Torsion-speciality of roots of bounded-height monic integer polynomials

Determine whether the set of all roots of monic polynomials in \(\mathbb Z[x]\) whose coefficients are bounded in absolute value by a fixed integer \(H\geq 1\) is torsion-special.

Background

For an infinite set of algebraic numbers, torsion-speciality means that Zariski closures of subsets of its Cartesian powers decompose into finite unions of varieties defined by multiplicative relations with roots of unity. The authors expect speciality to hold for substantially larger sets of algebraic numbers of growing degree and formulate the bounded-coefficient family as a concrete question. They subsequently prove an analogous speciality result almost surely for a randomly sampled family of polynomials, but the deterministic question for all monic bounded-coefficient polynomials is left unresolved.