The Escobar-Klein-Weigandt Conjecture on Cohen-Macaulay ASM Varieties
resolvedconfidence 70%
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Precise 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 $0$-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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fidelity, correctness, priority, or novelty.
What AI did
ChatGPT 5.4 Pro
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.
arXiv preprint, not peer-reviewed. The author reworked the model's argument into the paper's Section 4 and takes responsibility for it, but no independent check is on record.
arXiv:2605.08033 - Weak Order on the MacNeille Completion of Bruhat Order
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Known method families
argument (source-reported)
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
VibeMath has not independently verified the mathematical claim.
AI-attempt independence and training-data exposure are unknown unless explicitly documented.
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.