The Escobar-Klein-Weigandt Conjecture on Cohen-Macaulay ASM Varieties
Statement
Escobar, Klein and Weigandt proved that gradedness of an ASM weak order interval, constancy of Coxeter length across its fibres, and equidimensionality of the associated ASM varieties are mutually equivalent, and conjectured (Conjecture 3.21) that Cohen-Macaulayness of those varieties belongs on the same list. Proved, via a -Hecke monoid action on the MacNeille completion of Bruhat order and vertex-decomposability of certain unions of Knutson-Miller subword complexes.
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Comments
No person has examined this. Nothing here has been checked at all. say whether it holds →
proof attempt · #1
ChatGPT 5.4 Pro, with Colin DefantThe record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.
The paper is written as a case study in the workflow, and reports the interaction turn by turn. The author uploaded his own notes plus the Escobar-Klein-Weigandt paper, asked whether their ideas generalise to other Coxeter groups, then asked for a counterexample to Conjecture 3.21. After about 50 minutes the model reported it had found none and had verified the conjecture in small cases. Asked instead to prove it, it returned the main ingredients after roughly 19 minutes, and the author says the proof presented in Section 4 is essentially the one the model found, with the writing massaged and details added. He then re-ran the experiment in several fresh conversations to test what made it work, and reports that withholding his notes and asking directly for a proof usually failed, with the model recognising the statement as an open problem and declining.
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