, 7): + vals = [math.ceil(t) ** p * math.exp(-3 * t) for t in range(1, 13)] + bound = [(t + 1) ** p * math.exp(-3 * t) for t in range(1, 13)] + num &= all(v <= b + 1e-15 for v, b in zip(vals, bound)) + tmax = max(1.0, p / 3 - 1) # critical point of (t+1)^p e^{-3t} + sup = (tmax + 1) ** p * math.exp(-3 * tmax) + grid = [(t / 100 + 1) ** p * math.exp(-3 * (t / 100)) for t in range(100, 400000, 7)] + num &= max(grid) <= sup + 1e-9 and math.isfinite(sup) + ok &= all(math.ceil(t) > math.ceil(t - 1) for t in range(2, 13)) # E N_r / r^3 -> infinity along the grid (exact integers) + # sharp p: r = 2^{-p m}: E N^p = 1, E N = r^{3-3/p} exactly + for p in (2, 3, 4): + for m in (1, 2, 3): + r = F(1, 2 ** (p * m)) + n_r = 2 ** (3 * m) # = ceil(r^{-3/p}) exactly + ok &= n_r ** p * r ** 3 == 1 and le(F(1), F(2 ** p)) and n_r * r ** 3 == F(1, 2 ** (3 * m * (p - 1))) + ok &= n_r * r ** 3 == r ** 3 / r ** F(3, 1) * F(1, 2 ** (3 * m * (p - 1))) # r^{3-3/p} = 2^{-3m(p-1)} + # (N5), NUMERICAL (floating point): int_0^inf min(q, A e^{-t/B}) dt = B q (1 + log(A/q)), q <= A; Simpson quadrature at + # three parameter points corroborates the antiderivative identity proved in the review + for (A, B, q) in ((1.0, 1.0, 0.1), (20.0, 0.5, 0.001), (3.0, 2.0, 2.0)): + t0 = B * math.log(A / q) + n = 200000 + T = t0 + 60 * B + h = T / n + s = 0.0 + for i in range(n + 1): + t = i * h + w = 1 if i in (0, n) else (4 if i % 2 else 2) + s += w * min(q, A * math.exp(-t / B)) + quad = s * h / 3 + num &= abs(quad - B * q * (1 + math.log(A / q))) <= 1e-6 * B * q * (1 + math.log(A / q)) + # uniform tail of the (N4) example, NUMERICAL (floating point): P(N_r > t) = r^3 1{t < ceil(log 1/r)} <= e^3 e^{-3t} + for s_ in range(1, 15): + r3 = math.exp(-3 * s_) + for t10 in range(0, 10 * s_ + 30): + t = t10 / 10 + p_tail = r3 if t < math.ceil(s_) else 0.0 + num &= le(p_tail, math.exp(3) * math.exp(-3 * t) + 1e-300) + return {"exact": bool(ok), "numerical_corroboration": bool(num)} + + +def check_negatives(src): + rejected = [] + for fault in ("delete", "change", "symlink", "symlink-parent"): + with tempfile.TemporaryDirectory() as tmp: + root = pathlib.Path(tmp) + for path in INVENTORY: + dst = root / path + dst.parent.mkdir(parents=True, exist_ok=True) + shutil.copyfile(src / path, dst) + target = root / D4 + if fault == "delete": + target.unlink() + elif fault == "change": + target.write_bytes(target.read_bytes() + b"\n") + elif fault == "symlink": + moved = root / "elsewhere" / "PROOF.md" + moved.parent.mkdir() + shutil.move(str(target), str(moved)) + os.symlink(moved, target) + else: + moved = root / "elsewhere_dir" + shutil.move(str(target.parent), str(moved)) + os.symlink(moved, target.parent) + rejected.append(not identities_ok(root)) + return all(rejected) + + +def check_d4_duplicate(root, spec): + """Since ec6db8c (Math-#151) the live graph carries the D4 bytes twice; bind the duplicate to the D4 transition.""" + live = json.loads((root / GRAPH).read_text(encoding="utf-8"))["nodes"] + dup = live.get(D4_DUP) + old = live.get(D4_NODE) + t = next(t for t in spec["transitions"] if t["node"] == D4_NODE) + want = spec["live_duplicate"] + fp = t["proposed"]["fingerprint"] + if MUT == "duplicate-drift": + fp = "1" * 64 + if not isinstance(dup, dict) or not isinstance(old, dict): + return False + ok = dup.get("classification") == "PROVED_REVIEWED" and