The new t-structure detection conjecture for affine-flag D-modules

Let $\bD_{\mathrm{ren}}(\fD(\Fl^{\operatorname{aff}}_G)_\crit\operatorname{mod})$ carry the old and new t-structures, and let $J_\cla$ be the convolution objects indexed by $\cla\in\cLambda$. New t-structure detection conjecture. If $\CF\in\bD_{\mathrm{ren}}(\fD(\Fl^{\operatorname{aff}}_G)_\crit\operatorname{mod})$ satisfies

$$\CF\star J_\cla\in\bD_{\mathrm{ren}}^{\leq 0_{\mathrm{old}}}(\fD(\Fl^{\operatorname{aff}}_G)_\crit\operatorname{mod})$$

for every $\cla\in\cLambda$, then

$$\CF\in\bD_{\mathrm{ren}}^{\leq 0_{\mathrm{new}}}(\fD(\Fl^{\operatorname{aff}}_G)_\crit\operatorname{mod}).$$

The assertion concerns whether the defining convolution test detects the nonpositive part of the new t-structure; the source presents it as one of several unresolved basic questions.