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Complete the finite-volume lemma chain and consolidate A–D - #8
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…-side gates Preserve the fixed logarithmic return law, residual-depth domain and sufficient finite side n(T)=2 ceil(4.5T)+1. Add the Gate D lemma chain: analytic endpoint-gap lower bound, distinct normalized positive bound states and energies, truncated exponential weights, exact periodic-seam residual, midpoint transpose identity, and uniform amplitude comparison. Add eight small diagnostics separately from the original 272 controls. Collect A-D in PROOF_STATUS.md, retaining the absent separate reader report, incomplete priority and model-specific implementation obligations. The next phase is consolidated critical assessment, not an automatic new gate, model, manuscript or outside contact. All 27 protected scientific/history inputs, original references and comparison/workload policy remain unchanged. Remote tree 9ff1f79 matches the frozen local candidate. Fresh baseline passed all 5 suites, 28 groups and 272 controls byte-for-byte; all 52 existing supplementary tests and the first eight new diagnostics passed. The frozen candidate run and this revision's hosted evidence must be inspected before merge; baseline success is not prospective verification.
The new Gate D weight constants now state mu>0 explicitly, as required by the original ROUNDING proof and the bounded-weight monotone limit. Also remove a duplicate conjunction in STATUS. No protected proof, scientific script, diagnostic, reference or comparison policy changes. Refined tree 56f699c matches the staged final local source. The first candidate's full local execution and actual hosted run 37248955416 completed successfully; its evidence remains distinct. Fresh final-tree full local and hosted verification are required separately before merge. The small clarification does not change the coefficient, uniform domain or sufficient finite-size family.
Frozen candidate and document clarificationThe first frozen local candidate completed: all five scientific suites, 28 groups and 272 controls passed, with every original result byte-identical. All 60 supplementary checks passed. Before/after integrity snapshots agree; all 27 protected inputs are unchanged. The first full local report SHA-256 is Final head is now Actual first-candidate hosted run The leased-ref wrapper request was rejected at argument binding. The branch was inspected again at the unchanged first head, then updated with a non-force fast-forward. No force push or unrelated repository operation occurred. |
Completed exact-final-head verificationFinal head 7a1c58e, tree 56f699c6f336a43998782121382cbde3afc892ba. All three full frozen local executions (base, first candidate, final clarified candidate) passed 5 suites, 28 groups and 272 controls with every original result byte-identical. Final-tree before/after integrity snapshots agree, all 60 supplementary tests pass, all six final diagnostic JSON reports match the first candidate byte-for-byte, and the final patch exactly replays all 65 source files. Final local scientific report SHA-256: e1914985ae1e3fc5de7a67b018e2bff9c94a64a18c0f8ff4cf10dc6c9173c479. The actual final PR workflow 37249403431 completed successfully. Downloaded artifact 11320955909, SHA-256 38632669246984d119b2ce461cb6e1bab092527b1b88fdacbb95119cedb1ceb2, was inspected. Its complete source snapshot matches all 65 frozen final files exactly. Hosted agreement is not byte equality. The final PR passes every scientific assertion and the unchanged comparison policy. It has 518 floating-field differences (maximum absolute difference 7.92932386417533e-12), all accepted under the existing thresholds, and eight ODE workload-counter changes whose exact raw paths/reference/observed triples match HOSTED_IMPORT_REVIEW.json. Raw flags remain intact. All six diagnostic reports pass; complete numeric differences are retained, including the larger absolute but unnormalized-current field already distinguished in the amplitude diagnostic. The new finite-volume report has 83 numeric differences from local, maximum 2.1572218837639934e-13. No machine-level cause is asserted. The complete first-candidate hosted artifact is also retained and checked separately, not substituted for this final head. No cancelled or interrupted scientific execution is counted as complete. The positive-mu clarification and wrapper binding failure are recorded without changing a protected proof, script, reference, or tolerance. Decision: the exact checked head is suitable to merge under the existing policy. This supplies an explicit author-side Gate D route and consolidates A–D; it is not independent review, exhaustive priority, or an apparatus certificate. Actual post-merge main verification remains to be inspected separately. |
