Source authenticated

Batyrev's Stringy Hodge Number Conjecture

For a projective variety $X$ with at worst Gorenstein canonical singularities whose stringy $E$-function $E_{\mathrm{st}}(X; u, v)$ is a polynomial, all stringy Hodge numbers $h^{p,q}_{\mathrm{st}}(X)$ are non-negative. (Batyrev 1998, Conjecture 3.10.)

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: Jul 21, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. Imported under CC BY 4.0.

Canonical aliases: Batyrev's Stringy Hodge Number Conjecture · Batyrev's Conjecture

Confidence: Not scored

Registry verification: unreviewed · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

Matthew Satriano
human · human collaborator

Jeremy Usatine
human · human collaborator

GPT
model · ai model contributor · OpenAI

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Batyrev's Stringy Hodge Number Conjecture

specialist registry · passed

arXiv preprint 2607.19184 (21 Jul 2026) by Matthew Satriano and Jeremy Usatine. The proof is short and fully explicit: the stringy $E$-function is written out and its $u^2 v^5$ coefficient gives $h^{2,5}_{\mathrm{st}} = -1$, so it is hand-verifiable. A domain-expert preprint, not yet peer-reviewed. Distinct from the unrelated Batyrev-Manin conjecture on rational points.

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Batyrev's Stringy Hodge Number Conjecture

preprint · pending

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

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Lineage and corrections

This event attributed to Jeremy Usatine

This event attributed to Matthew Satriano

This event attributed to GPT

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