[aliromman]

Change and mathematical scope

Conditional κ increases from 0.00329394 (PR6545) to 0.00329492: +0.00000098, or +0.0297516%. This is the incremental gain over the strongest public proposal checked for this contribution. Inherited gains are excluded. The selected frontier is unchanged.

Keep PR6545's independent Gaussian retirement and PR6529's native word. Rebalance the four binary children from (7,2,2,7) to (7,2,5,4). The first 329 events and the retirement bases are unchanged. The full signed invoice gains 208[(H41−H40)−(H57−H56)], strictly positive for H_r=r^t, 0<t<1, by the decreasing derivative. This changes the construction and invoice; it does not just refine the old root's decimal value.

All 18 native calls, 17 thin queries, 13,756 productive fields and 67,096 paid Gaussian jobs remain. The 35-field caller has 611 events instead of 609. Both paid and productive rank mass fall by 832; the surplus remains 760. The two extra ordinary translations are included in the complete 254,932,208-operation upper bound, below the retained 10^9 allowance.

Start with the proof, complete receipt, tree data and literal caller.

Task and overlap

Base: canonical main 7c49fe32c55de02c2c873655c804b16e4c3fef0a, priority revision 8. The explicit user task asks for another κ improvement of any size. Card p104-side-correction is marked changed: the exact published retirement makes a different caller tree profitable. This contribution supplies the changed arbitrary-input caller and complete price.

Immediate source: PR6545 at 775722aa94a5e85b05d1d704d7dca10cbf016f0c. Its native source is PR6529 at 44b0d0e8961201ac1656490b4384a7752e1cd9c5; replay services are PR6524 at dd1a979bfff090fa6559cc3b7d4e7f5ab24b4f80. Exact sources, proofs and notices are retained with original paths, Git blobs and SHA256 values. No side-branch history or network fetch is needed for scientific replay.

Canonical claim. PR6545 had released its continuation, including retirement-aware price screens. This uses its published identity and claims no new retirement mechanism or global caller optimum. The other fixed-native contact search remains separate. The earlier full cache covered 497 open PRs and 6,487 Discussion records; live source claims, hubs and updated PRs through #6550 were checked again before submission. Canonical main and PR6545's head are unchanged. Unpublished work, arbitrary diffs and sparse historical notes remain coverage limits.

Validation

CPython 3.12.13, standard library:

python3.12 -B scripts/research_package.py --package research/retirement-rebalanced-query-tree

Normal and optimized registered replay pass. The verifier regenerates the complete native source, checks all 799 native columns and absolute phases, replays PR6545 and matches every frozen result, then checks all 1,225 new caller coefficients with forward and reverse engines. Exact dual pairs, all 7,488 physical contacts, the complete invoice, two rational moment engines, compiler and all 58 outer predicates pass. Thirteen new caller/invoice rejection controls and four source-corruption controls pass, alongside the retained controls.

The raw crossing is enclosed in (0.00329492611057136286764342, 0.00329492611057136286764343); tested saving is .003294925. Both rational engines reject the complete PR6545 invoice at the new claim. Its old tail decay fails here, so the new price uses decay 97/100 and reserve 10^(-27), at the same power 1920. All tail tests pass.

All 17 final committed files pass byte/mode checks. The official export passes integrity and declared-input checks. Normal and optimized direct replay pass from a read-only export with no Git metadata and an empty PATH; all 18 exported files, including metadata, remain unchanged. The final commit only updates the validation record after that replay. Hosted CI passed at head 11ca568cd1a16776ade02b4df09ea04a784cc674: 711 helper tests, both complete registered scientific replays and unchanged committed inputs. Completed logs were read once. GitHub's synthetic test tree matches the published/local tree; no actual merge occurred. See validation details.

The five inherited assumptions remain: native all-column behavior, owned erasure, compiler closure, precision/tape bounds and analytic recovery. Independent scientific review, formal-kernel verification and a materialized complete integer multiplier remain open. The optional full-history preflight is not claimed in this shallow checkout. No merge, closure or selected-result edit is included.

Credit

New allocation, proof, integration and checks: Ali Romman with substantial OpenAI Codex assistance; no subagents. Apache-2.0. Credit PR6545's retirement, PR5599/5602/5611/5615's handoff and basis methods, PR6348/6398's binary suppliers and mixed root, PR6529's native word and PR6524's replay services. Retain Rohan Arun, Erwan L., DreamingOfClouds, Cinna Davis, David Arias, Gareth Davidson, Jacob Alan Sussman, zxv, Cao Yifan, ywz65, Nick Petalas and all archived predecessor notices.

Open next questions

The smallest follow-up is independent review of the unchanged prefix, equal target group and exact invoice delta. Structured next questions also identify the missing exact caller needed for a larger gain. No broader construction scope is reserved.