Steenrod-operation polynomiality conjecture for $H^{\star}(K_{r\sigma+s})$

Let $K_{r\sigma+s}$ be a $C_2$-equivariant Eilenberg–Mac Lane space with fundamental class $\iota_{r\sigma+s}$. Let $Sq_{C_2}^{I}$ denote a $C_2$-equivariant Steenrod operation, let $e(I)$ be the degree associated to the multi-index $I$, and let $u$ denote the relevant coefficient-class element. For representations $V$ and $V'$, write $V<V'$ when $V'=V+W$ for an actual representation $W$ of positive degree.

Steenrod-operation polynomiality conjecture. $H^{\star}(K_{r\sigma+s})$ is a polynomial algebra on certain classes

$$\frac{Sq_{C_2}^{I}(\iota_{r\sigma+s})}{u^{\text{certain powers}}}$$

where $e(I)<r\sigma+s$.

The conjecture proposes a uniform description of the $RO(C_2)$-graded cohomology of equivariant Eilenberg–Mac Lane spaces in terms of equivariant Steenrod operations. The source states no proof or resolution; the precise powers of $u$ and the full choice of operations are left unspecified.