Make the positive-minimum return estimate uniform on the stated domain

[GoGoKo699]

Scientific outcome

Author-side Gate C for the existing fixed quadratic cycle, uniformly over 0<=b<=1-delta for fixed delta>0. No coefficient, observable or domain correction is introduced.

• Subtracting b from both the exact coefficient and reference k^2 leaves the central perturbation exactly independent of b. The narrow forbidden region is retained in an integrated estimate, not excised.
• The passive denominator uses Re(q)-|h|/2, not a sign of Im(h); the latter sign actually reverses in finite checked examples.
• On the full exact negative tail, W-u>=(delta/2)W. Positive spectral-measure identities make both defect terms nonnegative and yield I_minus(u)<=(2/delta)^(5/2) I_minus(0) at the same alpha/cutoff.
• Endpoint basis cancellation and the uniform Gate A comparison retain pi^2/[4L^2(1-b)^2]. The explicit supremum has conservative relative error O_delta(L^-1/4), without extending through b=1 or delta->0.

Seven new finite/symbolic diagnostics pass; they are not a sampling proof, long-duration physical simulations, or additions to the original 272 controls. Gate D and genuinely separate review remain open. No new model, detector, platform, manuscript or outreach.

Final candidate and preservation

Base f00281f; final head 05f5e47; exact tree 478ba79d3f0a08c0b1e2563be25909e983148b39 matches the frozen local 61-file tree. Nine changed files: four additions, five navigation/workflow modifications; no deletions. All 27 mapped inputs and original references/comparison/workload policy remain unchanged.

The first candidate passed. An extra exact-turning-point probe exposed unused singular wave-basis evaluation in the diagnostic RHS, not in the scalar equation. The refined evaluator and exact-point assertions repair it without changing an equation or tolerance. First script, raw probe and reversible repair are retained in archive/GATE_C_DIAGNOSTIC_REFINEMENT.md and the conversation evidence package. Refined and initial diagnostic result files are byte-identical.

Completed local verification and hosted boundary

Three frozen local runs (clean baseline, first candidate, refined final candidate) passed all 5 suites, 28 groups and 272 controls with every result byte-identical; each has identical before/after integrity snapshots and unchanged source hashes. The final report SHA-256 is fea030f032f583adab4c5f6e983211e64b918310575f8532f1fe8b371afeebe6. All 52 supplementary tests passed: 14 infrastructure, 5 predecessor, 6 operational, 7 residual, 7 amplitude, 6 reflection and 7 uniform-minimum. Complete patch replay reproduces all 61 final files exactly; diagnostic repair replays both directions.

Incoming source was recovered from the actual main artifact 11313273793, run 37229542484. The earlier alternate unmerged Gate B patch was not applied over the current upstream version. An early original-source run with navigation-only overlap and a rejected clean-baseline output path are retained separately, not mislabeled as frozen or completed runs.

The first hosted PR run 37231804719 passed and its artifact 11313644120 was inspected: source matches all 60 initial files; original outputs pass the unchanged comparison policy with the known 518 floating differences and 8 workload counters. Exact raw values and diagnostic differences are retained. Final-tree PR run 37232313736 and post-merge main require their own actual reports and artifact inspections; success is not inferred prospectively.

[GoGoKo699]

Diagnostic refinement before merge

The branch now points to 05f5e47, exact tree 478ba79d3f0a08c0b1e2563be25909e983148b39, matching the frozen local tree. Nine files differ from base: four additions, five navigation/workflow modifications, no deletions. All 27 protected inputs and references/policies are unchanged.

The first seven-test candidate passed. A subsequent exact-turning-point warning-as-error probe exposed unused singular wave-basis evaluation in the central diagnostic RHS. The scalar ODE coefficient is regular there; the helper unnecessarily calculated inverse powers of that coefficient. A coefficient-only evaluator and exact turning-point/origin assertions repair the diagnostic without changing the equation or any tolerance. The first passing script, actual failing probe and reversible repair are retained in archive/GATE_C_DIAGNOSTIC_REFINEMENT.md and the local evidence package.

The refined seven-test report passes and is byte-identical to the first passing report. The first candidate's completed scientific run is not relabeled as failed. Final refined-tree scientific/hosted reports are separate evidence and must be inspected before merge; post-merge main must be checked afterwards. This is author-side scrutiny, not independent review.

[GoGoKo699]

Completed final-candidate verification

Final head 05f5e47, tree 478ba79d3f0a08c0b1e2563be25909e983148b39. Three frozen local runs (clean base, first candidate, refined candidate) each passed all five scientific suites, 28 groups and 272 controls with byte-identical saved results, unchanged source hashes, and identical before/after integrity snapshots. Final report SHA-256: fea030f032f583adab4c5f6e983211e64b918310575f8532f1fe8b371afeebe6. All 52 supplementary tests passed separately. Full patch replay reproduces all 61 source files; the diagnostic refinement patch reverses and reapplies exactly.

