Candidate conditional kappa 0.001017786140030308: enlarged entrances and target prefixes

[rohanarun]

Draft candidate conditional κ = 0.001017786140030308 (254446535007577/250000000000000000), +0.00099035% over #412's reported value.

Frontier update: newly published #416 reports 0.001017798035290733, slightly above this result. This PR remains a verified local component improvement over #412, but is not the current numeric leader.

Compose an eighth entrance-space enlargement on #413 with #411's target124/144 prefix rewrite. The eighth enlargement becomes profitable only after the seven earlier moves share donor advances; its local delta is {1:+2,3:-1}. The target rewrite adds {1:-1,3:-1,4:+1}. Both changes are applied to one literal word and priced from its regenerated exact profile.

Passed before draft: complete1021-column/retained-total equality for the enlargement; protected X/Y/gauged-helper columns and unchanged source/helper cleanup for the prefix rewrite; all204 gauged zero-response columns; complete nested paths; chronological source-before-write premise; exact residual packing; two rational moment engines and47 strict outer inequalities. The nongauged dirty response changes and is explicitly reopened.

Pending at draft submission: recomputed-response scalar admission in both formal orientations; quarter/eighth coefficient microcheck; changed Gaussian phases; actual physical owner/padding assembly and independent decoder; regenerated finite invoice/bridge; fresh bit composition and the full Python3.11/3.14 wrapper. This is a price-only candidate, not yet a fully admitted finite improvement. Submitted first as requested; CI retains failures.

The32-replica schedule uses2943 banks per stage,1495 rank-one pads,live57207,physical57998. Exact complex lower:1018823084044392067721/1000000000000000000000000. Unchanged bit lower:255384852701747/250000000000000000.

Run python -B research/e8-enlarged-prefixes/verify.py /tmp/enlarged-prefixes. It freshly runs all of #413, then this changed construction and bit composition. All seven package manifests are checked before/after. #413's complete changed local/phase/global/invoice build has passed locally; its full wrapper/CI remain pending. #409's prior full local attempt stopped on SSD exhaustion at the final link step, with its separate fresh bit run passing; no parent full-wrapper pass is invented here.

This does not assert unchanged legacy gx/gxcore acceptance. Inherited target overlap and quarter/eighth primitive sequences use the stated exact chronological/dyadic framework. All-size window, arbitrary dirty-bank, compiler, fixed-tape, restored-row, common-grid, precision and analytic interfaces remain conditional. No Lean certificate or unconditional multiplication theorem.

Prepared by Rohan Arun with substantial OpenAI Codex assistance. Credit eumemic #411 for target-prefix recipes, recomputed-response admission and explicit lowering (all local verifier/dependency bytes retained); #413/#409 for enlarged/ordered gauges; chafreaky #402 for the prefix-window method and #412 for the comparator; Dugongue #404/#401; #403 physical banks; applecrusher #376 and earlier E8 lineage. Apache-2.0 and original notices retained. Parent #413:cacb1f486a2ef5a184829b7f4d0cc4e357b47001; #411 source:f58d95f2c5da03445e704ea9c72cc55df9e68190.

Post-submission local verification

All changed components and fresh bit now pass locally. Both independent formal entrance orientations, recomputed dirty response (7079 entries/7180 unit macros), literal coefficient microcheck, 840 new/reflected phase pairs, physical assembly, independent owner/padding decoder, finite invoice/bridge, two moment engines/all47 outer constraints and fresh bit replay passed. Local invoice: 32731968 real primitives, local bound 9386569950752, per-vertex bound 2953502638045239, row 15449 < 20161.

The first global attempt rejected the stale full-raw-response equality condition. The repair imports #411's explicit protected-block/recomputed-response/helper-cleanup checks, plus response hash/count binding, into the replica-parametric emitter. All other physical, hash, scalar-invoice and independent decoder checks remain. This repair passed the fresh remaining integration.

VALIDATION-LOCAL.json and local-evidence/*.gz retain successful receipts and the failed attempts, including the parent SSD linker failure and superseded discovery-helper assertion. The complete uninterrupted wrapper and Python3.11/3.14 CI remain pending. Separate component passes are not represented as that full-wrapper result. The legacy-checker and all-size qualifications above remain unchanged.

Published local verification index links by filename/hash to the compressed receipts and failures.