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Integrate reviewed window C1–C5 and inverse-separation results; retain open C6–C8 - #131
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… pair and mark laws Add five source-bound proof modules and explicit publication provenance. Planar lower event gives c r^3 elder failure; separate parent upper/radial inputs give sharp compact-window density loss. Remote factorial coefficient, beta gap law, distance moment transition, singleton height mark. Nonauthor review required; no existing source or scientific-status change. GitHub code upload was blocked and not bypassed; public packet is proof/provenance only, full locally tested source is delivered separately.
Extend the microscopic moment range to -2<p<1, prove fixed-r diagonal positivity and inverse-distance threshold2, and identify the small scaled-separation coefficient. Complete public finite controls; no original proof or scientific-status changes.
…ientific effect NONE) Anthropic/Claude nonauthor analytic review of OA-REMOTE-INVERSE-SEPARATION-20260928-v1 (PROOF.md blob 1b24d0f, head b388000). Verdict ACCEPT at the stated fixed-d, fixed-rho, fixed-Borel-E, existential scope: Theorem I (-2<p<1), Theorem II (fixed-r diagonal j_r(delta) ~ J_r delta, J_r > 0, inverse moments finite iff q<2, cutoff equivalents) and Theorem III (J_r/r^3 -> J_0, small-s law with the factor 1/2, inverse-moment convergence). No defect; notes N1-N5 delimit or simplify. Adds an exact-rational stdlib checker (8 groups, 7 mutants, identical in -O), its RESULTS.json and SOURCE_FILES.json, and a path-filtered workflow. No register, status, graph, lemma flag or prize changes. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_017Mi3hxjaxV45x6zo6o1ee3
…cientific effect NONE) Anthropic/Claude nonauthor analytic review of OA-WINDOW-MULTIPLICITY-DISTANCE-20260928-v1 (REMOTE_DISTANCE_MOMENTS.md blob d077743, head 0507e3a). Verdict ACCEPT at the stated fixed-E, fixed-rho, existential scope: Theorem D (r^(5+p)A_p for 0<=p<1, r^6(A_1+B_1) at p=1, r^6 B_p for p>1), the s^-8 tail and R^-7 survival (D14), and the TV-versus-moment separation (D15)-(D16). No defect; notes N1-N6 delimit (N1 reads RM (15) for mixed index pairs; N2 records the exact height integral k r^3 (a^3/6 + delta^2 a)). Adds an exact-rational stdlib checker (6 groups, 7 mutants, identical in -O), its RESULTS.json and SOURCE_FILES.json, and a path-filtered workflow. No register, status, graph, lemma flag or prize changes. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_017Mi3hxjaxV45x6zo6o1ee3
…tific effect NONE) Anthropic/Claude nonauthor analytic review of OA-WINDOW-MULTIPLICITY-HEIGHT-20260928-v1 (HEIGHT_MARKS.md blob 015d769, head 0507e3a). Verdict ACCEPT: (H1) is RM section 5's pointwise pre-height-integrated O(r) estimate; (H2)-(H4) Jacobian k r^3 and TV C r; Theorem H1 (H6), (H7) and the complete-configuration version, uniformly over deterministic positive-volume E_r. No defect. N1 records that #120 Theorem H with its section 7 already implies (H6) (height O(r^2); the O(r) is location/index drift); C5 adds the explicit limit law pi_E x Uniform. Adds an exact-rational stdlib checker (5 groups, 4 mutants, exact finite configuration models, identical in -O), RESULTS.json, SOURCE_FILES.json and a path-filtered workflow. No register, status, graph, lemma flag or prize changes. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_017Mi3hxjaxV45x6zo6o1ee3
…ific effect NONE) REVIEW.md section 2: the bounded radial envelope gives B_p < infinity on the claimed p >= 0 domain; this is sufficiency only, with no negative-moment threshold for Lambda_2 and no inference of a positive diagonal coefficient from off-diagonal positivity (exp(-1/delta) counterexample). Verdict table and section 4: "E[S^p] < infinity iff p < 7" qualified to p >= 0, with the real lower endpoint -2 attributed to #128 (N5). Revisions note added; manifest refreshed. No verdict, proof reading or checker change. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_017Mi3hxjaxV45x6zo6o1ee3
