Refine reviewed gen4 envelopes: conditional kappa = 0.000723571593879006127174

[DesmondForward]

This adds a small conditional parameter and envelope refinement of the reviewed PR279 gen4 construction:

• Baseline: kappa = 0.000723571590007464.
• Candidate: kappa = 361785796939503063587 / 500000000000000000000000 = 0.000723571593879006127174.
• Absolute gain: 3.871542127174e-12 (approximately 0.00000053506%). This remains below stronger concurrent submissions, including PR Conditional κ = 8.049462195041506e-4: two kernels and 15 extra retimings after #366 #369, and makes no global record claim.

The proof retains the physical word, frames, banks, literal stock, prime threshold and complex supplier. It uses the unrounded full Gaussian fallback count, tighter conditioning on invertibility, and disjoint good/bad power moments. Seven fixed ordinary-leaf levels and positive rational outer parameters complete the witness. All fallback, selector and finite primitive charges remain included; the reviewed selected-result record stays unchanged.

The package contains a conditional proof argument and attribution, deterministic source-bound certificate, one-command verifier, 15 regression/contract tests and dedicated Linux CI. Eleven improvement cycles preserve all 55 trials, including the non-improving beta search and rejected parameters. Evidence Forge retains the investigation and historical failures; its independent assessments establish captured JSON facts, not a formal theorem or external test execution.

Validation:

• Both rational moment engines, next coarse/headline exclusions, 47 strict inequalities, seven margins, finite cutoff gaps and nine adverse controls pass.
• All 15 new tests pass on Windows and Ubuntu/WSL; four existing selected-result tests pass.
• All nine mandatory stages of the fresh inherited physical replay passed, followed by the refined verifier (about 603 seconds total). Exact scope and receipt hashes are recorded in research/gen4-envelope-refinement/VALIDATION.md.
• Canonical certificate bytes match across Windows and Linux. The initial Windows legacy-encoding replay failure is retained; the launcher now explicitly uses UTF-8.
• make verify could not start locally because GNU Make is unavailable. The complete affected physical pipeline runs directly in Python; the existing broad CI remains separate.

The all-size compiler, common-chart, restored-row, selector/routing, prime-supply, precision/recovery, complex symbolic and analytic-transfer interfaces remain conditional. This is neither a full formal multiplication theorem nor a practical runtime improvement. Prepared with substantial OpenAI Codex assistance; predecessor credits and Apache-2.0 notices are retained.

[Mister-Meeseeks]

Thank you @DesmondForward. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Sharper gen4 envelope and recurrence accounting.

Review and limits: Dedicated Linux physical replay followed by refined exact assembly and rejection controls. This improves a historical checkpoint rather than the selected frontier.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: e2fae6a92775b8f609d917a9cc93b31e2559dd5f. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.