Cyclotomic ordering conjecture

This note describes a conjecture involving cyclotomic polynomials and some initial thoughts towards a solution. Given positive integers $m,n$, the conjecture is that either ${\mathrm{\Phi }}_m(q)⩽{\mathrm{\Phi }}_n(q)$ or ${\mathrm{\Phi }}_m(q)⩾{\mathrm{\Phi }}_n(q)$ holds for all integers $q⩾2$. Pomerance and Rubinstein-Salzedo proved the conjecture in a preprint called `Cyclotomic coincidences’ [arXiv:1903.01962].