$p$-adic non-vanishing conjecture for the WRT function

Let $M$ be an integral homology sphere and let $p$ be a prime. Its $p$-adic WRT function is

$$\tau ^p(M)=\operatorname{sp}_{U(\mathcal{O}_p)}(J_M)\colon U(\mathcal{O}_p)\to\mathcal{O}_p.$$

$p$-adic non-vanishing conjecture. The function $\tau ^p(M)$ is nowhere zero on $U(\mathcal{O}_p)$. The source presents this as a generalization of the root-of-unity non-vanishing conjecture; no resolution is given.