Remark: Family 192. A counterexample to the Gopalan–Servedio conjecture

Disproves the proposed square-root bound relating a Boolean function's linear Fourier coefficients to its polynomial degree. For every $C>0$, there is a sign-valued Boolean function $f$ with ${\sum }_i\hat{f}(\{i\})>C\sqrt{\mathrm{deg}(f)}$. Thus its total signed correlation with individual input bits can exceed the proposed bound by an arbitrary factor.

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.