The Mahowald-lift existence conjecture for equivariant self-maps

Suppose that $X\in\mathrm{Sp}^{C_2}_{(2),\omega}$ is a type $(n,n-1)$ complex. Suppose further that the modified inductive procedure produces a $v_n$-self map as a Mahowald invariant of an iterate $v^j$ of a $v_{n-1}$-self map on $X^{\Phi C_2}$. Mahowald-lift existence conjecture. A power $j$ satisfying these criteria always exists. If so, the corresponding Mahowald lift is a $v_{(n,n-1)}$-self map and its cofiber has type $(n+1,n)$. The assertion is presented as part of a proposed strategy for inductively constructing equivariant periodic self-maps; no resolution is supplied in the given text.