Repository navigation
Prove the owned-exit cut bound for P104 natives: ≥|W| owned exits per port-clique cut, tight on #6833's native, ruling out one-unit owned shortenings (no κ) - #6865
Open
DreamingOfClouds wants to merge 1 commit into
Conversation
…owned shortenings of the CrocSwap#6833 native infeasible (no κ) Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be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.
No κ claim. This adds
research/p104-owned-exit-cut-bound/, a registered research package for the cardp104-side-correction.Claim. For any native word obeying the frame law (public MOVEs strictly ascend; ADD, COPY and SCALE at a common frame; COPY only into a zeroed owned register; no owned register left at exit; owned MOVEs in any direction; dirty CLEAR, helpers and singular endpoint maps allowed), and any vector set
Q, the number of owned MOVE events from a frame meetingQto a frame missingQis at leastrank T[final publics outside U_Q, initial publics inside U_Q]. For a port cliqueW(q.q' = 1for all ports inW) andW <= Q <= A(W)this rank is|W|. The proof is a forward row-operation argument: the outside-rows matrix changes only by elementary row operations, deletions, and one new row per owned exit.Application. On the native word of #6833 (9|9 chain-nested root) the bound is tight on all 1967 maximal port cliques (owned exits =
|W|). Every one-unit end shortening of each owned lifetime is infeasible, each with a stored(W,Q)certificate: 246 core replacement frames and 547 ascending-start variants.Controls. 31,000 exact random legal words (owned moves in both directions, dirty CLEARs, singular maps): 0 violations. Control with public MOVEs allowed to descend: 65,551 violations.
Scope. A necessary condition in the abstract legal model; it bounds owned MOVE events, not dimension mass (the word is tight at 8 events), and a certificate shows only that the stated owned-move multiset is infeasible. It does not cover edits that change several lifetimes, add moves or change the root. No word is constructed and nothing is priced.
How to verify.
python3.12 -I -B research/p104-owned-exit-cut-bound/check.py(standard library only, about two minutes, reads only the two data files in the package) ends withPASS_P104_OWNED_EXIT_CUT_BOUND;python3.12 -B scripts/research_package.py --package research/p104-owned-exit-cut-boundprintsPASS_REGISTERED.Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.
🤖 Generated with Claude Code