Research: optimal clean root checkpoint saves 25–40% of binary product-shear calls

research/clean-checkpoint/CLAIM.txt

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+Track: recursive interfaces; OS-random assignment seed 54.
+Base: 66849e1475c930fd7732b1a0067ffee7e1e95f60.
+Scope: one explicitly clean length-L checkpoint at the root of PR628's dirty product-shear recursion, removing the final right-subtree cancellation and pricing the extra clean storage and both restoration passes. Investigate the optimal root split with unchanged balanced dirty subtrees, n=2..256; seed-selected demonstration n=54.
+Method: exact integer/noncommutative execution, complete leaf/resource recurrences, wrong-dirt and omitted-restoration controls. No kappa or rounded-accuracy improvement claim.
+Deliverable: standalone research note, executable checker and deterministic certificate.
+Candidates: (1) this clean checkpoint, (2) weighted dirty split tree, (3) stride-boundary fusion. Pick (1) because #663 audits the all-dirty dispatcher, #665 concerns spectral hosting, and neither supplies this changed-storage interface.
+Coordination: the open-issue query found only unpinned #650 (Discussions request), with no comments; no pinned sprint coordination issue was available. Claim recorded locally. Reviewed recent open PR metadata through #668 plus targeted clean/dirty, checkpoint/commutator and restoration/recursive searches.
+Expected finish: 2026-10-13 12:07 Asia/Shanghai (04:07 UTC). Last 10 minutes reserved for verification/packaging.
+
+RESULT — completed 2026-10-13, final verification/packaging phase.
+One clean-root adapter, exact optimal-split proof, full work/storage recurrence, 32,640 split checks, 498 noncommutative cases and 216 rounded dense comparisons. Generic n54: 3,136 -> 2,112 leaves; one clean plus five dirty arrays replaces six dirty arrays. No new kappa. Result: README.md; full proof: PROOF.md; certificate: EXPECTED.json.
+Fresh overlap review through #675 found concurrent #673 (head 0e35f56cab3cae1eb0a99447135569d687c5695a), whose distinct multiway echo is credited. Its phase-alias finding was incorporated as a root guard with five alias controls and a removed-guard rejection test; its original patch is pinned. This result retains balanced dirty subtrees and the same total scratch-array count, a different storage tradeoff.
+Verification: both local Python versions, isolated optimized execution, standalone relocation, four package corruption controls and selected-record integrity pass. Supported-Python root make verify passed seven historical groups then stopped at gen4 on missing SymPy; no full-suite pass claimed. Exact details: VALIDATION.md.
+Initial local handoff: local branch research/seed54-clean-checkpoint, clean patch plus standalone package; GitHub submission unavailable because the connected account has no push permission or existing accessible fork and the initially checked in-app browser was signed out. No coordination post or PR was created; no existing PR was changed. Selected frontier and upstream/ remain unchanged.
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+Publication preparation update — 2026-10-13. A user-authorized continuation found the Chrome session signed in as FanPUYen. Refreshed recent PR metadata through #709 and the targeted clean-checkpoint search (no matches). PR689 by Dillon Amburgey refines balanced ternary placement in PR673; this result instead changes the root storage contract while retaining balanced binary dirty children. No PR689 code is consumed. Publication status is tracked in the external handoff record.