  Inspired by the work of Hahn-Raksit-Wilson, we introduce a variant of the
even filtration which is naturally defined on $\mathbf{E}_{1}$-rings and their
modules. We show that our variant satisfies flat descent and so agrees with the
Hahn-Raksit-Wilson filtration on ring spectra of arithmetic interest, showing
that various "motivic" filtrations are in fact invariants of the
$\mathbf{E}_{1}$-structure alone. We prove that our filtration can be
calculated via appropriate resolutions in modules and apply it to the study of
even cohomology of connective $\mathbf{E}_{1}$-rings, proving vanishing above
the Milnor line, base-change formulas, and explicitly calculating cohomology in
low weights.
