Hyperbolic torsion polynomial detection conjecture for hyperbolic knots

Let $K$ be a hyperbolic knot in $S^3$, with hyperbolic torsion polynomial $4\mathcal{T}_K4$. Let $x(K)$ denote the Thurston norm, equivalently the genus for a knot in $S^3$.

Hyperbolic torsion polynomial detection conjecture. The hyperbolic torsion polynomial $4\mathcal{T}_K4$ determines $x(K)$, or equivalently its genus. Moreover, $K$ is fibered if and only if $4\mathcal{T}_K4$ is monic.

This conjecture proposes that the canonical hyperbolic torsion polynomial detects both the Thurston norm and fibering, despite the generally limited reliability of Alexander-type polynomials. The computations described in the paper support it for all $313{,}209$ hyperbolic knots with at most 15 crossings, but no resolution is supplied here.