What was already known
The 2005 Anstee–Sali conjecture predicted forb(n,F)=Θ(n^(X(F)−1)). Mubayi’s earlier hypergraph theorem supplies the lower-bound construction once applied to this family.
AI involvement
Wu used GPT-5.6 Sol to help identify the example. Wu checked and revised the model output; Anstee, Sali and Wu proved the matching upper bound.
GPT-5.6 Sol is expressly credited with helping find the counterexample family, a central step, while Wu and coauthors performed the final verification and upper-bound proof.
Importance
The example gives an infinite family of counterexamples to the conjecture.
Limitations
Anstee, Sali and Wu’s matching upper-bound induction is later human work. Wu’s earlier paper was withdrawn after merger into the current joint paper.
Technical verification
Wu reports independently reviewing and verifying the AI-assisted lower-bound example. The merged paper explains its deduction from Mubayi’s theorem. The matching upper bound is later human work.
Formal checking
Independent review and revision of model output, verification of its mathematical claims, and written deduction from Mubayi's extremal theorem
- Checker
- Pei Wu, original author and coauthor of the v3 paper
- Scope
- The AI-identified r-extension of C4 yields the n^(r-1/2) lower bound and contradicts the X(F)=r prediction for r >= 4
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors explain why Mubayi's extremal construction avoids the specified trace, prove X(F)=r, and show how the resulting exponent conflicts with the conjecture.
Correction and publication history
The example gives an infinite family of counterexamples to the conjecture.
Read this published revision