What was already known
Damnjanović–Đorđević and Bašić and coauthors conjectured the relevant formulas; the cited Chvátal path–clique theorem supplies a general upper bound.
AI involvement
The project reports that Claude autonomously produced the proof, scripts and Lean formalization after human initiation and operational supervision.
The repository explicitly reports autonomous Claude production; no evidence of substantive human mathematical direction was found.
- Supporting source (arxiv.org) — Conjecture 4.9; Theorem 4.13
Importance
Resolves the conjectured a=3 slice for both symmetry classes if the upper-bound transfer holds.
Limitations
Lean checks the universal lower bound, and exact certificates cover selected finite cases. A complete check of the upper-bound transfer to these dihedral and cyclic statements is not documented.
Technical verification
The lower bound is Lean checked and several finite instances have exact certificates. The universal upper bound is a cited theorem, with no documented complete check of its transfer to this dihedral/cyclic claim.
Independent checking
formal proof
- Checker
- Lean 4 kernel via project TheoremB.lean
- Scope
- lower bound for all b and Dih(3)=Sym(3)
- Basis
- Reported by the linked checker
Independent checking
exact SAT refutations and checked witnesses
- Checker
- kissat and drat-trim via project SAT package
- Scope
- dihedral cases b=2..7; Python covers b=3 upper bound
- Basis
- Reported by the linked checker
Human understanding
Default: no named human account explaining the proof is documented.
Correction and publication history
Resolves the conjectured a=3 slice for both symmetry classes if the upper-bound transfer holds.
Read this published revision