rpinho1/math-certificates

Math certificates (data)

Explicit, machine-checkable bounds on open optimization constants, mostly from Terence Tao's optimization-constants table, plus nine candidate linear codes for codetables.de. This dataset holds the data files: certificates, witnesses, tables and check outputs. The proofs, checkers, methods and the retro live in the GitHub repository rpinho/math-certificates.

Every file here is a byte-for-byte copy of the same path in that repository at commit 7944c62. MANIFEST.tsv gives each file's SHA-256, size and GitHub link, so you can check the bytes against the repository and run the checker in the matching GitHub folder on them.

This dataset: huggingface.co/datasets/rpinho1/math-certificates. Code and proofs: github.com/rpinho/math-certificates.

Status: read this first

Verification levels are defined in VERIFICATION_LEVELS.md. Every bound below is L0 as a whole: AI-written proofs, checkers by the same AI agent unless the GitHub row says otherwise, AI reviews, no human referee. The C91 finite certificate is L1 (checked by code from a different model). Most rows are candidates in open pull requests, not values on the table. The search, proofs and checks were done by AI agents (Claude, and OpenAI Codex models) under my direction.

Folder	Constant	Bound	Status at commit 7944c62
c42	C42, Turán's pure power-sum constant (42a)	≤ 0.6863607950; ≥ 1/2 + 2^-4096	Unrefereed, open PRs #305 and #310. The earlier 0.6888863712 is merged in Tao's table
c44	C44, relevant variables in bounded-degree Boolean functions (44a)	< 1.9916994577	Candidate and unrefereed, open PR #294; the first upper bound below 2, so read it with suspicion
c70	C70, reverse Brunn–Minkowski constant (70a)	≥ exp(1/(2e)) > 1.20194336847	Unrefereed; merged in Tao's table (#259)
c86	C86, Schur–Siegel–Smyth trace constant (86a)	≤ 1.8054939963	Candidate, open PR #298, first filed at 1.80560940; a clean-room AI referee on a different model found it holds, no human review. The earlier 1.8117251 is merged in Tao's table
c82	C82, essential minimum of the Zhang–Zagier height (82a)	< 0.2519923410	Candidate and unrefereed, open PR #330. The earlier 0.2534449 is merged in Tao's table
c68	C68, Korenblum's constant in the Bergman space (68a)	≥ 0.447	Candidate and unrefereed, open PR #299
c91	C91, average edit distance of two random binary strings	≥ 0.265988	Unrefereed, open PR #306; finite part L1
c89b	C89b, Ramsey multiplicity constant of K5	< 0.001648970526	Candidate and unrefereed, open PR #307
c89c	C89c, Ramsey multiplicity constant of K6	≥ 0.000033123924116	Candidate and unrefereed, open PR #308
c57c	C57c, univalent Bloch–Landau constant (57c)	≥ 0.61230	Candidate and unrefereed, open PR #311
c47	C47, centred Hardy–Littlewood maximal constant over squares, d = 2 (47a)	≥ 1.7055022252	Candidate, open PR #350; a clean-room AI referee on a different model found it holds, no human review
c22b	C22b, tight alternating knot constant (22b)	≤ 7.087559024	Candidate, open PR #347; a clean-room AI referee on a different model found it holds, no human review; prose reductions need mathematical review
c38	Connective constant of the square lattice (38a)	≥ 2.6275696	Candidate and unrefereed, open PR #328; the renewal argument needs mathematical review
c30	Growth rate of 1324-avoiding permutations (30a)	≥ 10.42, conditional	Candidate and unrefereed, open PR #317; conditional on BBEP and Norton's unrefereed v3
c31b	Four-letter LCS constant	≥ 0.617356908308	Not filed; a precision refinement of Leandre Jack's construction
c10a	Real Grothendieck constant (10a)	none	Replay receipts of other people's bounds. Not my bounds
tetrahedron-cover	openai/math problem 100	< 0.499613830783714149	Preprint hexagon:2610.00304
codetables	Nine linear codes over GF(5) and GF(9)	lower bounds on d	Candidates; none is yet accepted or listed in codetables.de

The GitHub README has the full rows: previous bests, who each result builds on, reviews and replays.

What is not here

Code, proofs, papers, reviews, logs, per-folder SHA256SUMS and third-party source snapshots (sources/, prior_sources/) stay on GitHub only. Some checkers regenerate large intermediate files; those are listed with their hashes in each GitHub folder.

License

MIT, copyright Ricardo Pinho, as in the GitHub repository. Two folders also carry third-party data under its own license: c82/degree104-joint and c82/degree104-cvp include coefficient data from vidigoat/optimization-records by V. Patankar (MIT); see THIRD_PARTY_NOTICE.md and LICENSE-vidigoat-optimization-records.txt in those folders.

References

• T. Tao et al., Optimization constants table (teorth/optimizationproblems).
• M. Grassl, Bounds on the minimum distance of linear codes.
• Each folder's README, PROOF.md and PRIOR_ART.md on GitHub credit the constructions, data and people each result builds on.