Toda's Gepner conjecture for the quintic threefold

Theorem 1.1: every smooth complex quintic threefold has a numerical Bridgeland stability condition, with support property on $K_{\mathrm{num}}(X)_{\mathbb R}$ , on which $\Phi$ acts by rotating the charge by $e^{2\pi i/5}$ and shifting phases by $2/5$ , normalized by $Z(\mathcal O_x)=-1$ . The construction is a double tilt starting at slope $-1/2$ , refined to a periodic grid of aisles. It relies on Xu's 2026 inequality. It does not prove Toda's general strong Bogomolov-Gieseker conjecture, treat other Calabi-Yau hypersurfaces, or describe the full stability manifold near the Gepner point.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 24, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. 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: Toda's Gepner conjecture for the quintic threefold · Toda's quintic Gepner conjecture

Confidence: Not scored

Registry verification: unreviewed · announcement · candidate

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VibeMathed
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Unreleased internal OpenAI model
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Named evidence

VibeMathed record: Toda's Gepner conjecture for the quintic threefold

specialist registry · passed

No independent mathematician has checked this yet. Checked here: Theorem 1.1 of the principal manuscript was read against Toda's conjecture; it gives a numerical Bridgeland stability condition with the support property on the full numerical Grothendieck group, $Z(\Phi E)=e^{2\pi i/5}Z(E)$ , $\Phi\mathcal P(\varphi)=\mathcal P(\varphi+2/5)$ and $Z(\mathcal O_x)=-1$ , on every smooth quintic, and identifies the charge with Toda's by uniqueness of the normalized eigenform. A reader should know that the slope-sheaf input is taken from Xu's stronger Bogomolov-Gieseker inequality on the quintic (arXiv 2511.21288v2, 2026), an external preprint not checked here. Not refereed. No Lean formalization in the release.

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Companion: A Gepner stability condition on every smooth quintic threefold

paper · pending

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

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A curve-class corrected Bogomolov-Gieseker inequality on every polarized threefold

witness · pending

paper link supplied by the VibeMathed registry.

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Toda, Gepner point and strong Bogomolov-Gieseker inequality for quintic 3-folds (Conjecture 3.1)

specialist registry · pending

problem-record link supplied by the VibeMathed registry.

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Lineage and corrections

Toda, Gepner point and strong Bogomolov-Gieseker inequality for quintic 3-folds (Conjecture 3.1) evidence for this event

This event attributed to Unreleased internal OpenAI model

A curve-class corrected Bogomolov-Gieseker inequality on every polarized threefold evidence for this event

VibeMathed record: Toda's Gepner conjecture for the quintic threefold evidence for this event

Companion: A Gepner stability condition on every smooth quintic threefold evidence for this event

Toda's Gepner conjecture for the quintic threefold parent of this event

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