Problem detail · source-aware

Positivity on Deligne–Mumford Stacks Without the Torsion-Free Hypothesis

resolvedconfidence 70%

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Precise statement

Casalaina-Martin and Zhjeqi proved that the first Chern class of every torsion-free coherent quotient of a tensor power of the logarithmic cotangent sheaf is pseudo-effective, noting in Remark 4.5 that torsion-freeness was imposed only for technical reasons. Can it be dropped? Yes.

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

ChatGPT 5.5 Pro + Danus

The main result was obtained with ChatGPT 5.5 Pro and the Danus system, an agent built on Rethlas; human verification and polishing came afterwards. The authors caution that AI limitations mean related literature may have been missed.

Provider: unknown · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

No independent check. The authors verified and polished the AI-produced argument themselves and explicitly flag that relevant references may have been missed. Preprint, not refereed.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

  1. arXiv

    VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

argument (source-reported)

Source-reported tools: argument.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

  • VibeMath has not independently verified the mathematical claim.
  • AI-attempt independence and training-data exposure are unknown unless explicitly documented.
  • VibeMath has not independently audited the mathematical statement, proof, or novelty claim.