ChatGPT-5.6 Sol Helps Prove the Chudnovsky and Demailly Conjectures for Arbitrary Finite Point Sets
Tài Huy Hà and Aniketh Sivakumar claim proofs of the Chudnovsky and Demailly conjectures for arbitrary finite point sets in projective space over algebraically closed characteristic-zero fields; ChatGPT-5.6 Sol suggested the positive-characteristic strategy and broad plan, while the authors report developing and verifying the proofs.
In a preprint first uploaded on August 17, 2026, Tài Huy Hà and Aniketh Sivakumar claim proofs of the Chudnovsky and Demailly conjectures for every finite set of points in projective space over an algebraically closed field of characteristic zero. Their result removes restrictions on the number or position of the points and establishes Demailly's Waldschmidt-constant inequality in full generality for this setting.
The proof first moves the interpolation problem from projective to affine space, establishes a stronger finite inequality in sufficiently large positive characteristic using Hasse derivatives and Frobenius decomposition, and then specializes back to characteristic zero. ChatGPT-5.6 Sol reportedly suggested the positive-characteristic strategy, the broad proof plan, and outlines for key results in the Chudnovsky case.
The authors state that they subsequently developed, wrote, and independently verified all mathematical arguments and accept responsibility for the paper. The result addresses these two conjectures for arbitrary finite point sets, while other interpolation problems discussed in the paper, including higher-multiplicity questions related to SHGH and Nagata-type conjectures, remain open.