Disputed

The log abundance conjecture in characteristic zero (rational boundary, every dimension), with canonical nonvanishing

Theorem 1.1: for a normal projective lc pair $(X,B)$ over an algebraically closed field of characteristic zero, with $B$ effective rational and $K_X+B$ $\mathbb Q$ -Cartier and nef, some positive Cartier multiple of $K_X+B$ is globally generated. The induction also gives good minimal models for lc pairs with pseudo-effective real adjoint and, over $\mathbb C$ , canonical nonvanishing for smooth projective varieties in every dimension; consequences include rational slc abundance (Fujino-Gongyo) and finite generation of lc rings. Not shown: semiampleness with real boundaries, positive characteristic, or any bound on the multiple. The family's compact Kahler log abundance theorem assumes logarithmic Iitaka subadditivity (claimed in family 033) and is not part of this entry.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 24, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: contested. 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: The log abundance conjecture in characteristic zero (rational boundary, every dimension), with canonical nonvanishing · Log abundance conjecture

Confidence: Not scored

Registry verification: contested · announcement · candidate

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Attribution

VibeMathed
registry · event recorded by

Unreleased internal OpenAI model
model · ai model contributor · OpenAI

Evidence vector

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Named evidence

VibeMathed record: The log abundance conjecture in characteristic zero (rational boundary, every dimension), with canonical nonvanishing

specialist registry · passed

No independent mathematician has checked this yet. Checked here: Theorem 1.1 and the introduction of 'Log abundance in characteristic zero' were read against the conjecture as stated there; the claim is unconditional and covers every dimension. The proof (a dimension induction using a signed-boundary criterion, Hodge-module lifting through infinitesimal neighbourhoods and Hashizume's reduction to smooth nonvanishing) was not refereed. No Lean formalization. A reader should know that the release is not consistent about whether projective abundance is unconditional: the October 5 companion on Kahler fourfolds proves projective log abundance in its appendices and calls it a conditional resolution, not an unconditional abundance theorem, assuming logarithmic Iitaka subadditivity, while this September 24 manuscript claims it outright. The family's effective Iitaka, index and Campana-Peternell results use this manuscript as an input. Listed as Contested because the release itself disagrees on whether the theorem is conditional; see the claim issue.

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Input manuscript: Log abundance in characteristic zero

paper · pending

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

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Kahler version (conditional on log Iitaka subadditivity): Log abundance for compact Kähler spaces under logarithmic Iita

paper · pending

paper link supplied by the VibeMathed registry.

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Fourfold nonvanishing by minimal metrics and moving jets

paper · pending

paper link supplied by the VibeMathed registry.

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Lifting sections from the reduced support of an adjoint

paper · pending

paper link supplied by the VibeMathed registry.

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Minimal metrics and interior injectivity for nef adjoints

paper · pending

paper link supplied by the VibeMathed registry.

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Abundance after nonvanishing for compact Kähler fourfolds

paper · pending

paper link supplied by the VibeMathed registry.

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Conditional good minimal models for compact Kähler fourfolds

paper · pending

paper link supplied by the VibeMathed registry.

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Existence of minimal models for generalized lc pairs (OpenAI math release)

witness · pending

other link supplied by the VibeMathed registry.

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Revised edition (October 6, 2026): Conditional good minimal models for compact Kähler fourfolds

paper · pending

paper link supplied by the VibeMathed registry.

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Revised edition (October 6, 2026): Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivity

paper · pending

paper link supplied by the VibeMathed registry.

Source ↗

Lineage and corrections

This event attributed to Unreleased internal OpenAI model

Revised edition (October 6, 2026): Conditional good minimal models for compact Kähler fourfolds evidence for this event

Kahler version (conditional on log Iitaka subadditivity): Log abundance for compact Kähler spaces under logarithmic Iita evidence for this event

Input manuscript: Log abundance in characteristic zero evidence for this event

Revised edition (October 6, 2026): Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivity evidence for this event

Minimal metrics and interior injectivity for nef adjoints evidence for this event

VibeMathed record: The log abundance conjecture in characteristic zero (rational boundary, every dimension), with canonical nonvanishing evidence for this event

Abundance after nonvanishing for compact Kähler fourfolds evidence for this event

Fourfold nonvanishing by minimal metrics and moving jets evidence for this event

The log abundance conjecture in characteristic zero (rational boundary, every dimension), with canonical nonvanishing parent of this event

Existence of minimal models for generalized lc pairs (OpenAI math release) evidence for this event

Lifting sections from the reduced support of an adjoint evidence for this event

Conditional good minimal models for compact Kähler fourfolds evidence for this event

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