The monic Alexander polynomial conjecture for twisted torus knots

A twisted torus knot is a knot obtained by twisting a torus knot along an appropriate unknotted circle. Its Alexander polynomial is denoted by $\Delta_K(t)$.

Twisted torus knot fiberedness conjecture. A twisted torus knot is fibered if and only if its Alexander polynomial is monic.

This would extend the classical result for alternating knots, where monicity of the Alexander polynomial characterizes fiberedness. The conjecture is motivated by computations for twisted torus knots with $s<0$ and standard braid diagrams having at most $100$ crossings, but its general status remains open.