GPT-5.6 Sol-Assisted Counterexamples Disprove Sato's Weak F-Equivalence Conjecture

In a manuscript dated August 15, 2026, Avik Chakravarty, Daebeom Choi, and Shengjing Xu disprove Sato's weak $F$-equivalence conjecture in every dimension $d\geq3$. The conjecture asserted that every nonsingular projective toric weak Fano $d$-fold can be connected to $\mathbb{P}^d$ by toric blow-ups, blow-downs, and flops while all intermediate varieties remain nonsingular, projective, toric, and weak Fano.

The authors construct smooth projective crepant models of centered reflexive simplices. A rigidity property of their ray polytopes rules out every weak-Fano-preserving equivariant blow-up or blow-down throughout the relevant flop class. They then formulate a Gorenstein weak $F$-equivalence refinement and prove it in dimensions at most three, as well as for their counterexample family in all dimensions; the higher-dimensional refined conjecture remains open.

The paper states that GPT-5.6 Sol produced the key construction for the three-dimensional counterexample after the authors submitted Sato's conjecture to the system. The authors extended it to all $d\geq3$, and also used AI assistance for the dimension-three proof of the refinement; they report independently verifying and revising the AI-assisted parts.