What was already known
OpenAI’s earlier work proved the sharp volume inequality, while the equality case remained open beyond dimension two and special classes. Liu already knew the K-stability/Fano equality analogy.
AI involvement
Liu proposed the initial analogy and saturation route. Danus supplied the central radial-degeneration, Prékopa-rigidity and critical-lattice mechanisms and a complete proof; Liu explained and polished it.
Danus supplied the central new second-half mechanisms and complete argument within a project and first-half strategy initiated by Liu.
Importance
Completes the equality characterization in Ehrhart’s longstanding volume conjecture.
Limitations
Liu reports human verification but does not specify its coverage or a completed rigorous review of the whole theorem. Danus’s internal checking process has no public certificate in the cited account.
Technical verification
The author reports human verification after Danus produced the complete proof, but does not describe its coverage or a completed rigorous check of Theorem 1.3. This supports only a partial rating. Danus's internal proof-checking pipeline is opaque and is not counted as a documented machine method.
Independent checking
post-generation human verification and polishing reported by the author
- Checker
- Jihao Liu, author
- Scope
- The final proof of the equality characterization in Theorem 1.3, with exact checked scope unspecified
- Basis
- Reported by the linked checker
Human understanding
Liu identifies the human starting analogy, explains the all-point jet saturation, toric degeneration, Prékopa rigidity and critical-lattice endgame, and distinguishes what Danus discovered beyond the analogy.
Correction and publication history
Completes the equality characterization in Ehrhart’s longstanding volume conjecture.
Read this published revision