The strong polynomial-count conjecture for complex varieties

Let $\mathcal{X}$ be a reduced $\mathbb{Z}$-scheme and let $X=\mathcal{X}(\mathbb{C})$ be the associated complex algebraic variety. Say that $X$ is strongly polynomial count when its point counts become polynomial after restricting to finite fields arising from a suitable finitely generated coefficient ring, and say that it is polynomial motivic when $[X]=P(q)$ in $\mathrm{K}\mathbf{Var}_{\mathbb{C}}$ for some $P(t)\in\mathbb{Z}[t]$. The strong polynomial-count conjecture. $X$ is strongly polynomial count if and only if it is polynomial motivic, and the counting and motivic polynomials agree. This is proposed as a refinement of the asymptotic polynomial-count claim after the latter is refuted by torus-knot representation varieties; the source states that this refined conjecture remains open.