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Breakthrough Tracker record

Specialists give a concise preprint proof of Brennan's conjecture

Binder, Ivrii, Prause and Smirnov prove the universal integral-means bound B_b(t) at most t squared over 4 for t between minus 2 and 2, which yields Brennan's integrability range 4/3 less than p less than 4.

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Stable ID
math-brennan-conjecture-proof-2026
Revision
math-brennan-conjecture-proof-2026.v1
Field
Mathematics · Complex analysis, conformal mapping and integral means spectra
Evidence
Tier 1 · Peer reviewed: No
Record state
Provisional · Independently validated preprint proof
Last checked

AI role

The authors developed the concise proof while checking OpenAI manuscripts on Brennan's and Kraetzer's conjectures. The published argument is a human-authored specialist validation of an AI-originated route.

Record details

Problem or result
Brennan's conjecture via the universal integral means spectrum
Authors
Ilia Binder, Oleg Ivrii, István Prause and Stanislav Smirnov
Institutions
University of Toronto; Tel Aviv University; Åbo Akademi University; University of Geneva
Result date
Preprint submitted October 16, 2026

Why it matters

Brennan's conjecture is a long-standing problem in geometric function theory. Four specialists independently reconstructed a short mathematical route instead of merely repeating an institutional claim.

Limits

The note is not peer reviewed. It announces a stricter interior inequality but defers those details to a later paper, so the tracker does not treat that stronger statement as established here or generalize this validation to the rest of the OpenAI catalogue.

Sources

  1. Primary: Binder, Ivrii, Prause and Smirnov Brennan preprint
  2. Related artifact: OpenAI mathematics repository

Correction and revision history

  1. 2026-10-19 — Added after primary-source, scope, status, AI-role and limitation review.

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