κ = 6.94787513005285e-4: plateau retiming on PR210's 471-source word

[sennemmi]

Status and relationship to PR210

This is a Draft stacked on PR210 head df95878d11190518e45ef9717c9ee05011f88ace.
The branch parent is that exact commit. Because the target base is main while PR210 is still open, GitHub's comparison includes PR210's pending cumulative changes; this PR's new contribution is the frame-plateau search and exact reprice documented under research/coordinated-crossover-pr200/search/.

Result

The candidate certificate gives conditional
κ = 694787513005285/10^18 = 0.000694787513005285, an exact gain of
4793314502/10^18 over PR210's 694782719690783/10^18.

The deterministic search retimes 19 operation frames in 14 accepted moves:

• op 18750: rank 5 → 6;
• five adjacent pairs (23544/23545, 23591/23592, 23638/23639, 23685/23686, 23732/23733): rank 9 → 12;
• eight operations (27900, 27904, 27908, 27912, 28052, 28056, 28060, 28064): rank 13 → 14.

The d log d score proposes moves only. Exact frame containment, nondegeneracy and nested role chains admit the moves. The physical word and scalar operations remain those of PR210. The raw child-histogram delta has weighted-rank change zero and 27 fewer children per vertex. The normalized profile keeps m=72, W=438838, rank mass 31549872, deficit 46464 and maximum child 22. Bit saving improves by 4799982097/10^18; the bit side remains binding. The exact 47-constraint assembly rejects the adjacent 10^-18 grid point.

Local checks completed

• joint-plateau-search-prdf958.py --verify-committed: deterministic 14-move replay, 19 changed operation frames; passed.
• Candidate source-boundary geometry checks for 440 borrowed sources, three rank-19 gauges and 28 source-backed gauges: passed, including reflected frame paths and target chronology.
• pack_joint.py: 231 charts and 3,594,888 bank assignments; passed.
• Exact parent profile calibration reproduced PR210's κ. Candidate price_joint.py reproduced the committed candidate certificate and all 47 positive rational constraints.
• The full scalar replay has not been run locally. It is the required Draft CI gate, along with repository-wide CI.

CI coverage required before review

The package's immutable offline verifier now replays the deterministic search before running the full scalar word, source/dirty restoration, target ledgers, charts, banks, complex lift, independent paid moments and exact assembly. The continued-kappa workflow runs that verifier and checks for workspace changes. The repository workflow runs all 16 make verify-* groups on Python 3.11, 3.13 and 3.14, ranked-pair finite verification, and the historical/Gaussian/matrix formal jobs. The Draft should remain pending until these checks finish successfully.

Public frontier and limits

The pre-submission 229-PR inventory is in research/coordinated-crossover-pr200/search/FRONTIER-SNAPSHOT.md. At the latest check PR210 remained open with all 57 GitHub checks passing. PR227 replays an older, lower PR210 head; the higher prices in PR219 and PR224 still have open physical construction obligations.

This remains a conditional finite supplier certificate. The all-size compiler, weighted/restored selector, source-line, routing, prime, precision, fixed analytic tape and finite-bridge assumptions remain inherited. No unconditional integer-multiplication theorem is claimed. NOTICE records PR210 and all inherited authors, upstream PRs, licenses and AI-assistance disclosures, plus this extension's sennemmi/OpenAI Codex provenance.

Reproduce with:

python3 -B research/coordinated-crossover-pr200/search/joint-plateau-search-prdf958.py --verify-committed
python3 -B research/coordinated-crossover-pr200/verify.py --temp-root /tmp

[sennemmi]

Archiving this Draft as part of the research closeout. Its independent contribution was plateau retiming on PR #210's 471-source word, with reported conditional κ 6.94787513005285e-4. The full research-artifact, terminal and recycled-bit workflows passed at head e3bf56ac17e4f3f005062626f81fae40809a4355; upstream PR #210 remains open. The method and certificates remain in this PR's history. Later fixed-prime work, including #261, superseded this portfolio result, so no further maintenance is planned.