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Improve T16 kappa with bounded full-bin reallocation - #3465

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Mister-Meeseeks merged 2 commits into
CrocSwap:mainfrom
hexapode:codex/t16-rank7-full-patterns
Oct 18, 2026
Merged

Mister-Meeseeks merged 2 commits into
CrocSwap:mainfrom
hexapode:codex/t16-rank7-full-patterns

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@hexapode hexapode commented Oct 18, 2026 •

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This improves the T16 construction of #3457 from κ = 0.001727153212938552593775 − 10⁻⁴⁶ − 10⁻⁷⁰ to κ = 0.001727254340596650594393 − 10⁻⁴⁶ − 10⁻⁷⁰ through a bounded reallocation using previously omitted full-bin patterns.

This supersedes #3457’s allocation while retaining its 408-helper supplier, T16 chronology, source closure and admission machinery. It remains a scoped T16 improvement below T740; the selected frontier is unchanged. The branch descends from #3457, so its main-relative diff includes that package. The incremental change is its new certificate, expected values, positive-control expectation and documented bounded domain.

The certificate uses 189 allocations and 1,222 flows for the same 58,752 helper occurrences. Its idle-profile delta is −229 H1 + 110 H2 + H3 − 2 H5 + 2 H8. This equals 110(H2−2H1) + (H3−3H1) + 2(H8−H5−3H1), strictly negative by concavity throughout the relevant exponent interval. Verification uses deterministic reconstruction and exact arithmetic, with no optimizer dependency and no optimality claim.

Validation: complete changed-owner/controller/physical/outer admission; exact dual-engine pricing; normal and optimized reconstruction rejection tests; materialization controls; complete admission replay from the exact committed Git-free export, with all 569 exported files unchanged (including inode checks). The exported replay returned PASS_T16_RANK7_PROVIDER_COMPOSITION and release SHA256 84cd1526d22620aeffafe35f45ae73131c8098f30452a1f08b8ec0eee244e09b. The full invoice retains 91 private buffers and 14,845 physical families. Native providers are explicitly reused from authenticated prior fresh PR3148 executions. All inherited all-size and analytic assumptions remain conditional.

PREDECESSOR-3457.json preserves the prior result and source identities; BOUNDED-DOMAIN.md names the omitted patterns, finite discovery scope and exact gain argument. Private optimization tooling is excluded. OpenAI Codex assisted with discovery, reconstruction, audits and tests.

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