Improve kappa with an eight-replica rank-seven construction

[hexapode]

This composes the current 408-helper rank-seven supplier with an eight-replica schedule derived from the actual PR3413 chronology. Complete finite admission gives κ = 0.001728992447095271166656 − 10⁻⁴⁶ − 10⁻⁷⁰, improving our T16 result in #3465 (0.001727254340596650594393 − the same margins).

This remains below the stronger T740 endpoint. It is a smaller-replica construction with a newly certified allocation, not a global frontier or first-ever T8 claim. The selected result is unchanged. It builds on #3133/#3148’s supplier and #3413/#3457/#3465’s source-bound chronology and allocation machinery.

The literal certificate covers 72 calls and 29,376 helper occurrences through 106 allocations and 645 flows. Both current provider interfaces independently accept the owner map. The complete paid profile is {1:177140, 2:52128, 3:16950, 4:7344, 5:1612, 7:2, 8:576, 48:3050}. The full invoice charges 91 private buffers and 7,677 physical families.

The existing admission adapter, parent lift and block-norm checker already support arbitrary positive replica counts; no predicates were relaxed for T8. The public package fixes T=8 and checks that its schedule is the exact retained-replica projection of the authenticated T16 chronology. Malformed replica labels, missing calls and reversed per-replica stages are rejected. Exact rational pricing uses the T8 width and deficit, not the former T16 normalization.

Validation: complete owner/parent/controller/physical/outer admission; independent release/hash/invoice checks; two exact moment engines and scientific rejection controls. Native providers are explicitly reused from authenticated prior fresh PR3148 executions. The inherited all-size implementation and analytic assumptions remain conditional. An additional complete replay of the exact committed Git-free export also passed (release SHA256 70d74a0fbb9936b563e4208530ab5e44042112b70483f2b9cf521cf47eb76a68). All 571 exported files remained byte-for-byte and inode-identical.

Private solver/helper tooling is excluded. Source pins, predecessor credit, bounded discovery scope and open next questions are included. OpenAI Codex assisted with discovery, exact reconstruction, audits and tests.