The Ciliberto et al. Question on Effective Divisors of Positive Self-Intersection

Precise statement

Ciliberto, Knutsen, Lesieutre, Lozovanu, Miranda, Mustopa and Testa asked a question about effective divisors of positive self-intersection on smooth projective surfaces. The answer is negative, witnessed by a very non-movable effective divisor.

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 and Rethlas

The author states the main result is obtained by generative AI, particularly ChatGPT 5.5 Pro and the Rethlas system. This is the fourth note in a short series where the same author publishes machine-obtained answers to named questions in birational geometry, each with the same one-sentence disclosure.

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

Verification boundary

unreviewed

No independent check. The counterexample is an explicit divisor, so it is checkable directly. arXiv preprint, not peer-reviewed.

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

Timeline

1. 2026-05-20

   arXiv:2605.20594 - An example of a very non-movable effective divisor

   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

construction (source-reported)

Source-reported tools: construction.

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.