Remark: Family 072. Brennan's conjecture and a counterexample to Kraetzer's prediction

Proves Brennan's conjecture: for every conformal bijection $\varphi$ from a simply connected plane domain onto the disk, $|{\varphi }^{\prime }{|}^s$ is area-integrable for $4/3<s<4$. The sharp universal integral-means identity is $B_{\mathcal{S}}(t)=|t|-1$ for $t\le -2$. A strict bound $B_b(-1)<1/4$ for bounded univalent functions disproves Kraetzer's prediction at that parameter.

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.