What was already known
Earlier smooth fourfold examples lacked an extremal metric but did not establish K-polystability against every algebraic test configuration.
AI involvement
Liu selected a decisive target and directed GPT-5.6 Sol, Fable 5 and Danus. The systems produced the counterexample and argument; Liu discussed, polished and checked the final exposition.
AI systems supplied the central construction and universal proof, with a crucial human choice of target in the original run.
Importance
Refutes the stated cscK Yau–Tian–Donaldson equivalence if the proof holds.
Limitations
The claim uses the normal-test-configuration convention. It does not refute Fano or stronger stability correspondences. Liu reports a final check without specifying complete coverage of the universal stability proof.
Technical verification
Liu reports a final human checking round but does not describe complete rigorous coverage of Theorem A.
Independent checking
final human polishing and checking, scope unspecified
- Checker
- Jihao Liu
- Scope
- final manuscript for Theorem A
- Basis
- Reported by the linked checker
Human understanding
Liu’s authored proof sketch and detailed sections explain the construction and the hard zero-invariant classification.
Correction and publication history
The counterexample is restricted to the stated cscK stability convention.
Read this published revision