What was already known
Kollár and Zhuang proved the bound under Euler-characteristic conditions that do not cover Calabi–Yau threefolds; the odd-dimensional extension was conjectural.
AI involvement
Liu and Wang credit ChatGPT 5.5 Pro with the proof sketch and Danus with verification and writeup, followed by their own checking and polishing.
The authors attribute the counterexample proof to ChatGPT and Danus before human verification.
Importance
A concrete threefold and group action disprove that proposed extension.
Limitations
The example does not challenge Kollár and Zhuang’s proved theorem. The authors report human verification, but the paper does not divide the checking steps between them.
Technical verification
Liu and Wang expressly report checking the completed elementary proof; no proof-assistant check is documented.
Independent checking
Reported human verification of the completed proof after Danus
- Checker
- Jihao Liu and Yanze Wang, paper authors
- Scope
- The Fermat-quintic faithful rank-four action and violation of Moraga's odd-dimensional bound
- Basis
- Reported by the linked checker
Human understanding
No named human explanation of the AI-written central argument is documented; Few is the evidence default.
Correction and publication history
This refutes the conjectured odd-dimensional extension, not the proved Euler-characteristic case.
Read this published revision