Repository navigation
Conversation
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Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be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.
In the canonical shortest eight-field scalar root, a common rank-four stage at sites (1,2) forces a commuting common stage at (5,6) to have rank at least five. With rank-two endpoints and one granted fragment from each pure paired bank, every possible second-stage rank has a strictly worse complete invoice than an orientation-matched #6726 allocation, for every positive child allocation, binary subtree and 0<κ<1.
The new result combines universal actual-prefix geometry with complete cost accounting. Rank five has a forced target inventory and difference 104*(H(8C+1)-H(8C)-1)<0; an independent eight-inventory classification excludes all larger ranks in this fragment contract. Credit zxv #6726, thu-nmrc #6717, Ali Romman and Cinna Davis; their source constructions are inherited.
Reproduce (Python 3.12, stdlib):
Expected PASS_REGISTERED_RESEARCH_PACKAGE. Primary and separate invoice checks pass normally and with -O. Independent geometry checks cover all 6,561 F3 parameters and six rank-five cases. Formal arbitrary-input identities, 16 allocation/orientation fixtures, all eight inventories, failed-prefix/missing-idle/endpoint controls, source pins, committed bytes/modes and unchanged Git-free primary replay pass.
No new κ. Scope: char!=2, the stated shortest scalar word, common commuting stages and exactly one fragment per nonempty pure bank. Fragments are granted, not constructed. Extra retirements, other fragment distributions, placements, larger first pairs and coupled controls remain open. The numerical ceiling corollary is conditional on #6726's unreplayed allocation-tail certificate; pointwise dominance is independent of it. All five framework assumptions remain.
By @CubeJerry with substantial OpenAI Codex assistance and separate geometry/accounting reviews. No human/proof-kernel acceptance, selected cold replay or full-history preflight. Base 7c49fe3; exact source heads and digests: ORIGINS.json. Proof, sources and reviews. Complete remote tree equals the tested tree.
Selected-baseline source bindings and metadata passed the required orientation check; this was not a construction cold replay.