Conditional κ = 0.001622285497914735: exact per-time-Hall owner map for the PR604 cold-ended witness

[jeremykothe2]

Summary

Conditional κ = 0.001622285497914735. This is +1.0004e-6 (+0.062%) over PR604's current head (0.00162128508944984, 1b795c5, which re-solved its owner map) and +0.132% over PR604's original commit af8c23b (0.001620147045734211), on which this package is built. The conservative model gives 0.001622285495037214.

This PR is DreamingOfClouds' PR604 at af8c23b (complex-571-cold14: 14 cold factory-scratch helpers per call ending at 4-dimensional frames, on our PR601 witness) with an improved literal owner map only. Dispatch is unchanged: ck ×44, atm3 ×22, jp8 ×6. The map comes from an exact per-time-Hall (König-realizable) exact-window owner MIP: it enforces one helper per port per call within each owner group, which PR604 names as the binding owner-side constraint. It was solved by RINS around the exact-window LP vertex. Objective 523256.223 against an LP of 523256.174 at this dispatch (PR604: 523259.607). Idle remainders become {1:1, 7:1, 32:1, 48:2100}. Against PR604's package, only data/OWNERS.json.gz, data/PLAN.json (windows and profile) and data/SPEC.json (expected values) differ. All construction code, cold_end and every other step, controls, proofs and the verifier are PR604's, byte for byte. The package directory is renamed complex-571-cold14-r1 so it doesn't collide with PR604's, and README, NOTICE and verify.sh name it accordingly.

All of PR604's soundness argument applies unchanged: Lean via #593/#599 (hpe_word_multi, exact_cold), exact (N) checks for every (0, U_b) pair, the guarded refactored cleanup, and wrapper-order enforcement. An owner map only changes which helper sits in which owner slot. PR604's strict physical owner audit, invoice and assembly re-check that from scratch.

Verification

research/complex-571-cold14-r1/verify.sh /tmp/complex-571-cold14-r1 ..   # SOURCE_ROOT holds worktrees pr568 pr569 pr571 pr575 pr583 at the pinned commits

Local result (Windows, CPython 3.11.11): the commit was preflighted from a fresh clone first (committed blobs equal the MANIFEST, every file LF, pin check passes). The official run from that clean clone of 10255d4 then gave PASS_COLD14_NATIVE_COMPLEX_AND_CITED_BIT, κ 0.001622285497914735, 55/55 stages exit 0, 451 s, with no reused baseline or locals. The receipt records MANIFEST sha256 515ea2b9…, equal to the committed MANIFEST.

GitHub CI has not run, and I make no claim about it.

Declarative inputs

Unlike our PR591–PR603, this package doesn't yet ship data/WITNESS.json, data/EXPECTED.json or data/cand.json, because our witness tools don't yet support PR604's cold_end step. Those files will follow as a separate commit on this PR, after their own official verify.

Credits

• DreamingOfClouds: PR604 (the cold-ended construction, cold_end, verifier changes and package), PR599, PR509 and PR516 (Lean).
• jeremykothe2: PR607, PR601, PR600, PR596, PR593, PR592 and PR591 (the hyperplane-end base), and this owner map.
• The pinned PR568, PR569, PR571, PR575 and PR583 packages and all earlier contributors are listed in NOTICE.md.

AI disclosure and authorship: Claude Opus 5.5 (Anthropic), running in the omp coding harness, found this owner map and prepared the PR. Jeremy Kothe (jeremykothe2) directed and reviewed it and is submitting it.

Scope

The result is conditional on the inherited all-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape/exact recovery, analytic transfer and the bit H1–H5 assumptions. It inherits PR604's draft status: PR604's own heavy verification was still running when this was opened. It is finite exact evidence, not an unconditional theorem, a complete Lean proof, or a practical speedup.