[jeremykothe2]

Summary

Conditional κ = 0.001625715867072461. This is +3.51e-7 over PR610 (0.00162536523418317) and +3.43e-6 over our PR609. The conservative model gives 0.001625715864253489.

This PR uses DreamingOfClouds' PR604 cold-ended provider words (complex-571-cold14 at af8c23b: 14 cold factory-scratch helpers per call ending at 4-dimensional frames, on our PR601 witness) unchanged. Code, cold_end step, controls and verifier are PR604's, byte for byte. Only the dispatch and literal owner map change:

• dispatch jp8 ×70, atm3 ×2 (atm3 at stages 0 and 2);
• an exact-window, per-time-Hall (König-realizable) owner MIP, solved by RINS around the free-dispatch exact-window LP vertex. The MIP stopped at its 150 s time limit with a gap of 1.43e-7, so the map is not proved optimal.

The second provider sits at an even stage on purpose. PR604's wrong_selected_call assembly control needs each provider's first call to have another provider's call at the same stage parity, and a dispatch with atm3 at stages 0 and 1 fails that control. Because ck is not dispatched, ck is removed from the SPEC's providers and build, as the verifier requires: they must equal the dispatched set. The 114 assembly controls and 23 audit mutations are the full two-provider sets, and strict mode rejects every one.

All of PR604's soundness argument applies unchanged. An owner map changes only which helper sits in which owner slot, and PR604's strict physical owner audit, invoice and assembly re-check it from scratch.

Declarative inputs ship in this first commit:

• data/WITNESS.json (inputs only);
• data/EXPECTED.json (expected values, generated by recomputation with generic tools extended to PR604's cold_end step);
• data/cand.json (the search-side candidate, package-relative);
• data/search/ (the warm-start map and plan, PR604's template plan, the LP pattern sets and the dispatch);
• a definition-first README.

Rebuilding data/PLAN.json from the solver output reproduces it byte for byte. One inherited SPEC value is corrected: entering_helper_roles goes from 16344 (stale since PR601) to the audited 16584. PR604's verify.py does not read this key.

Verification

research/complex-571-cold14-f6/verify.sh /tmp/complex-571-cold14-f6 ..   # 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, spec.py check OK). The official run from that clean clone of 6cfd7e2 then gave PASS_COLD14_NATIVE_COMPLEX_AND_CITED_BIT, κ 0.001625715867072461, 42/42 stages exit 0, 439 s, with no reused baseline or locals. The receipt records MANIFEST sha256 e373aa05…, equal to the committed MANIFEST. Separately, a strict generic verify from data/WITNESS.json + data/EXPECTED.json passed (41/41 stages, same κ).

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

Credits

• DreamingOfClouds: PR604 (the cold-ended construction, cold_end, verifier changes and package), PR599, PR509 and PR516 (Lean).
• jeremykothe2: PR609, 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 dispatch and owner map, built the declarative inputs 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 builds on PR604, which is not merged. It is finite exact evidence, not an unconditional theorem, a complete Lean proof, or a practical speedup.