What was already known
Casalaina-Martin and Zhjeqi proved the result for torsion-free quotients and left the torsion case open.
AI involvement
Hou and Liu credit ChatGPT 5.5 Pro and Danus with obtaining the main result. They verified, polished, wrote and explained the proof; the source does not assign individual steps between the models.
The paper attributes the main theorem's discovery to the named AI systems but does not establish independent model origination or leadership over the human project.
Importance
The proof closes the stated torsion gap in the stack-positivity theorem.
Limitations
The earlier torsion-free theorem supplies an essential input. No independent external proof check is documented.
Technical verification
The authors explicitly report human verification after the AI work and present the complete short argument: inverse image is torsion-free, its quotient defines the torsion first Chern class, that class is effective, and it adds to the prior torsion-free pseudo-effective class. This is a source-reported author check, not an AIProofWatch reproduction.
Formal checking
Reported human verification and polishing of the AI-derived result, with a complete written proof in Sections 3–4
- Checker
- Shengyu Hou and Jihao Liu, paper authors
- Scope
- Theorems A and B removing the torsion-free quotient hypothesis
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Hou and Liu explain why the inverse image of the torsion subsheaf remains torsion-free and how the resulting effective class combines with the earlier positivity theorem.
Correction and publication history
The proof closes the stated torsion gap in the stack-positivity theorem.
Read this published revision