Weight-detection conjecture for étale homology

Let $X$ be a scheme, let $M$ be a compact Voevodsky motive over $X$, and let $nge 0$. Write $DM_c(X)_{{w_{Chow}}ge -n}$ for the nonnegative part of the Chow weight structure, and let $H^{et}_{{\mathbb{Q}_l}}$ be the rational $l$-adic étale homology theory. For $p,q\in\mathbb{Z}$, let $E_2^{pq}T_{{w_{Chow}}(X)}(H^{et}_{{\mathbb{Q}_l}},M)$ denote the corresponding weight spectral sequence terms.

Weight-detection conjecture. For every $r,n\ge 0$, if

$$E_2^{pq}T_{{w_{Chow}}(X)}(H^{et}_{{\mathbb{Q}_l}},M)=0$$

for all $q\in\mathbb{Z}$ and $p>n$, then $M\in DM_c(X)_{{w_{Chow}}\ge -n}$. The restricted assertion $WD_r^n(X)$ is that the same implication holds under the additional assumption $M\in\widetilde{N}_r(X)$.

This conjecture proposes detecting lower bounds for the Chow weight of a motive through vanishing of the higher terms of its étale weight spectral sequence. The source formulates both the unrestricted and the $\widetilde{N}_r(X)$-restricted versions, but gives no resolution status.