Research: uniform owner-profile optimum through saving exponent 1/3

[cbethin]

PR795 proves optimality of the SW4 owner profile at PR741's admitted endpoint. This extends its packing argument to every real 0 < b <= 1/3, independently of the fixed local paid profile. The selected PR799 construction has the same inventory and attains the optimum. No new κ is claimed.

For 72 complete calls, the stated five helper widths, 112 bins per window, and the current four-capacity inventory, every different feasible idle profile has strictly larger sum I(r) r^(1-b) than {48:2396,44:1,3:1,1:1}. Assignments with the same profile tie. Future local circuit changes can reuse this conclusion if they preserve those packing data and admit the assignment. This removes a repeated owner-search question; it does not exclude changed inventories, dispatch, split helpers, or hosting rules.

The new integer-price exclusions remove all two-part remainders [r,48-r] with 33 <= r <= 44. PR795's concavity and eleven-step reduction then leave twelve analytic inequalities. A complete generalized Descartes argument and exact cube-root bounds prove them over the entire interval. The separate checker uses count-vector enumeration, all 147266 capped partitions of 48, and rational Taylor/Bernstein bounds on the continuum. It imports neither the primary checker nor PR795's implementation. Both methods share the explicitly stated packing model and written concavity/period reduction.

python3 -B research/owner-profile-uniform/reproduce.py

Expected: PASS_UNIFORM_OWNER_PACKAGE (standard-library Python 3.11+).

Validation passes on Python 3.14.6 and optimized 3.13.11: twelve interval certificates, 1163 independent width patterns, all 36288 archived PR799 owner roles, both archived native paid profiles, nine rejection controls, two boundary controls, portable minimal closure, corrupted-source rejection, existing-output preservation, and selected-record integrity. The source pins identify the actual retained PR799 replay archive. This is a fresh recount of archived data, not a fresh full native construction replay. No full repository suite, new Linux CI, Lean formalization, or independent human mathematical review is claimed.

Only research/owner-profile-uniform/ is added. The selected frontier and upstream/ are unchanged. Base: f567884aeb8851b6e794af1184119a3bfbe1e631; OS-random track seed: 99 (research consolidation). Exact sources: PR795 56b626800c85026b10dada646c80c6b58179b427, PR799 80e6463157cfc80b85af09e7e2f14748fe2dac60.

Credit: chafreaky's PR795 supplies the integer dual and concavity reduction, with the PR741/685/660 owner lineage. Jeremy Kothe supplies PR799's X4 and the PR699 SW4 lineage; earlier ends, promotions, gauge, supplier, and recurrence work retain their attribution. The complete notices and inherited all-size/compiler, realization, hosting, precision/tape and analytic assumptions remain explicit. Prepared by Charles Bethin with substantial OpenAI Codex assistance. Apache-2.0.