[aliromman]

The rank-four chart in PR5756 is optimal over all 8,283,458 canonical subspaces of F2^9 for its fixed scalar block, throughout the current exponent range. An exact dimension reduction covers every subspace; 134 representatives supply 2,412 checks against the actual native rank engine. At the published κ, changing even one of the 18 independent local copies loses the complete caller's margin. Further gains must change the scalar assignment, use several charts, or change the helper contract.

The proof also classifies the recursive tariff for every 0≤C≤1. Among the 67 nested charts the only switch is in (.14739606083204,.14739606083205). Allowing every canonical chart gives a global switch in (.12477498342317,.12477498342318), from the unique rank-four chart to the full rank-nine chart. These are formal block tariff thresholds, not multiplication exponents. Explicit balancing transfers, positive power decompositions and exact rational interval bounds prove the ordering.

A separate complete replay reconstructs PR5756's word from PR5751 and the exact PR5739 edit list. Every word field agrees apart from the schema label. The local, native, physical and complete-price receipts agree, including κ=.00311313795, 13,390 productive fields and 66,852 paid calls. The 12,958 fields in PR5756's body at audit time are stale prose; its JSON agrees with 13,390. PR5756 receives composition and κ credit. This PR claims no new κ.

Validation covers all 776 arbitrary scalar inputs, separate transpose audits, 2,927 distinct native maps with phases, the full caller, both moment engines, compiler and all outer checks. The original four registered normal/optimized commands passed in 585.62 seconds. The added global optimizer passed normally and optimized in 2.34/2.25 seconds; all six commands are registered. Eleven actual source-byte corruptions reject. Metadata, committed bytes/modes, official export and final sealed replay pass; the validation record gives exact scientific commits and times. No single six-command runner pass is claimed.

Proof and scope, exact optimization receipt, complete replay receipt, canonical investigation.

Run python3.12 -B scripts/research_package.py --package research/p104-split-block-composition.

Limits: one common canonical chart per fixed block with separate boundary charges. Arbitrary Clifford coframes, changed scalar assignments, shared queries and cross-call corrections remain open. The broader tariff model does not admit every nonnested transition. Five inherited all-size assumptions and independent scientific acceptance remain. Full-history ancestry preflight is unrun in the shallow checkout; hosted CI is separate. Base 553d26d; latest canonical main de5ec2e and priority 8 were rechecked. No selected-frontier change, merge or closure.

Credit Joel Pulikkan/GamingPuzzled with Claude Opus 5.5 assistance for PR5739/5756, flyingviper for PR5718, PR5751 and all retained native/helper/controller/compiler/BIT authors. New proof and audit by Ali Romman with substantial OpenAI Codex assistance; no subagents. Apache-2.0.