Conditional kappa 0.001013370540420331: 64-replica response-subspace banks

[rohanarun]

Preserve PR401's full local response-subspace construction and improve only its global replica packing. Conditional κ = 0.001013370540420331 (1013370540420331/10^18): +0.00588694% over #401, and +0.001244% over the subsequent #402 (0.001013357935292321). This does not include #402's separate target re-synthesis.

64 replicas permit 5983 banks per stage, with 3863 rank-one paddings. Compared with eight scaled copies of #401, this saves one bank per stage and replaces eight rank-ten paddings with seven rank-one paddings. The raw word, 119 entrance gauges, both local orientations, Gaussian phases and two-sided adapters are unchanged. Live stock is 115287; physical stock 116078; rank mass 8395983; deficit 19968; all 576 local invocations and 137088 bank boundary adapters are charged. The freshly derived row coefficient is 15451 < 20161.

Complex lower bound: 202879700395696507197/200000000000000000000000. Bit lower bound: 255384852701747/250000000000000000.

Verification at draft submission

• Fresh PR401 reconstruction, all dirty-column local checks, Gaussian phases, original banks, independent decoder and outer pricing passed locally.
• Changed 64-replica global template, every inverse owner route, padding schedule, three expansion mutations, eight bank mutations, independently recomputed invoice and exact finite bridge passed.
• Two exact moment engines, retained fallback, six bootstrap levels and all 47 strict outer inequalities passed.
• Fresh bit replay at the changed complex bound passed.
• Full clean wrapper CI on Python 3.11 and 3.14 PASS, run 38127329705, unchanged head 4e3ef5fe92652b1a740b32cbea90d0fea678062e. Both artifact receipts match the local profile, invoice and exact bound. All 66 repository checks now pass. Draft-first submission as requested. The earlier local optional bit attempt failed only on macOS bits/stdc++.h; the separate replay passed with a portable header. Failures are retained locally; CI uploads outputs even on failure.

Run python -B research/e8-response-bank64/verify.py /tmp/response-bank64. The wrapper freshly replays the complete immutable PR401 supplier, regenerates the changed construction, then freshly replays the bit component. It checks every file manifest before and after. The full original 136-file supplier package is included with byte-preserving Git attributes, avoiding missing-source or newline problems.

The finite packing witness, unsuccessful smaller-replica searches, exact adaptation ledger, proof and verification code are in research/e8-response-bank64. Immutable source research/e8-response-subspaces is pinned to Dugongue #401 commit 7844f72c6051a4408284c3092490687061675c1a. Parent #400 preserves prior research; its numeric gain is not added here.

Scope and credits

This is a conditional finite construction. Inherited all-size window, arbitrary-correlated bank, recursive compiler, ordinary-call/fixed-tape, common-grid, restored-row, precision and analytic contracts remain assumptions. No unconditional multiplication exponent or formal Lean theorem is claimed.

Credit Dugongue for #401's response subspaces and normalization, #398/#390 and the preserved upstream lineage; chafreaky for the subsequent independent #402. New replica packing and verification by Rohan Arun with substantial OpenAI Codex assistance. Apache-2.0; all supplier notices retained.

[Mister-Meeseeks]

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

Contribution: 64-replica response-subspace banks.

Review and limits: Complete response supplier replay and fresh bit component. Replication is charged in the actual bank inventory; it is not free amplification.

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: 4e3ef5fe92652b1a740b32cbea90d0fea678062e. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.