Shifted Bernoulli full-shift probability conjecture

Fix $q\in(0,1)$, and let $\mathbb{D}_{n,q}$ be the Bernoulli random digraph on $n$ vertices. Write $\Sigma_{\mathbb{D}_{n,q}}$ for its associated shift of finite type, and let $\zeta$ denote the Riemann zeta function.

Shifted Bernoulli full-shift probability conjecture.

$$\lim_{n\to\infty}\mathbb{P}\left(\sigma\colon\Sigma_{\mathbb{D}_{n,q}}\to\Sigma_{\mathbb{D}_{n,q}}\text{ is flow equivalent to a full shift}\right)=\frac{1}{2}\prod_{p\text{ prime}}\left(1+\frac{1}{p^2-p}\right)\prod_{k=2}^{\infty}\zeta(k)^{-1}\approx0.42347.$$

This conjecture concerns the asymptotic full-shift probability for Bernoulli random digraphs; the supplied context presents it as an expectation supported by data, with no resolution stated.