What was already known
Ciliberto and coauthors asked in 2017 whether such a uniform multiple exists for effective divisors with one section and positive self-intersection.
AI involvement
Jihao Liu says ChatGPT 5.5 Pro found the example. Rethlas identified an error in its first section-vanishing proof and supplied the retained repair; Liu directed and released the work.
The initial example came from GPT-5.5 Pro with no mathematical hint, and the essential repair was also model-generated through Rethlas; Liu directed and released the work.
Importance
Answers that algebraic-geometry question negatively with an explicit family.
Limitations
The first model proof of section vanishing was wrong and a later model run supplied the repair. The paper does not document a completed rigorous check of the corrected final argument; help checking an earlier blueprint does not establish that scope.
Technical verification
A model-based verifier detected the original error and Rethlas repaired it, but the paper does not document a completed rigorous human or machine check of the corrected section-vanishing argument. Assistance checking an earlier blueprint does not establish final-proof coverage.
Human understanding
The disclosure describes an AI-origin example and AI correction, without a named human explaining the corrected section-vanishing mechanism. Few is the evidence default, not a claim that Liu cannot understand it.
Correction and publication history
If correct, answers that algebraic-geometry question negatively with an explicit family.
Read this published revision