Source authenticated

Brennan's conjecture

Theorem 1.1: for every $\varepsilon>0$ there is $C_\varepsilon$ with $M_{-2}[f'](r)\le C_\varepsilon(1-r)^{-1-\varepsilon}$ for all $f\in\mathcal S$ and $1/2\le r<1$ ; $B_{\mathcal S}(-2)=1$ ; and every conformal bijection $\varphi:W\to\mathbb D$ has $|\varphi'|^s$ area-integrable for $4/3<s<4$ . Also $B_{\mathcal S}(t)=|t|-1$ for all $t\le-2$ , and the Koebe function shows both endpoints fail. Not shown: the integral-means spectrum at other interior exponents; the companion's $B_b(-1)<1/4$ is a separate entry.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 24, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: Brennan's conjecture

Confidence: Not scored

Registry verification: lean checked · announcement · candidate

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Attribution

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Unreleased internal OpenAI model
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Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Brennan's conjecture

specialist registry · passed

No independent mathematician has checked this yet. Checked here: the abstract, Theorem 1.1 and the history section of 'Brennan's conjecture and sharp inverse-square integral means', read against Brennan's conjecture as recorded by Bertilsson. The proof (an operator on normalized half-plane maps, an eigen-law, and a critical-point pairing) was not refereed. Lean: formalization.yaml lists OAI.Brennan.main_theorem (lean/OAI/Analysis/IntegralMeans/Main.lean, comparator ComparatorChallenges/Brennan.lean). Its statement was read: a uniform bound M_{-2}[f'](r) <= C_eps (1-r)^(-1-eps) over the schlicht class, spectrum(-2) = 1, and for every open connected simply connected W with nontrivial spherical boundary and holomorphic bijection phi onto the disk, |phi'|^s integrable on W for 4/3 < s < 4, plus the disk form for -2 < t < 2/3. That is the headline. OAI.Brennan.Sharp.sharp_endpoints states divergence for the Koebe map at both endpoints. Permitted axioms propext, Quot.sound, Classical.choice. Not rebuilt here.

Source ↗

Brennan's conjecture and sharp inverse-square integral means

paper · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Kraetzer's conjecture on the universal integral means spectrum

witness · pending

paper link supplied by the VibeMathed registry.

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Lean: Brennan main theorem

lean artifact · pending

lean-proof link supplied by the VibeMathed registry.