A counterexample to the cyclic arrangement conjecture
Abstract
The cyclic arrangement conjecture fails at the nonnegative parameters a=6 and b=1.
Javaheri’s arXiv:2610.33653v1 Conjecture 1.3 identifies the largest dimension in which a cyclic power inequality holds with the largest dimension selected by a sine threshold. The formal statement keeps the real nonnegative parameter domain, the cyclic successor, the extended-natural least-upper-bound definition of the valid dimension, and the greatest-element definition of the threshold dimension.
Theorem 1.1 (The universal dimension identity is false).
Lean statement: D5/S0/Certificates/Polynomials/JavaheriArrangementDimensionRefutation.result
Proof. Machine-checked in Lean as D5/S0/Certificates/Polynomials/JavaheriArrangementDimensionRefutation.result (✓ std3). ∎
Resolves. Problems/javaheri-2026-cyclic-arrangement-conjecture-refutation (refuted) by D5/S0/Certificates/Polynomials/JavaheriArrangementDimensionRefutation.result.
Citation. Mohammad Javaheri (2026). A new arrangement inequality (revised and extended version). DOI: 10.48550/arXiv.2610.33653. URL: https://arxiv.org/abs/2610.33653v1.
Commentary.
At a=6 and b=1, the threshold set has greatest element 3. The positive cyclic triple (6,5,5) makes the difference between the two sides equal to 364, so dimension 3 is not valid. The least-upper-bound specification of a valid dimension therefore cannot equal the threshold greatest element, contradicting the universal conjecture.