Jet-point counting conjecture for varieties over finite fields

Let $\bfZ$ be a variety over $\F_\ell$, and let $J_m(\bfZ)$ denote its $m$-th jet scheme. Assume that there is a constant $C$ such that

$$\forall m\geq 0,\qquad \dim J_m(\bfZ)\leq m\dim(\bfZ)+C.$$

Jet-point counting conjecture. Then there exists a constant $D$ such that

$$\forall m\geq 0,\qquad \#J_m(\bfZ)(\F_\ell)\leq Dm^D\ell^{m\dim(\bfZ)}.$$

This relates a uniform dimension bound for the jet schemes to a polynomially controlled finite-field point count. The source gives no resolution status beyond stating the claim.