The secondary semiclassical limit conjecture

Assume that $\operatorname{char} k=0$. Let $A$ and $A'$ be suitably generic members of some flat family of quantized coordinate rings for an affine variety $V$ with semiclassical limit $\mathcal O(V)$. Secondary semiclassical limit conjecture. There exist compatible homeomorphisms

$$\operatorname{Spec} A \longrightarrow \operatorname{Spec} A'$$

and

$$\operatorname{Prim} A \longrightarrow \operatorname{Prim} A'.$$

Whenever the primary semiclassical limit conjecture holds, the considered generic quantized coordinate rings have homeomorphic prime and primitive spectra; positive-characteristic examples show that the characteristic-zero hypothesis is significant.