What was already known
Conjecture 109 proposed the bound for every finite connected graph.
AI involvement
Andrii Vlasenko directed and released the work. His provenance record credits GPT-5.6 Sol Max with the search, witness, proof, formalization and verifier code.
The first-person repository assigns essentially every retained mathematical and checking artifact to the model, while recording human direction of the investigation.
Importance
One finite witness refutes the universal graph inequality.
Limitations
The Lean check covers the 13-vertex witness. The repository also gives a symbolic counterexample family, which is outside that formal check.
Technical verification
The repository reports a Lean 4 proof that the original universal inequality is false using an exact 13-vertex witness, plus exhaustive Python and independent C++ checks of its finite invariants. The general family is not required for the refutation; the reported checks were not rerun here.
Independent checking
Lean proof against the formal-conjectures definitions and a pinned Lean 4.27 build
- Checker
- Lean 4 kernel, reported by Vlasenko
- Scope
- The formal Conjecture 109 inequality is false for the connected 13-vertex witness with invariants 7, 9 and 2
- Basis
- Reported by the linked checker
Independent checking
Independent exact exhaustive subset and graph invariant calculations
- Checker
- The repository's Python and C++ verifiers
- Scope
- The same 13-vertex graph's independence, bipartite and residue values
- Basis
- Reported by the linked checker
Human understanding
The published explanation was model-written according to the provenance disclosure; no identified person's independent account of the residue and family mechanism was located. Few is the evidence default.
Correction and publication history
One finite witness refutes the universal graph inequality.
Read this published revision