Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 375-01. A positive resolution of De Giorgi's conjecture in dimension eight
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OpenAI@2026-10-07#rem:oai-p-375-01
Authors: OpenAI. Family 375.
Title: A positive resolution of De Giorgi's conjecture in dimension eight.
Abstract: We resolve De Giorgi's conjecture positively in dimension eight: every entire C2 solution $u:{}mathbb R{}8{}to(-1,1)$ of ${}Delta u=u{}3-u$ with an everywhere positive directional derivative is a planar heteroclinic. We prove that every stable solution $v:{}mathbb R{}7{}to[-1,1]$ of this equation is a constant well or a planar heteroclinic, without an energy-growth assumption.
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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