Torsion-growth conjecture for Artin kernels

Let $L$ be a flag complex, let $\varphi\colon A_L\to\mathbb{Z}$ be an epimorphism, and let $BB_L^\varphi$ be the associated Artin kernel. Suppose $BB_L^\varphi$ is of type $\mathsf{FP}_n$, and let $(G_n)$ be any residual chain. The Artin-kernel torsion-growth conjecture. For $p\leqslant n$,

$$t_p^{(2)}(BB_L^\varphi)=\limsup_{n\to\infty}\frac{\log\lvert H_p(G_n;\mathbb{Z})_{\mathrm{tors}}\rvert}{[BB_L^\varphi:G_n]}=\sum_{v\in L^{(0)}}\lvert\varphi(v)\rvert\,\lvert H_{p-1}(\operatorname{lk}(v);\mathbb{Z})_{\mathrm{tors}}\rvert.$$

This conjectures an analogue for Artin kernels of the known torsion-growth formula for right-angled Artin groups. The source gives no resolution.