Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 090-01. An atomic certificate for triangular-lattice universal optimality
Manuscript map · lines 4215–4224
OpenAI@2026-10-07#rem:oai-p-090-01
Authors: OpenAI. Family 090.
Title: An atomic certificate for triangular-lattice universal optimality.
Abstract: We prove that the density-one triangular lattice minimizes the lower energy per particle for every nonnegative completely monotone function of squared distance, among all locally finite planar configurations of centered disk density one. The comparison includes infinite energies. The proof constructs sharp Gaussian Fourier minorants using an atomic interpolation certificate.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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