Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 090-03. A sharp Fourier certificate for planar circle packing
Manuscript map · lines 4235–4244
OpenAI@2026-10-07#rem:oai-p-090-03
Authors: OpenAI. Family 090.
Title: A sharp Fourier certificate for planar circle packing.
Abstract: We resolve the planar Cohn–Elkies sharpness conjecture: the two-point Fourier bound attains the optimal circle-packing density ${}pi/(2{}sqrt3)$. We construct a radial Schwartz certificate and prove its global sign conditions using rigorous interval arithmetic and analytic estimates. The same certificate recovers the classical uniqueness of the triangular packing among periodic equality cases.
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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