Completed post-merge verification and A-D handoffPR #8 is merged as 5f372c4, with checked tree 56f699c6f336a43998782121382cbde3afc892ba. Work was confined to GoGoKo699/Logarithmic-Threshold-Return. The actual main push workflow 37249858942 completed successfully. Every step passed: 14 infrastructure, five predecessor, six operational, seven model-residual, seven amplitude, six reflection, seven uniform-minimum and eight finite-volume checks; integrity/link checks; all five preserved scientific suites; and the no-source-rewrite check. Downloaded main artifact 11320971618, SHA-256 defefaed4d403c83d550a9b1bc35d3ad235bbae23c51877b61856e5846b6603a, was inspected. Its source snapshot exactly matches all 65 frozen final files and identifies the actual merge commit. Numerical distinctionAll three complete frozen local executions (base, first candidate and final clarified candidate) passed five suites, 28 groups and 272 controls with every original result byte-identical. The final run also passed all 60 supplementary checks; its six diagnostic JSON reports match the first local candidate byte-for-byte. Final scientific report SHA-256: e1914985ae1e3fc5de7a67b018e2bff9c94a64a18c0f8ff4cf10dc6c9173c479. The final patch was replayed against the base and matched all 65 final files exactly. First PR run 37248955416, final PR run 37249403431, and main run 37249858942 all passed the existing comparison policy, but are not byte-identical to the original references. Each has 518 floating-field differences, maximum absolute difference 7.92932386417533e-12, all within the unchanged thresholds. Each has eight ODE workload-counter changes whose exact raw paths, reference values and observed values match the existing HOSTED_IMPORT_REVIEW.json. The raw rejection flags remain intact and are handled by the unchanged source-scoped workload review. No machine-level cause is asserted. All hosted diagnostic reports pass. Their full differences from local are retained. The new finite-volume report has 83 numeric differences, maximum 2.1572218837639934e-13. The amplitude diagnostic's largest absolute difference concerns an unnormalized current of order 2.6e9, not a probability; that distinction remains explicit. No numerical reference, tolerance, scientific script or workload policy was changed to obtain a pass. There was no failed Gate D scientific diagnostic. The first note's positive-weight requirement was made explicit as mu>0, consistent with the protected original proof; both frozen versions and complete runs are retained. The public-clone DNS failure, rejected interactive launch and rejected leased-ref wrapper binding are recorded as operational failures, not completed scientific executions. The successful branch update was a non-force fast-forward after rereading its unchanged head. Scientific conclusion and phase boundaryAll 27 protected scientific/history inputs, original numerical references and the comparison/workload policy are unchanged. Gate D supplies an explicit author-side chain for distinct endpoint energies and normalized positive states, an analytic localization margin, truncated-weight limits, the periodic seam and the midpoint transpose identity. Its finite-volume bound is uniform without requiring a minimum instantaneous gap, and preserves n(T)=2 ceil(4.5T)+1 as a sufficient, non-optimized family. The eight small diagnostics are not an all-size proof by sampling or additional members of the original 272 controls. PROOF_STATUS.md now consolidates the four author-side gates. This completes the bounded proof-expansion phase, not a genuinely separate review, exhaustive priority assessment or exact apparatus implementation. Those obligations remain explicit. The next task is critical assessment of this fixed route and concrete objections, not an automatic Gate E, new model, detector, ramp, platform or generic citation campaign. Manuscript drafting, release and all outside contact remain on hold. No other repository or third-party PDF was included. |
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Scientific decision
The Gate D author-side audit preserves the law, observable, uniform positive-minimum domain and existing sufficient finite-size family. It does not optimize volume or supply an independent report.
Preservation and verification
Base aa41737. Frozen candidate tree 9ff1f79e06c91e70d9a2dfb918be9d04a64d3535 exactly matches the remote tree. Ten changed files: four additions, six modifications, no deletions. All 27 mapped scientific/history inputs, original reference results and comparison/workload policy remain unchanged.
Fresh frozen baseline: five suites, 28 groups and 272 controls all passed with byte-identical results; all 52 existing supplementary checks passed. The first eight Gate D diagnostics passed without a scientific failure. Frozen candidate execution is retained separately; its completion and this PR's actual hosted artifact must be inspected before merge, followed by the actual main run afterwards.
The recovered base hosted artifact passes the unchanged policy but is not byte-identical; its 518 floating differences and eight workload counters remain documented separately. The public-clone DNS failure and rejected interactive launch are recorded as operational failures, not scientific runs.
No protected proof change, third-party PDF, other-repository modification, manuscript, release, new platform/detector/ramp or outside contact.