Zero-full Hausdorff-measure conjecture for independent prime divisors

Let $C(b,D)$ be a generalized Cantor set with Hausdorff dimension $cgamma$, with $D$ containing at least one of $0$ and $b-1$. Let $t\geq 2$ be an integer such that the sets of prime divisors of $b$ and $t$ are different. Let $f$ be a dimension function such that $r^{-\gamma}f(r)$ is monotonic, and let $cpsi:\mathbb{N}\to(0,\infty)$ be a function. Independent-prime-divisor zero-full law conjecture.

$$\mathcal{H}^{f}(W_t(\psi)\cap C(b,D))= \begin{cases} 0,&\text{if }\displaystyle\sum_{n=1}^{\infty}f(\psi(n))t^n\psi(n)^{1-\gamma}<\infty,\\\\ \mathcal{H}^{f}(C(b,D)),&\text{if }\displaystyle\sum_{n=1}^{\infty}f(\psi(n))t^n\psi(n)^{1-\gamma}=\infty. \end{cases}$$

The conjecture is based on a heuristic that the points with denominators $t^n$ are distributed randomly relative to the $b$-adic intervals intersecting the Cantor set. It would extend zero-full laws to the case where $b$ and $t$ have different prime divisors.