Conditional kappa 0.001013417593791468: target re-synthesis with 64-replica banks

[rohanarun]

Combine chafreaky's PR402 exact target re-synthesis with our PR403 64-replica bank packing: conditional κ = 0.001013417593791468 (253354398447867/250000000000000000), +0.00464325% over #403 and +0.00588721% over #402.

A later refreshed comparison finds #404 (0.001016422320428301) above this result. This PR preserves and verifies the independent #402 + #403 composition; it does not claim the current lead.

Targets 177 and 220 change chains (3,5) to (6,2). The complete raw operator stays identical to #401 on all 1021 initial columns. We retain #401's original old-response/full-cleanup bracket and its 119 entrance gauges, then apply #403's 5983-bank-per-stage packing across 64 replicas. No helper residual changes.

This also freshly checks #402's reopened finite obligations: exact Gaussian phases of the changed target edges and literal scalar/compiler costs. All new/reflected phase pairs pass, and the full changed invoice is recomputed: local bound 7426971483782, per-vertex bound 4739351817956823, row 15451 < 20161. Live stock 115287, physical stock 116078, rank mass 8395983, deficit 19968.

Complex lower: 126805706357749635841/125000000000000000000000. Bit lower: 255384852701747/250000000000000000.

Draft verification

Local constituent checks PASS: independent full raw-operator reconstruction and mutations; both dirty scalar and formal entrance-chart orientations; dynamic Gaussian edge compilation; all 26 two-sided residual phase identities; every bank inverse route and chronological schedule; independent global decoder with eight adverse controls; regenerated scalar invoice and exact finite bridge; two exact moments, retained fallback, six bootstrap levels and all 47 strict inequalities; fresh bit replay at the changed complex bound.

The complete packaged wrapper CI on Python 3.11 and 3.14 is pending at draft submission. It freshly executes the full immutable #401 supplier before the entire changed pipeline and fresh bit replay. #403's full wrapper has already passed both Python versions in run 38127329705.

Run python -B research/e8-response-resynth-bank64/verify.py /tmp/resynth-bank64. The new package contains the exact adaptation ledger, immutable PR402 reconstruction sources/designs, manifests, proof and local evidence; inherited packages are byte-preserved. CI retains failed output too.

Scope and credit

Conditional finite construction only. Inherited all-size window, correlated-bank, recursive compiler, ordinary-call/fixed-tape, grid, restored-row, precision and analytic contracts remain assumptions. No unconditional multiplication exponent or formal Lean proof.

Credit chafreaky / Chafik Boukhalfa for #402's exact value-level target re-synthesis; Dugongue for #401 response subspaces, full local admission and two-sided normalization, and #398/#390; all source notices and upstream lineage are retained. This new composition, independent replay and invoice integration is by Rohan Arun with substantial OpenAI Codex assistance, Apache-2.0. PR402 pins commit 7883c63ec724999b921c2304b66648cbb9e7a112; parent #403 pins 4e3ef5fe92652b1a740b32cbea90d0fea678062e.