A strict inverse-first-power bound for univalent functions
We prove a uniform upper bound for inverse-first-power integral means of normalized univalent disk maps with exponent strictly below 1/4. Consequently, the bounded universal integral-means spectrum satisfies $B_b(-1)\lt 1/4$, disproving Kraetzer's conjectured spectrum at p = −1.
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Brennan's Conjecture and the Universal Integral Means SpectrumarXiv.orgIlia Binder, Oleg Ivrii, Istvan Prause, Stanislav SmirnovOct 16, 2026in the index
In October 2026, OpenAI released two preprints \cite{openai-brennan,openai-kraetzer}, establishing Brennan's celebrated conjecture~\cite{brennan,brennan2} and disproving Kraetzer's more general $t^2/4$ conjecture \cite{kraetzer, kraetzer-thesis}. While validating these results, we observed that…