Independent exact certificate of PR741 owner-profile optimality

[chafreaky]

This proves that PR741's idle profile {48:2396,44:1,3:1,1:1} is optimal for its fixed native supplier, 72 complete calls and capacity inventory. Every different idle profile fails the exact moment at the admitted PR741 endpoint; maps with the same profile tie. No new κ is claimed.

Five integer helper-width prices and four capacity bonuses exclude both the all-rank-48 profile and {48:2396,44:1,4:1}, with an integer contradiction of 25. Concavity and a positive eleven-step period reduce every remaining profile to 13 strict rational moment checks.

The independent checker uses count-vector enumeration, a separate base-two interval engine, and an integer dynamic program over all 115,057 possible non-48 masses. It directly covers every feasible number of rank-48 residuals without relying on the 13-case reduction. Eight mutations cover native widths and billing, ownership, chronology, dual prices and endpoint hypotheses.

python3 -B research/sw4-owner-optimality/verify.py --out /tmp/owner-proof
python3 -B research/sw4-owner-optimality/independent_check.py --out /tmp/owner-proof/INDEPENDENT.json
python3 -B research/sw4-owner-optimality/controls.py --out /tmp/owner-proof/CONTROLS.json

The package uses Python 3.11+ and the standard library. Fresh macOS 3.11/3.14 and Linux 3.14 runs pass in normal and optimized modes, with byte-identical mathematical artifacts. Sources and validation are pinned in the package and companion validation directory. The complete native scalar/phase/controller admission remains in PR741 and is not rerun here.

PR699 previously reported packing optimality for this shared width inventory. This supplies a solver-free proof for that packing shape, evaluated at PR741's stronger endpoint. Credits retain PR741/PR685/PR660's owner map and integer flow lineage; PR699's SW4 construction; PR676's p6n ends; PR664's promotions; the underlying gauge/no-triangle/native-audit lineages; and both unchanged interval checkers. Prepared with substantial OpenAI Codex assistance.

The result does not constrain changed local programs or widths, provider mixtures, dispatch counts, capacity inventories, split helper invocations or different hosting contracts. All inherited all-size, physical-realization and analytic-transfer obligations remain. No unconditional multiplication theorem or κ = 1 is claimed.