  For every smooth proper scheme over a finite field $\mathbb{F}_q$, Bilu, Ho,
Srinivasan, Vogt, and Wickelgren introduced the dlog zeta function with
coefficients in the Grothendieck-Witt ring $\mathrm{GW}(\mathbb{F}_q)$,
enriching the dlog of the classical Weil zeta function with coefficients in
$\mathbb{Z}$. They defined a notion of dlog rationality of such dlog zeta
functions, which enriches the rationality of the Weil zeta function, and showed
the dlog rationality for simple cellular schemes. In this paper, we show that
for any smooth proper schemes over $\mathbb{F}_q$, the dlog zeta function is
rational, but not necessarily dlog rational.
