Repository navigation
Construct the selected complex stopping cutoff from Gamma headers with paid unary arithmetic and preserved caller tapes - #7350
Open
CubeJerry wants to merge 1 commit into
Conversation
…h paid unary arithmetic and preserved caller tapes
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Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be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.
Result
Produce C=min(ceil(d^(1/Q)),e+1), Q=10^14, directly from Gamma(p)Gamma(d) on an eleven-tape literal program; link it to the unchanged rank-one controller and retire every private marker.
Novelty and predecessors
The selected epsilon=1-1/Q makes paid unary preparation O(h+d*C)=O(p), including head returns, erasures and historical unary-d backing. The stopping exponent differs from the outer exponent.
Verification
357 author cases plus 117 independent dense-CPU cases, proof/cost review and mutations. Run python3 -B research/selected-header-cutoff/verify.py.
Limits and kappa
Valid header and post-reservation WIDTH are inputs; no final grants/payload. No new kappa; 0.00363005817 remains conditional.
Credit
Prepared for @CubeJerry with substantial OpenAI assistance; credit predecessor authors and PRs as detailed in the package.
Full proof, reproducibility, negative controls and provenance: https://github.com/CubeJerry/integer-mult-bounds/tree/da3f01ded52e84388d9b40b70590dd4dce6f51b4/research/selected-header-cutoff