The algebraic transfer isomorphism conjecture in bidegree $(5,5+n_d)$

Let $\mathscr A_2$ be the mod-$2$ Steenrod algebra, let $n_d$ be the internal degree sequence used in the paper, and let $Tr_5^{\mathscr A_2}$ denote the fifth algebraic transfer. Algebraic transfer isomorphism conjecture. The algebraic transfer is an isomorphism in bidegree $(5,5+n_d)$ for every $d\geqslant 0$. This extends the known detection and dimension calculations discussed in the paper; the assertion is proposed as an open conjecture for the full family of degrees $n_d$.