What was already known
Escobar, Klein and Weigandt proved equivalence of the combinatorial conditions and equidimensionality, checked small cases, and conjectured the Cohen–Macaulay implication.
AI involvement
Defant says ChatGPT 5.4 Pro produced the proof route after he provided his notes and the prior paper. Defant added details and rewrote the exposition, including the route through subword complexes and Gröbner degeneration.
The abstract and §7 expressly describe the conjecture proof as obtained autonomously by ChatGPT 5.4 Pro after Defant supplied the problem and relevant sources; later human exposition does not erase that origin.
Importance
The result completes the proposed structural characterization of Cohen–Macaulay ASM varieties.
Limitations
The paper presents a full argument but does not document a completed human proof check or machine verification. The finite search through size seven does not verify the general theorem.
Technical verification
The v2 paper presents a complete argument and reports finite n<=7 exploration before the proof, but it does not document a completed human review of the entire argument or a machine check. Author writing and referee comments alone do not establish Formal.
Human understanding
Defant explains the route from vertex-decomposable unions of subword complexes to Cohen–Macaulay Stanley–Reisner rings and then to the ASM variety through the antidiagonal initial ideal, adding details to the model proof.
Correction and publication history
If correct, the result completes the proposed structural characterization of Cohen–Macaulay ASM varieties.
Read this published revision