Detection of the element t by the sixth algebraic transfer

Let $\mathscr A$ be the Steenrod algebra over $\mathbb F_2$, and let

$$t\in \operatorname{Ext}^{6,6+36}_{\mathscr A}(\mathbb F_2,\mathbb F_2)$$

be the specified nonzero element. Let $Tr_6(\mathbb F_2)$ denote the sixth algebraic transfer.

Detection conjecture. The nonzero element $t$ is detected by the sixth algebraic transfer $Tr_6(\mathbb F_2)$.

The claim concerns whether the element $t$ lies in the image of the sixth algebraic transfer. The source explicitly says that this is not known before proposing the claim, and provides no resolution, so the conjecture remains open.