Polynomial-growth monodromy conjecture for first homology torsion growth

Let $F_m$ be a finitely generated free group, let $\varphi$ be an automorphism, and set

$$\Gamma=F_m\rtimes_\varphi\mathbb{Z}.$$

Assume that $\varphi$ is polynomially growing of degree $d$. For a Farber sequence $(\Gamma_n)_{n\in\mathbb{N}}$ of finite-index subgroups of $\Gamma$, write $H_1(\Gamma_n;\mathbb{Z})_{\mathrm{tors}}$ for the torsion subgroup of first homology. Polynomial-growth torsion-growth conjecture. There exists $c\in\mathbb{R}_{\geq 0}$ such that

$$\lim_{n\to\infty}\frac{|H_1(\Gamma_n;\mathbb{Z})_{\mathrm{tors}}|}{|\Gamma:\Gamma_n|^d}=c.$$

The conjecture proposes a precise polynomial asymptotic for first-homology torsion, independent of the chosen Farber sequence. The paper establishes vanishing of normalized torsion growth for polynomially growing monodromy, but the sharper degree-$d$ asymptotic is presented as a conjecture and is not resolved here.