[chafreaky]

This proves an exact ceiling for all 72-call choices of PR615's two native suppliers and all whole-helper packings into its fixed owner capacity inventory, using the inherited native moment and outer conversion:

κ < 1628658892827744394867 / 1001628658892827744394867 < 0.001626010676080313339617167.

The proof relaxes timing and includes fragmented idle capacity. Integer pattern weights and 92 rational inequalities replace the numerical LP optimality claim. Independent enumeration checks all 915 relevant integer multisets. The certificate has no solver or floating-point dependency.

The package also refines PR615's outer output grid from 10^-18 to 10^-24, certifying κ = 0.001626010676080313339567, within 51/10^24 of this family's ceiling. This is only a rounding refinement: the native words, recipes, owner assignment, moments, bootstrap steps and strict outer inequalities are unchanged. The next-grid rejection now tests the next 10^-24 tick.

This is not a frontier-record claim. PR617 changes the suppliers and is outside this ceiling. I independently replayed its exact head 904d62855723c00f8acef9a287a10768598fdeb2 with 42 fresh stages and a separate owner-map/moment check, obtaining its higher conditional κ of 0.001635183729255778. Its separate evidence is not part of this package.

Validation included here:

• Fresh macOS and Linux aarch64 Python 3.14.8 replays: 42 stages each, no baseline/local reuse; 271.526 s and 313.749 s.
• All 43 receipt artifacts and 42 raw stage logs per platform retained and hash-verified, including from the actual committed Git archive.
• Exact ceiling and outer-refinement certificates byte-identical across platforms.
• Five malformed-input controls rejected with Python assertions disabled; seven bootstrap steps, 47 strict outer constraints per model and fine-grid/slack rejection controls independently recomputed.
• Primary verifier byte-identical to PR615; source contracts unchanged. Only two arithmetic expressions change in the inherited runtime. Broad whitespace checks report retained whitespace in pinned inherited sources; new files pass the scoped check.
• A dedicated Python 3.11/3.14 CI workflow is included; CI results are not claimed yet.

Core proof and replay: research/complex-pr615-ceiling/. Raw evidence and search provenance: research/complex-pr615-ceiling-validation/.

Construction credit belongs to jeremykothe2 (PR615 and predecessors), DreamingOfClouds (PR604 and predecessors), and the earlier contributors retained in NOTICE. The new ceiling, supplemental checks and rounding refinement were prepared with OpenAI Codex. A four-branch fresh-context search selected the refinement; parent research supplied the ceiling. This applies the fork/select/continue method from https://arxiv.org/html/2610.07447v1 without claiming a controlled efficiency experiment.

The ceiling is restricted to these suppliers, this capacity geometry and this moment/outer interface. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape/exact recovery, analytic transfer and bit H1-H5 assumptions remain conditional. This is not κ=1, an unconditional multiplication theorem, or a complete Lean proof.