Problem detail · source-aware
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Reading computed the order dimension of the poset of regions for most finite Coxeter arrangements, observed that an exceptional type whose dimension exceeds its rank would be the first known simplicial arrangement with that property, and recorded the general guess that every simplicial region poset has dimension equal to its rank (Problem 9.3 of his 2016 chapter); Segovia later asked the analogous question for oriented-poset lattices. False: the order dimension of the poset of regions can exceed the rank - the Coxeter arrangements $H_4$ and $E_6$ satisfy $\dim W(H_4) \ge 5$ and $\dim W(E_6) \ge 7$.
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The declaration, in full: "The small obstruction subgraphs were found by ChatGPT 5.6 Sol Ultra. The human input was the belief that the rank guess is incorrect, and one should look for counterexamples." The obstruction subgraphs are the entire content of the disproof, so the model produced the central objects under human direction.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Checked by this site on 17 August 2026 against the paper's LaTeX (arXiv:2608.14092): the declaration is verbatim, and the problem attribution is precise - Reading's Problem 9.3 (2016) with the H_4/E_6 background from his 2003 computations, plus Segovia's analogous question. The obstruction subgraphs were not re-verified here. Days-old preprint, no independent review.
Correctness: unknown · statement fidelity: unaudited · peer review: none
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VibeMath has not independently audited the mathematical statement, proof, or novelty claim.