Repository navigation
Prove the sharp joint dirty-word interval envelope (no new κ) - #6770
Merged
Mister-Meeseeks merged 2 commits intoNov 10, 2026
Merged
Mister-Meeseeks merged 2 commits into
Mister-Meeseeks merged 2 commits into
Conversation
Closes the gap between the retained lower family and interval upper bound. Includes exact finite corroboration and scoped independent AI review. Prepared for @CubeJerry with OpenAI Codex assistance. No new kappa.
Retain exact reviewed scientific hashes and distinguish the specified-word theorem from caller admission. No scientific files changed. Prepared for @CubeJerry with substantial OpenAI Codex assistance.
This was referenced Nov 6, 2026
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Summary
Prove the sharp height-uniform interval envelope F(h)=floor(h^2/2)+h+2 for the unchanged #628 balanced word: every ordered pair of ideal-leaf cuts, both orientations and shared dirty scratch. The new upper proof matches #1374's credited lower family and closes #5872's gap. #1085's entry invariant and #1278's phase/squarefree results remain explicit premises.
Canonical base and source pin: 7c49fe3. Exact source-file hashes are in SOURCES.json.
Evidence
Expected: PASS_CHRONOLOGICAL_DIRTY_INTERVALS. Normal/optimized registered and read-only Git-free replays passed: 95,735 prefix boundaries, 89,528 intervals, 2,118 phase identities and 15 controls. A separately written compressed scalar engine checks attaining witnesses through h=32. Separate proof/code review found no unresolved gap under the imported premises.
Limitations and next questions
No new κ. The bound is sharp across each height, not necessarily at every n; fixed-n sharpness remains open. Rounded callers, actual error support and the complete precision/physical invoice need separate integration. Five selected assumptions remain. Full-history validation was unavailable in the shallow checkout.
Attribution
@CubeJerry, with substantial OpenAI Codex assistance. Full proof, predecessor credit and exact review hashes: research package. Original notices retained; no independent human or proof-kernel acceptance claimed.