Integral surjectivity conjecture for the logarithmic cycle class map

Let $X/{\mathbb C}$ be a smooth projective variety and $m\geq 1$. Consider the integral logarithmic map

$$d\log_m:\textup{CH}^{m}(\operatorname{Spec}({\mathbb C}(X)),m)\to \Gamma\big(H^{m}({\mathbb C}(X),{\mathbb Z}(m))\big).$$

Integral $d\log$ conjecture. The map $d\log_m$ is surjective. The rationalized map is the generic-point cycle class map $\lim(\textup{cl}_{m,m})$; the source notes that rational surjectivity is equivalent to integral surjectivity, but does not establish either one.