What was already known
Whether every Heyting algebra could arise as a topos subterminal lattice was open. Earlier positive results addressed a narrower logical setting.
AI involvement
Ye proposed the F₂ target and strategy; Xu directed and simplified a parallel search. ChatGPT supplied the central reachability construction within that human direction.
The model supplied the central reachability-predicate and Bellissima argument, while humans proposed the target and strategy, steered the search and completed the final proof.
Importance
Provides a counterexample to a longstanding categorical-logic representation question.
Limitations
Xu scrutinized model-generated steps and the authors rewrote the argument, but a completed rigorous check of the full final proof is not documented. The AI transcripts are unavailable.
Technical verification
Xu reports adversarial scrutiny of the AI’s steps and the authors reviewed/edited the final content, but no completed rigorous check of the entire final proof is documented.
Independent checking
Xu reports adversarial scrutiny of the AI’s steps and the authors reviewed/edited the final content, but no completed rigorous check of the entire final proof is documented.
- Checker
- Yiqi Xu
- Scope
- model-generated steps toward the F₂ Bellissima–reachability obstruction
- Basis
- Reported by the linked checker
Human understanding
Xu explicitly disentangled and reorganized the reasoning and simplified its central Kripke-model and separation mechanism; the paper explains the obstruction.
Correction and publication history
Provides a counterexample to a longstanding categorical-logic representation question.
Read this published revision