The Hamaker-Reiner Conjecture on ASM Weak Order Intervals
resolvedconfidence 70%
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise statement
Hamaker and Reiner conjectured that the order complex of an open interval $(u,w)$ in the ASM weak order is contractible unless $w$ is the long element of a standard parabolic subgroup, in which case it is homotopy equivalent to a sphere. False: there is an interval in the ASM weak order on $S_n$ whose order complex is not contractible even though $w$ has no such form, detected by a nonzero Mobius function value.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement
fidelity, correctness, priority, or novelty.
What AI did
ChatGPT 5.4 Pro
Arrived as a refusal to do what it was asked. Having polished the author's notes, the model was asked what else was worth exploring around weak order on MacNeille completions and suggested proving the Hamaker-Reiner conjecture. The author asked it to prove that conjecture; instead it returned the counterexample that appears as Figure 1 of the paper. The author describes both this and the Escobar-Klein-Weigandt proof as obtained autonomously.
arXiv preprint, not peer-reviewed. The refutation is a single explicit interval whose order complex has nonzero Mobius function, printed in full in the paper, so it is checkable by finite computation.
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
construction (source-reported)
Source-reported tools: construction.
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.