What was already known
The elementary bound was 2^(n−1). Simonovits and Sós conjectured the sharper 2^(n−3) bound.
AI involvement
Keevash says GPT-6 Astra found the proof after a hint from him. He simplified and rewrote it and explains the expansion and cycle-probability argument.
The author explicitly attributes discovery of the proof to Astra, after his hint, while taking credit for simplification and final exposition.
Importance
Gives the first fixed improvement over the half-density bound toward the Simonovits–Sós conjecture.
Limitations
The sharp 2^(n−3) conjecture remains open. The paper gives a proof but does not document a completed technical check; Keevash’s precise hint to the model is undisclosed.
Technical verification
A complete proof is published, but the reviewed source does not explicitly document a completed check of the argument by a named human or machine. This is the default for missing check evidence.
Human understanding
Keevash rewrote and explains the central isoperimetric reduction, Plünnecke step and bounded-codegree cycle estimate.
Correction and publication history
Gives the first fixed improvement over the half-density bound toward the Simonovits–Sós conjecture.
Read this published revision