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physics.comp-ph2025
Computer-Assisted Proofs for Geometric Optimization: From Crystallization to Carbon Nanotubes
Miguel Ayala, Rustum Choksi, Benedikt Wirth
We present a framework based on computer-assisted proofs that turns geometry optimization simulations for atomistic structures into mathematical proofs. Starting from a numerically…
math.MG2025
On the number of defects in optimal quantizers on closed surfaces: the hexagonal torus
Jack Edward Tisdell, Rustum Choksi, Xin Yang Lu
We present a strategy for proving an asymptotic upper bound on the number of defects (non-hexagonal Voronoi cells) in the generator optimal quantizer on a closed surface (i.e.,…