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Prove and measure a simplified prefix-completion support bound - #6046
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This publishes the October 23 scoped prefix-completion study: a remaining-tail distance envelope safely rejects incomplete singleton-coordinate walks that cannot supply every pair-XOR, and a reflection argument eliminates the future-pair loop entirely. It adds a scoped research archive, with no maintained-engine or selected-frontier change.
At five labels and length twelve, an independent position-block oracle and canonical traversal agree on all 3,695 simple closed words and all 828 universal words. The envelope rejects 67 additional prefixes that pass the old controls and the frozen #5001 matching-capacity predicate. The package records full-set hashes, 44,340 completion checks, 108,195 exact matching-predicate comparisons and 203,225 actual-completion split checks.
The complete runtime result is negative: 147 sequential fresh processes show 9.25% median paired overhead versus cheap bounds, despite fewer visited prefixes. Accordingly, this does not propose engine integration or a larger census. Historical TASK/VALIDATION publication fields and timing receipts are preserved; PUBLICATION.md identifies this October 28 publication checkpoint on main 721c038.
Validation: fresh registered normal and optimized replays both pass. The original session additionally checked seven code mutants, two integrity controls, and read-only Git-free committed-export replay. The publication byte check is run at the submitted commit. Python 3.12, standard library only; reproduce with
python -B scripts/research_package.py --package research/five-label-prefix-completionor the direct commands in README.md.Credit Ali Romman (#4992/#5001), Mihir Srivastava (#4907), Nick Petalas (#4894/#3005), Ross Richardson (#943), Nicholas Stone (#2973), unpaidmoon (#4148), James Reed (#3096), and the retained predecessor lineage. Prepared for SHIN09-git with substantial OpenAI Codex assistance. No independent human or formal proof-kernel review, supplier admission, seven-label theorem or new kappa is claimed.
The package's hosted scientific replay passed. Its research-package bytes are unchanged at the current head. Full current CI is blocked by two shared navigation-test failures already present on canonical base 721c038; PR6050 separately repairs them. This PR's final diff contains only the research package.