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Dihedral and cyclic Ramsey numbers of the alternating 3-path

The a = 3 slice is settled outright. The parent conjecture's dihedral side has since been resolved for every a >= 4 as well (see the related entry), so Conjecture 4.9's claim 1 + (a-1)(b-1) now stands proved for all a >= 3; the trivial a = 1, 2 cases and the cyclic analogue for a >= 4 remain formally unaddressed.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Aug 12, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: site-confirmed. Publication: preprint. AI contribution: ai-discovered. Imported under CC BY 4.0.

Canonical aliases: Dihedral and cyclic Ramsey numbers of the alternating 3-path · $R_{dih}(P_3^{alt},K_b)=2b-1$

Confidence: Not scored

Registry verification: site confirmed · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

Claude Fable 5
model · ai model contributor · Anthropic

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Dihedral and cyclic Ramsey numbers of the alternating 3-path

specialist registry · passed

Reproduced here on 13 August 2026. The Lean development builds clean (exit 0) on the pinned toolchain (v4.12.0, core only, no Mathlib), and #print axioms shows all five main theorems depending on exactly propext, Classical.choice and Quot.sound. No Lean.ofReduceBool; with comments stripped the source has zero sorry, admit, axiom declarations and native_decide, and its 23 decide calls are kernel-reduced. A naive grep says otherwise only because those words appear in the file's own docs. The Python checker runs as described: Dih(3) has order 6 and equals Sym(3), and the lower-bound witnesses hold for b = 2..8. The general upper bound is not formalized; it cites Chvatal 1977, whose arithmetic holds. The SAT claim, unconfirmed at review, was substantiated the same day at commit 01a50c7. The DRAT files were not replayed, since replaying a shipped proof is the weaker check; instead all twelve CNFs were re-solved here with CaDiCaL, every verdict matching their kissat logs - satisfiable at $n=2b-2$, unsatisfiable at $n=2b-1$, for b = 2..7. The six satisfiable instances had their witnesses re-substituted clause by clause and all satisfy, and the b = 3 legs agree with this site's own exhaustive enumeration, anchoring their encoder against an independent computation. The certificates are regenerated rather than the originals, disclosed unprompted, which costs nothing here. Still unconfirmed: no human peer review, this being a self-submission reviewed by AI agents in-pipeline.

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Basic, Damnjanovic, Stevanovic and Stosic (Conjecture 4.23)

specialist registry · pending

problem-record link supplied by the VibeMathed registry.

Source ↗

sat/ - regenerated CNFs, DRAT certificates, witnesses and solver logs (commit 01a50c7)

code · pending

code link supplied by the VibeMathed registry.

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Dihedral and cyclic Ramsey numbers of the alternating 3-path

preprint · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.