Polynomial interpolation and the Waldschmidt constant of points in projective space

Abstract

We establish Chudnovsky's Conjecture and, more generally, Demailly's Conjecture for any finite set of points in $\mathbb{P}^n_k$, where $k$ is an algebraically closed field of characteristic 0. The key idea of passing to positive characteristic, as well as the broad plan of the proof, was suggested by ChatGPT-5.6 Sol. All mathematical arguments and proofs in this paper were developed, written, and verified by the authors.