dup.get("controlling") is False + ok &= dup.get("fingerprint") == fp == want["fingerprint"] == INVENTORY[t["proposed"]["source"]][0] + ok &= dup.get("source") == t["proposed"]["source"] == want["source"] + ok &= dup.get("component_of") == want["component_of"] + ok &= any("main#76" in str(b.get("review")) and b.get("verdict") == "ACCEPT" for b in dup.get("review_basis", [])) + ok &= old.get("fingerprint") == dup.get("fingerprint") and old.get("classification") == t["current"]["classification"] + return bool(ok) + + +def snapshot(root, graph): + """Source snapshot in the shape of git_transition_audit.read_snapshot, taken from the working tree.""" + out = {} + for nid, node in graph["nodes"].items(): + ref = node.get("source") + if ref is None: + out[nid] = {"kind": "record_only"} + continue + if ref.startswith(("https://", "http://", "external:")): + out[nid] = {"kind": "external_unresolved", "reference": ref} + continue + p = root / ref.rstrip("/") + if p.is_file(): + data = p.read_bytes() + out[nid] = {"kind": "blob", "reference": ref, "bytes": len(data), "sha256": hashlib.sha256(data).hexdigest()} + elif p.is_dir(): + h = hashlib.sha256() + for f in sorted(x for x in p.rglob("*") if x.is_file() and "__pycache__" not in x.parts): + h.update(str(f.relative_to(p)).encode("utf-8") + b"\0" + hashlib.sha256(f.read_bytes()).digest()) + out[nid] = {"kind": "tree", "reference": ref, "sha256": h.hexdigest()} + else: + out[nid] = {"kind": "missing", "reference": ref} + return out + + +def check_propagation(root, spec, new): + """Two-commit mutations on the proposed graph through the production loss-only rule (reverse_impact_between with + source snapshots): evidence and consumed-source changes must reach the objects they support (OpenAI 5360320845, + 5360327058; Codex 4139807558, 4139807567). Nothing scientific is decided here.""" + if new is None: + return False, {} + hg = load_hard_gate(root) + g = copy.deepcopy(new) + if MUT == "region-unlinked": + g["edges"] = [e for e in g["edges"] if e.get("relation") != "covered_by"] + if MUT == "review-metadata-only": + drop = {c["id"] for c in spec["proposed_graph_nodes"] if str(c.get("component_role", "")).startswith("review_record")} + g["nodes"] = {k: v for k, v in g["nodes"].items() if k not in drop} + g["edges"] = [e for e in g["edges"] if e["from"] not in drop and e["to"] not in drop] + base = snapshot(root, g) + by_source = {} + for nid, n in g["nodes"].items(): + if n.get("source"): + by_source.setdefault(n["source"], []).append(nid) + + def run(edit): + g2, s2 = copy.deepcopy(g), copy.deepcopy(base) + edit(g2, s2) + try: + return set(hg.reverse_impact_between(g, g2, old_sources=base, new_sources=s2)["impacted"]) + except Exception: + return None + + def source_edit(path, kind="blob"): + def f(g2, s2): + for nid in by_source.get(path, []): + s2[nid] = ({"kind": "blob", "reference": path, "bytes": 1, "sha256": "1" * 64} if kind == "blob" + else {"kind": "missing", "reference": path}) + return f + + def fp_edit(g2, s2): + g2["nodes"][D4_NODE]["fingerprint"] = "2" * 64 + + eight = {t["node"] for t in spec["transitions"]} + cases = { + "d4-proof-edit-reaches-region-and-consumer": (source_edit(D4), {D4_NODE, "math.rn-region.fixed-remote", "math.rn-mesoscopic-reduction"}), + "annulus-proof-edit-reaches-region": (source_edit("frontiers/rn_thin_tube_20260925/FIXED_ANNULUS_CANDIDATE.md"), + {"math.rn-fixed-annulus-window", "math.rn-region.fixed-annulus-window"}), + "interface-review-deleted-reaches-interface-consumers-regions": (source_edit(HERE + "/RN_COUNT_INTERFACE_REVIEW.md", "missing"), + {IFACE, D4_NODE, "math.rn-fixed-annulus-window", "math.rn-region.fixed-remote", "math.rn-region.fixed-annulus-window"}), + "external-review-record-edit-reaches-d2-d3-d4-d6": (source_edit(HERE + "/EXTERNAL_REVIEWS.md"), + {"math.lifetime-remainder", "math.side24-coefficient", D4_NODE, "math.p15-full-price", "math.rn-region.fixed-remote"}), + "two-scale-addendum-edit-reaches-annulus-and-region": (source_edit("frontiers/rn_thin_tube_20260925/TWO_SCALE_ADDENDUM.md"), + {"math.rn-fixed-annulus-window", "math.rn-region.fixed-annulus-window"}), + "realized-covers-edit-reaches-d6": (source_edit("frontiers/three_fronts_20260924/P15_REALIZED_COVERS.md"), {"math.p15-full-price"}), + "d4-fingerprint-edit-reaches-region": (fp_edit, {D4_NODE, "math.rn-region.fixed-remote"}), + } + results = {} + for name, (edit, must) in cases.items(): + imp = run(edit) + results[name] = imp is not None and must <= imp + imp = run(source_edit("reviews/d5_collar_count_20260928/REVIEW.md")) + results["unrelated-edit-leaves-the-eight-untouched"] = imp is not None and not (imp & eight) + imp = run(lambda g2, s2: None) + results["no-op-impacts-nothing"] = imp == set() + return bool(all(results.values()) and len(results) == 9), results + + +def main(): + global MUT + ap = argparse.ArgumentParser() + ap.add_argument("--mutant", choices=MUTANTS) + MUT = ap.parse_args().mutant + root = pathlib.Path(".").resolve() + spec = load_spec(root) + ident = identities_ok(root) + trans_ok, new = check_transitions(root, spec) + gate_ok, gate = check_gate(root, spec, new) + prop_ok, prop = check_propagation(root, spec, new) + iface = check_interface() + checks = {"IDENTITIES": ident, "VERDICTS": ident and check_verdicts(root), "BASELINE": check_baseline(root, spec), + "TRANSITIONS": trans_ok, "GATE": gate_ok, "PROPAGATION": prop_ok, + "INTERFACE": iface["exact"] and iface["numerical_corroboration"], "NEGATIVES": check_negatives(root), + "D4_DUPLICATE": check_d4_duplicate(root, spec)} + passed = all(checks.values()) and len(checks) == 9 + print(json.dumps({"object": "REGISTER-ALIGNMENT-20260930-v1", "checks": checks, "passed": passed, + "inventory_files": len(INVENTORY), "transitions": len(spec["transitions"]), + "component_nodes": len(spec["proposed_graph_nodes"]), "edges_added": len(spec["proposed_graph_edges"]), + "gate": gate, "propagation": prop, + "interface_evidence": {"exact_rational": ["(N1) Holder p=2,3 on finite rational spaces", "(N2) exponent identity", + "(N3) conditional-mean identity", "sharp-p example at r=2^-pm", + "(N4) integer monotonicity of ceil(t)"], + "numerical_corroboration_floating_point": ["(N4) grid maximum of (t+1)^p e^-3t", + "(N5) Simpson quadrature at three parameter points", + "(N4) example uniform tail on a grid"], + "results": iface}, + "scope": "identity, verdict-row, live-baseline, transition-shape, hard-gate replay, two-commit propagation, " + "interface arithmetic (exact and numerical parts labelled), filesystem-negative and live D4-duplicate " + "checks; no mathematics is re-proved; nothing is written"}, indent=2, sort_keys=True)) + return 0 if passed else 1 + + +if __name__ == "__main__": + sys.exit(main())