Candidate conditional kappa 0.001018475695250068: grouped entrance capacity and shared-frame enlargement

[rohanarun]

Conditional κ = 0.001018475695250068 (254618923812517/250000000000000000), 0.01380345% above #423.

On our #418 word, compose #414's four grouped promotions, #420's pivot 672, #421's two full rank-two promotions, then 13 of #423's 14 entrance enlargements. Pivot 785 is not an entrance on our word and is explicitly excluded; the unadapted transfer rejects. The final construction has 215 gauges and 587 entrance instructions. The last stage changes no scalar instruction and shares the frame costs of the paired 914/960 enlargement.

Validation of the current mathematical code (228c86d9a884dc827d90ccdadf7781ba46fb5eea) passed:

• All 1,021 complete and retained-snapshot columns through three hash-bound stages; literal shear multiplication in the first two, unchanged operators in the third; all gauged responses zero; chronological A/B frame propagation, snapshot/final endpoints, reverted-frame and omitted-gate controls.
• Both formal scalar orientations, arbitrary dirty restoration, private erasure, chronological target bracket, 7,017 freshly recomputed response entries and 7,118 unit response macros.
• 960 new/reflected exact Gaussian phase pairs and 16 signed coefficient-word microchecks.
• Actual physical owner/padding assembly, independent decoder and eight structural controls, regenerated finite invoice, reserve bridge, two rational moment engines and all 47 strict outer inequalities.
• Fresh bit composition at this exact complex bound. All nine package manifests passed.

18 committed receipts, including rejected transfers and failed attempts contain source and compressed hashes. They also preserve earlier candidate passes separately. The preceding rank-two version's physical template write failed with OSError: [Errno 28] No space left on device; that failure was not a mathematical assertion failure. The current enlarged word passed its own fresh physical replay after lossless archival and byte-identical archive deduplication.

Full local wrapper passed: the complete nested parent/new replay and fresh bit composition passed against abd6c8f8173497980f1f3e3da023252b2c172719; its receipt is included in local-evidence/full-wrapper-result.json. Python 3.11/3.14 GitHub CI remains pending. The PR remains a draft.

16 replicas; 1,465 banks per stage; 28,545 live and 29,336 physical registers. The invoice charges 16,387,872 real primitives, local bound 9,415,823,881,912, 61,920 bank-boundary adapters and row reserve 15,447 < 20,161. Complex lower: 1019514045526403509333/1000000000000000000000000; unchanged bit lower: 255384852701747/250000000000000000.

Run python -B research/e8-grouped-closure/verify.py /absolute/path/to/new/output. It freshly replays #418, all three immutable constructors, the current finite assembly and fresh bit, checking nine manifests before and after.

This uses the broader chronological/dyadic conditional framework of #418/#423. No unchanged legacy gx/gxcore E4/E5 acceptance, Lean proof or unconditional exponent is claimed. Inherited all-size window, arbitrary dirty-bank, compiler, fixed-tape, restored-row, common-grid, precision and analytic assumptions remain.

Prepared by Rohan Arun with substantial OpenAI Codex assistance. Credit eumemic #414/#420/#421 for the seven promotions, #423 for backward-capacity/shared-frame enlargements, #416/#421/#423 immutable constructors, #411 prefixes/lowering; Rohan #418/#415/#413/#409; chafreaky #419 (comparison and byte-identical #414 data retrieval) and #402; Dugongue #404/#401; #403 banks; applecrusher #376 and Sussman E8 lineage. Original licenses/notices retained. Parent #418: ff8737920a4bb1a910eb069a5f86db6efdefa589; #423: 997613cb3064b4096b996409a671e558251d55f8.