The Anstee-Sali Conjecture on Forbidden Configurations
For a forbidden configuration F, the Anstee-Sali conjecture predicts that forb(m, F) is Theta(m^(X(F)-1)), where X(F) comes from an explicit product construction. Disproved: the 4-uniform family on six vertices formed by a two-vertex core joined to the edges of a 4-cycle has X(F) = 4, so the conjecture predicts Theta(m^3), while a random-alteration argument gives Omega(m^(10/3)).
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Extremal set theory
- Posed by
- Richard Anstee, Attila Sali
- Year posed
- 2005
- Years open
- 21y
- Solved
- 2026-08-07
- Model
- GPT-5.6 Sol
- Vendor
- OpenAI
- Collaborators
- Pei Wu
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 20 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The abstract ends "The example was found by GPT-5.6 Sol", and a dedicated disclosure section repeats it: "The authors used GPT-5.6 Sol for finding the example. The authors reviewed and revised all outputs, verified results, and take full responsibility for the final manuscript."
Verification
A preprint days old, with no independent review.
Source
- PaperarXiv