Conditional κ = 0.001138823042306561: retain rank138 with complete 32-replica banks

[chafreaky]

Conditional κ = 0.001138823042306561 (1138823042306561 / 10^18). This retains two rank-one kernel pivots that eight-replica bank packing discarded. Thirty-two independent replicas fill every width-64 bank exactly, admitting entrance rank 138 without padding. The bit lower endpoint is 0.001140121438872176364117.

This is about 0.00219% above #441 at 6160c13526f5f957902910b462164c93c1d8f39a. #442 reports a larger bound using its additional idle-data hosting extension. This PR isolates replica banking within the preceding helper-bank interface and supplies a construction that can be composed with later hosting work.

The word starts from #436's R740 producer, uses 57 primitive A-frame changes and a re-derived 114-pivot/103-donor kernel, then independently rechecks #441's paired and window B-frame choices on the new word. The scalar ADD operands and order are preserved by retiming. Sixteen explicit residual isometries place 32 replicas into 2,891 complete banks per stage: 56,739 live and 56,748 physical families, deficit 9,984.

Validation: full Linux verifier and macOS cross-check pass; native make verify-joint passes (16 tests). The release checks pinned source bytes, complete parent reconstruction, frozen transformations, all 980 local arbitrary-dirt columns, both reflected streams, the one-replica 7,620-column global identity, all 288 emitted invocations and 213,120 helper assignments, exact projectors and residual routes, five reconstruction controls, 14 template mutations, two rational moment engines, a fresh finite invoice, six bootstrap levels and 47 strict outer inequalities. The prefix needs 123 bits (charged 128); the two-level coefficient needs 286 bits (charged 512). Eight-replica admission of the untrimmed selection is explicitly rejected. The adjacent 10^-18 κ grid point is rejected.

python3 -m pip install -r research/e8-r740-replica32/parent436/requirements.txt
bash research/e8-r740-replica32/verify.sh /tmp/e8-r740-replica32-full

The complex lower endpoint 0.001183986549206329 is cited from #433; its Gaussian phases are not replayed by this package. The all-size compiler, correlated dirty-bank, compressed-window, restored-work, tape/common-grid, precision and analytic interfaces remain assumptions. No unconditional theorem or new Lean proof is claimed.

Prepared by chafreaky with substantial OpenAI Codex assistance. Credit eumemic #436/#440/#441, our #417/#439 kernel and residual-route lineage, Rohan Arun #434/#435/#438, icekylinx #433, Zhihao Chen #425/#386, Dylan Crow #370, ai-nanachi #426, applecrusher #376, Jacob Sussman and the retained earlier contributors. Source-specific licenses, notices, assistance disclosures and exact pins are preserved.

[Mister-Meeseeks]

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

Contribution: 32-replica banks retaining two additional kernel pivots.

Review and limits: Complete bank tiling pays for all replicas and routes. The unchanged complex endpoint is cited, with its Gaussian phases not freshly replayed by this package.

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: 5a514e94f156edcc5fd827b87494d962f79d0f6c. Publication: 64039f1bd3b6a523b96083fd858ad040a75e3030.