Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 354-01. The Isoperimetric Conjecture for the Cubic Flat Three-Torus
Manuscript map · lines 9225–9234
OpenAI@2026-10-07#rem:oai-p-354-01
Authors: OpenAI. Family 354.
Title: The Isoperimetric Conjecture for the Cubic Flat Three-Torus.
Abstract: We prove the isoperimetric conjecture for the cubic flat three-torus and classify all minimizers, including the equality cases at the transition volumes $4{}pi/81$ and $1/{}pi$. The minimizing regions are balls, circular tubes about shortest closed geodesics, coordinate slabs, and their complements.
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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