Large systoles in every sufficiently large genus

The theorem improves the best lower bound valid in *every* sufficiently large genus from asymptotic constant $2/9$ to $1$ . The every-genus ladder it climbs is Katz-Sabourau's $19/120$ and then Liu-Petri's $2/9$ , the latter also by a random construction. Constant $1$ was already reached by Petri-Walker along a subsequence of genera, following Erdos-Sachs, so the new contribution is achieving it uniformly rather than the constant itself. The asymptotic problem stays open, and the remaining gap is wide: Brooks and Buser-Sarnak give $\limsup\ge4/3$ , while the elementary area bound is $\max\mathrm{sys}(S)\le2\log(4g-2)$ , asymptotically $2\log g$ . So this closes much of the liminf gap and determines no optimal constant.

Exact FrontierDelta

proved→proved

Scope and record

Occurred: Oct 29, 2026

Delta type: REGISTRY REVISION

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. 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: Large systoles in every sufficiently large genus · Large systoles of hyperbolic surfaces

Confidence: Not scored

Registry verification: unreviewed · preprint · partial

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VibeMathed
registry · event recorded by

GPT-5.6 Sol
model · ai model contributor · OpenAI

Yifei Cai
human · human collaborator

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VibeMathed record: Large systoles in every sufficiently large genus

specialist registry · passed

Unreviewed: an arXiv preprint one day old (v1, 27 August 2026, math.GT), unrefereed, with no formalization and no computational certificate, so there was nothing mechanical to re-run and no mathematics was checked here. What was verified on 28 August 2026: the paper exists at arXiv:2608.26660 with this title and author; the theorem and the $\liminf\ge1$ corollary are its abstract and Theorem 1; the AI declaration is section 1.3, quoted in the AI-role note; and every prior-work claim is as the introduction states - Katz-Sabourau's $19/120$ , Liu-Petri's $2/9$ , Petri-Walker's constant $1$ along a subsequence, Brooks and Buser-Sarnak's $\limsup\ge4/3$ , and the area bound $\max\mathrm{sys}\le2\log(4g-2)$ .

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Large systoles in every sufficiently large genus

preprint · pending

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

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