Actual final PR workflow 37232313736 completed successfully. Downloaded artifact 11314656411, SHA-256 09c7363f6dc41cc94393eebe1bc44eb847df3933971adf48848d388e7574f7ae, was inspected. Its tracked-source snapshot matches the complete 61-file frozen local tree, with no missing or changed files.

Hosted agreement is not byte equality. The final PR has 518 changed floating fields, maximum absolute difference 7.9293e-12, all within the unchanged declared thresholds. Its eight raw rejected ODE-work counter paths and exact reference/observed values match HOSTED_IMPORT_REVIEW.json. The existing workload policy classifies those counters separately; raw flags remain present. Both hosted PR runs have identical scientific differences. No tolerance, reference, original scientific script, or workload policy changed.

The five supplementary JSON reports also pass; their full differences are retained. Maximum absolute differences from local: operational 6e-16; model residual 5.9214e-14; amplitude 7e-7 (including its pre-existing unnormalized-current diagnostic); reflection 1.9411e-13; uniform minimum 3.03875e-12. Their initial/final hosted differences are identical. No machine-level cause is asserted.

The checked candidate is suitable for merge under the existing policy. Gate C is an explicit author-side uniform argument, not a separate-reader report. All 27 protected inputs remain unchanged. Actual post-merge main verification must still be inspected separately.

[GoGoKo699]

Completed post-merge verification and handoff

PR #7 is merged as aa41737, with checked tree 478ba79d3f0a08c0b1e2563be25909e983148b39. Work was confined to GoGoKo699/Logarithmic-Threshold-Return, using the actual merged Gate B base f00281f rather than the earlier alternate local patch.

Actual main push workflow 37232743508 completed successfully. Every step passed, including all 52 supplementary checks, integrity/link checks, all five original scientific suites, and the no-source-rewrite gate. Downloaded main artifact 11314532263, SHA-256 5b1ddfa74592fb47d2863c2cdf97da8cfe90f04d3fe4232d62014e8702decb64, was inspected. Its complete source snapshot matches all 61 frozen local files exactly, with no missing or extra tracked files.

Exact numerical distinction

Three frozen local runs (clean baseline, first candidate, refined candidate) each passed 5 suites, 28 groups, 272 controls with every original result byte-identical. Each source tree stayed unchanged and each before/after integrity snapshot matched. The final local report SHA-256 is fea030f032f583adab4c5f6e983211e64b918310575f8532f1fe8b371afeebe6.

Both PR runs and the actual main run passed the unchanged comparison policy but were not byte-identical to the original references. Each contains the same 518 floating-field differences, maximum absolute difference 7.9293e-12, all within the unchanged thresholds, and the same 8 ODE-work counter changes. Their raw paths and exact reference/observed integer values match the existing HOSTED_IMPORT_REVIEW.json. Raw rejection flags remain retained; the existing policy treats those counters separately. No numerical tolerance, reference, original scientific script or workload policy changed.

Main and final PR supplementary differences also match exactly. All supplementary tests pass. The 7 new uniform-minimum tests have 45 changed numeric fields relative to local, maximum absolute difference 3.03875e-12; complete values and all other diagnostic differences are retained in the artifact inspections. No machine-level cause is asserted.

Retained diagnostic refinement and scope

The first seven-test candidate passed; an extra exact-turning-point probe then exposed unused singular wave-basis evaluation in its regular central ODE coefficient. A coefficient-only evaluator and exact turning-point/origin assertions repair that diagnostic. Its numeric report remains byte-identical locally before/after refinement. The original passing script, actual failing probe and reversible patch are retained. Operational launch, navigation-overlap and supplemental packaging/inspection errors are recorded separately, not misrepresented as failures of the completed frozen scientific suites.

All 27 protected scientific/history inputs remain unchanged. Full final-patch replay reproduces all 61 files; the diagnostic repair replays in both directions. No third-party PDF or other repository is included.

Gate C now has an explicit author-side uniform route: offset-independent central transfer with the full forbidden region included; a passive denominator independent of the sign of Im(h); exact shifted negative-tail domination; and uniform endpoint/coefficient bookkeeping. The original coefficient and domain are preserved. The estimate is for a fixed margin delta>0, not delta->0, b=1, or fixed positive u at arbitrarily long times. Seven finite diagnostics are not a supremum proof or additions to the original 272 controls.

Next bounded task: Gate D, finite-volume initial states, periodic seam and return-amplitude error, without optimizing lattice size. A genuinely separate proof report, model-matched implementation and exhaustive priority remain unestablished. Manuscript drafting, broad generic source accumulation and outside contact remain on hold.