AI Proof WatchKeep up with AI contributions

AI-found graphs refute Graffiti 154 under a standard-deviation reading

Lollipop graphs with 118 or 120 vertices violate Graffiti Conjecture 154 when “deviation” means the standard deviation of adjacency eigenvalues. A 144-vertex graph violates it under both standard average-distance conventions.

Sources for this record

What was already known

The conjecture survived earlier computational attacks; a 2025 study searched graphs only through 50 vertices.

AI involvement AI-centered

Claude agents proposed the counterexamples in John Erlbacher’s directed Demonstrandum campaign. Erlbacher audited its verification gates.

Claude agents supplied retained counterexamples under Erlbacher’s direction; individual-result autonomy is not documented.

Importance Notable

Resolves a longstanding reading of a spectral graph conjecture with exact finite counterexamples.

Limitations

The counterexamples do not refute the mean-absolute-deviation reading. The reported smallest size applies only within the lollipop family.

Technical verification Formal (exact computation)

Two independently written exact checkers reportedly certify the finite standard-deviation violations.

Independent checking

exact computation

Checker
check_graffiti154.py and independent codex_referee_audit.py
Scope
Lollipop graph violations of Conjecture 154 under the standard-deviation reading
Basis
Reported by the linked checker
Evidence source

Human understanding Few

Human gate auditing is documented, but no named person explains this individual construction; Few is the evidence default.

Correction and publication history