Repository navigation
Prove all-width resonant rank and explicit image recovery - #4885
Merged
Mister-Meeseeks merged 1 commit intoOct 23, 2026
Merged
Conversation
This was referenced Oct 23, 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
2 participants
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Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be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.
For the exact resonant channel coefficient from #4797, prove its rank for every integer f >= 1, answering the general-width question in #4825. The rank is
3*(8^f+(-8)^f)/256 + (4^f+(-4)^f)/64 - (2^f+(-2)^f)/8.Odd widths vanish; the first even-width ranks are 1, 100, 6256 and 395200. The same exact group-algebra certificate constructs fixed polynomial support projectors and the Moore-Penrose pseudoinverse, with a width-independent inverse-norm bound. It recovers the accessible input projection from every channel output without assuming a decoder oracle.
This is a partial-channel theorem, not a complete multiplication supplier or a new kappa. The requested kappa improvement was not obtained. A paid consumer, the missing complementary coordinates and a complete source-uniform native ledger remain necessary for that goal. The explicit native recovery program charges fixed rational scalar operations and includes a conservative O(N w) basic-arithmetic fallback.
Validation: the registered research-package replay and committed-byte audit pass. Exact unbounded integer arithmetic checks a degree-18 identity on a 21,504-element group; normal and optimized Python replay agree. A separate literal tensor implementation checks widths 1, 2 and 3, absolute phase and pseudoinverse scaling. Separate optimized subprocess mutations reject changed source bytes, an altered annihilator and discarded phases. Three-agent work includes independent review. Offline standard-library Python 3.10+; no solver, Git, GPU or network is required for the exported scientific checks. Hosted Linux CI and a Lean kernel audit were not run.
Credits: JoyboyBrian #4797 (coefficient and partial-channel question), Nick Petalas #4825 (exact width-four rank and general-width question), Yiyang #4710 (phase repair), lee-phys #4688 (two-image prefix), Jacob Sussman #4628 (small-unit/free alphabet), and #4751 (retained-owner arithmetic scope). Prepared by Dugongue with OpenAI Codex and three agents. Standard group-algebra/projector/pseudoinverse methods are not claimed as new. Apache-2.0 and explicit predecessor attribution are retained.
Only research/resonant-all-width-projector is added. Canonical main is pinned at 624de9d. The selected frontier and authoritative MathProof DAG are unchanged.