bibkey: javaheri2026arrangement
authors: Mohammad Javaheri
year: 2026
title: "A new arrangement inequality (revised and extended version)"
doi: 10.48550/arXiv.2610.33653
url: https://arxiv.org/abs/2610.33653v1
claim: "Conjecture 1.3: for all nonnegative real a,b with a+b != 1, the largest cyclic dimension satisfying (sum x_i)(sum x_i^a x_(i+1)^b) <= (sum x_i^((a+b+1)/2))^2 equals the largest n with n=1 or (a+b-1)^2 <= 8ab sin^2(pi/n)."
strata_touched:
  - D5/S0/Certificates/Polynomials/JavaheriArrangementDimensionRefutation
license: citation-only
triage: anchor

A new arrangement inequality

Mohammad Javaheri’s revised preprint defines the cyclic arrangement inequality for nonnegative real parameters and cyclic nonnegative tuples, and defines the largest valid dimension together with the threshold dimension from the sine condition. Conjecture 1.3 asserts equality of these two dimensions for every allowed parameter pair.

Verified locator

• DOI: 10.48550/arXiv.2610.33653
• URL: https://arxiv.org/abs/2610.33653v1
• Locator: arXiv:2610.33653v1, Section 1, Conjecture 1.3 and Theorem 1.2.

The revised arXiv record lists v1 as the inspected source version. The formal result refutes the literal universal conjecture at the parameter pair (6,1).