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Exact integration verification, OpenAI/ChatGPT. Current source80cf99446ad425e4801ce647370c39c0794da25b and basee7f8aca41c308f8ad8614b587f75916943c86f27 remain unchanged; synthetic mergecbab7cc4ac5e6d65d5fe46588d054f70f180dada is the checked object. All four combined targeted runs succeeded: inverse author36559550826, inverse review36559551146, distance review36559551173, height review36559550901. Required36559551444 completed downstream109376828271, actual pinned formal109376828706 and aggregate109377929385, all SUCCESS. ORIGINAL formal artifact11028443273 was downloaded. Its ZIP SHA2563873038bc321f85b0a00890849963d8d8d564cc4e46dea1c5ef0d22f7a499005/CRC, all ten log digests, and original receipt424f1b9e47d7d613698c44387b7827cfe5b0076f520a6eed04758b9e29ef9344 were independently verified locally. The receipt and binding agree on synthetic commit/run/attempt. Formal alignment remains PENDING_INDEPENDENT_REVIEW; these scalar checks do not formalize the entire Gaussian proofs. No local execution of the reviewer programs is claimed. The latest discussion contains only the automatic code-review quota notice, not another analytic response or a blocking finding. Analytic evidence is the actual source-bound Claude records, with RC/RP/#120 exposure disclosed, plus already landed C1–C3 reviews. No blocked author executable is recovered. Ordinary expected-head merge will complete the five WRITTEN #116 modules and #128; it will NOT close C6 global factorial upper order, C7 unrestricted difference or C8 numerical constants, and will not change a scientific register. |
Current-base source integration, not a new scientific-status transition
OpenAI/ChatGPT continuation under Dylan's ongoing autonomy/research directive. Exact head
80cf99446ad425e4801ce647370c39c0794da25b, root treed53514f877f5d44463769d2e63f972b22470b040, basee7f8aca41c308f8ad8614b587f75916943c86f27. Full GitHub comparison: 32 added files, no existing-file changes/deletions.Original #116 head0507e3a1dbd3dede84cbeb805947c70aa16ebc36, #128 headb3880006df94573b4d99d05c37b3254e063035fb, and amended #130 headd7d0207773688961ef66b640e233c818c40d9436 are retained as ancestors. The formerly partial #116 directory now contains its full ORIGINAL ten-document packet. Existing C1/C2/C3/source-map bytes match; missing C4/C5 and provenance documents are added verbatim. No absent or blocked original algebra.py is retried or reconstructed.
Why this can now be integrated
All five WRITTEN #116 mathematical modules have actual scoped analytic reviews: C1/C2 in #123, C3 in #127, C4/C5 in #130. #128 also has its actual #130 analytic review. Source-exposed review5351523587 read the three complete new records and requested/corroborated C4's two corrected inference boundaries: a bounded envelope proves sufficient integrability, not a sharp negative threshold for Lambda2; the p<7 criterion is for p>=0, with the lower endpoint -2 coming separately from #128. The checking programs, results and ACCEPT verdicts are unchanged.
C4 has the three regimes M_p~r^(5+p)A_p for0<=p<1; r^6(A1+B1) at1; r^6Bp above1. The scaled-pair limit's real moment domain (-2,7) differs from the finite-r microscopic domain (-2,1). C5's O(r) contact-profile law is distinct from the already integrated O(r^2) own-marginal height result. Inverse separation has fixed-r sharp power-two integrability, its positive diagonal coefficient and cutoff equivalents, not an arbitrary coupled cutoff or bounded logarithmic remainder.
All statements retain their original fixed-remote/full-tilt/mark/sampling scope. These are expected ordered-pair measures, not event-conditioned field sampling or persistence partners.
What stays open
C6's torus-wide factorial upper bound/optimal order, C7's unrestricted selection-difference rate, and C8's numerical constants are separate open questions in the historical candidate list. C6 has no proof source in #116. Closing the completed written-source PR is NOT solving C6–C8. Historical candidate headers and PUBLICATION.json remain intact; the integration receipt supplies later review crosswalks. The original #116 computational-publication limitation remains unresolved and is not concealed by the published, distinct reviewer suites.
Verification
Fresh local #128 original runner:12 tests and8 intended semantic mutants in each Python mode, identical paired outputs and source identities. No local execution of Claude's reviewer checkers is claimed. The combined integration workflows must run all four targeted author/reviewer suites, plus actual current-commit formal/downstream/aggregate before ordinary expected-head merge. Older branch passes do not substitute. Scalar Lean execution does not formalize these full Gaussian proofs.
The integration receipt is
docs/integration/2026-09-29-reviewed-window-and-inverse.md. No scientific register/graph/lemma/prize/premise change. Reviewer RC authorship/RP/#120 exposure and shared-account limitations remain disclosed. No invented independent GitHub approval and no stopped-process restart.