Remark: Family 314. The chromatic Smith fixed-point problem for finite p -groups

Determines the optimal chromatic loss from geometric $H$-fixed points to geometric $G$-fixed points for every subgroup $H$ of a finite $p$-group $G$. At every nonnegative height, the loss equals the shortest subnormal-chain length from $H$ to $G$ with cyclic quotients. Each quotient counts once regardless of order, and finite spectra witness sharpness.

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.