{"id":"openai-math/A-strict-inverse-first-power-bound-for-univalent-functions","pdf":"https://github.com/openai/math/blob/main/preprints/A-strict-inverse-first-power-bound-for-univalent-functions-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-strict-inverse-first-power-bound-for-univalent-functions-September-24-2026","tags":["complex-analysis","univalent-functions","integral-means"],"score":0,"title":"A strict inverse-first-power bound for univalent functions","domain":"Real and complex analysis","family":"072","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CA","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-09-24","reactions":{},"discussion":[{"url":"https://arxiv.org/abs/2610.23853","date":"2026-10-16","kind":"web","site":"arXiv.org","text":"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…","added":"2026-10-24","title":"Brennan's Conjecture and the Universal Integral Means Spectrum","author":"Ilia Binder, Oleg Ivrii, Istvan Prause, Stanislav Smirnov","record":"arxiv/2610.23853"}],"formalized":true,"family_title":"Brennan's conjecture and the integral-means spectrum"}