Conditional κ = 0.001673636244951726 via reordered T16 augmenting chain

[hexapode]

Composes three neutral paired-call reorderings and owner repairs with PR #3375, then a ten-helper augmenting chain and two residual consolidations. The exact conditional κ increases from 0.001673628681907313 to 0.001673636244951726 (gain 7.563044413×10⁻⁹); conservative κ is 0.001673636242098946.

The aggregate paid delta is H1 - H3 - 2 H7 + H16. All 69,120 whole-helper roles and 144 complete invocations remain admitted; rank mass is 1,041,408 and deficit 5,120. The complex supplier remains binding. This is a finite packing contribution within the inherited conditional framework, not a complete multiplication theorem or an optimality claim.

Unlike fixed-order cycles, the construction changes the paired call chronology while preserving each replica's source-event order. A narrowly extended, attributed T16 lift independently derives windows, provider timestamps and the schedule digest. All downstream physical/controller/invoice/supplier checks remain intact. The 10,017 actual charts fit the unchanged finite stock; complete invoice comparison allows only source-binding hashes and the actual permutation of the same full call records. Charged prefix stays 512 bits and row coefficient 16,469.

Validation: exact six-stage reconstruction with full owner audits; native and conservative exact prices; all eleven strict admission stages, including all 47 outer margins and 69/12/15/6 rejection controls; nine behavioral tests under normal and optimized Python, including six malformed-lift controls; metadata/source pins and committed export checks. Private independent reconstruction agrees with the canonical final payload. The committed 63-file export also passed a fresh full replay without Git; all 64 exported files (including the transport manifest) remained unchanged. Local checks are not a hosted-CI claim.

The package is research/t16-reordered-augmenting-chain. It pins PR #3375 at 62fd8039cc40749cea6238e7807db9a63b4d6765, retains predecessor source/attribution, and includes explicit replay data. No private search tools or solver dependencies are committed. Canonical selected results and frozen predecessor packages are unchanged. The recent fixed-map obstruction #3369 does not cover the changed chronology; #3378/#3379 do not provide a newer physical packing gain.

Credit is retained for Hao Yan's T16 controller/independent audit, Philippe Van Velzen's strict admission, and the contributors in the PR3308/3338/3354/3359/3366/3375 lineage. Prepared by Pierre (hexapode) with substantial OpenAI Codex assistance; no independent human review is claimed.