Source authenticated

Kraetzer's conjecture on the universal integral means spectrum

Theorem 1.1: there are constants $0<\varepsilon<1/4$ and $C$ with $M_{-1}[f'](r)\le C(1-r)^{-1/4+\varepsilon}$ for every $f\in\mathcal S$ and $1/2\le r<1$ , so $B_b(-1)<1/4=p^2/4$ at $p=-1$ and Kraetzer's formula is false. The bound needs no bounded image or boundary regularity. Not shown: the true value of $B_b(-1)$ or any explicit gap, and nothing about $p=1$ or the Carleson-Jones question; Brennan's value $B(-2)=1$ , also predicted by Kraetzer, is proved in the companion (separate entry).

Exact FrontierDelta

Prior state unknown→disproved

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: Kraetzer's conjecture on the universal integral means spectrum · Kraetzer's conjecture

Confidence: Not scored

Registry verification: lean checked · announcement · candidate

Open the source record ↗

Attribution

VibeMathed
registry · event recorded by

Unreleased internal OpenAI model
model · ai model contributor · OpenAI

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Kraetzer's conjecture on the universal integral means spectrum

specialist registry · passed

No independent mathematician has checked this yet. Checked here: the abstract and Theorem 1.1 of 'A strict inverse-first-power bound for univalent functions', read against Kraetzer's formula as the paper quotes it (1996 paper, 2000 thesis, Beliaev's restatement). The proof was not refereed. Lean: formalization.yaml lists OAI.StrictInverseFirstPower.main (lean/OAI/Analysis/StrictMeans/Main.lean, comparator ComparatorChallenges/StrictMeans.lean). Its statement was read: there are 0 < eps < 1/4 and C with M_{-1}[f'](r) <= C (1-r)^(-1/4+eps) for every normalized univalent f, the bounded spectrum at -1 is below 1/4, and it is not the case that boundedSpectrum p equals the piecewise Kraetzer prediction for all p. That is the headline. Not rebuilt here. The gap eps is existential; no numerical value is given.

Source ↗

Kraetzer's conjecture on the universal integral means spectrum

witness · pending

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

Source ↗

Brennan's conjecture and sharp inverse-square integral means

paper · pending

paper link supplied by the VibeMathed registry.

Source ↗

Lean: strict inverse-first-power bound

lean artifact · pending

lean-proof link supplied by the VibeMathed registry.

Source ↗

Kraetzer 1996, Experimental bounds for the universal integral means spectrum

specialist registry · pending

problem-record link supplied by the VibeMathed registry.

Source ↗

Artifacts and verifiers

Lean: strict inverse-first-power bound

lean artifact · pending

Artifact ↗

Compute record

No linked compute attempts recorded.

Lineage and corrections

Brennan's conjecture and sharp inverse-square integral means evidence for this event

Kraetzer 1996, Experimental bounds for the universal integral means spectrum evidence for this event

This event attributed to Unreleased internal OpenAI model

Kraetzer's conjecture on the universal integral means spectrum parent of this event

Kraetzer's conjecture on the universal integral means spectrum evidence for this event

VibeMathed record: Kraetzer's conjecture on the universal integral means spectrum evidence for this event

Lean: strict inverse-first-power bound evidence for this event

Act on this frontier

Verify, challenge, or extend the result.

Help verify Open canonical problem Explore evidence graph