Hausdorff-dimension separation conjecture for Cantor series

Let $Q$ be a basic sequence. Hausdorff-dimension separation conjecture. If $Q$ is infinite in limit and $t$-divergent, and $\{1,\ldots,t\}=A\mathbin{\dot\cup}B$, then the set

$$\bigcap_{k\in A}\mathscr{N}_k(Q)\backslash\bigcap_{j\in B}\mathscr{N}_j(Q)$$

has a specified Hausdorff dimension. If $Q$ is infinite in limit and fully divergent, and $\mathbb{N}=C\mathbin{\dot\cup}D$, then the set

$$\bigcap_{k\in C}\mathscr{N}_k(Q)\backslash\bigcap_{j\in D}\mathscr{N}_j(Q)$$

has a specified Hausdorff dimension. The supplied statement omits the values of both Hausdorff dimensions, so the mathematical assertion is incomplete in the source span. It is presented as an extension of the finite- and infinite-order separation conjectures and remains open.