Remark: Family 375. De Giorgi's conjecture in dimension eight

Proves De Giorgi's conjecture at its sharp dimension-eight endpoint: every entire $C^2$ solution $u:{\mathbb{R}}^8\to (-1,1)$ of $\Delta u=u^3-u$ that is strictly increasing in one direction depends on only one linear coordinate. A stronger theorem classifies all stable entire solutions $v:{\mathbb{R}}^7\to [-1,1]$ as constant wells or planar transitions, without an energy-growth assumption.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.