  Let $kq$ denote the very effective cover of Hermitian K-theory. We apply the
$kq$-based motivic Adams spectral sequence, or $kq$-resolution, to
computational motivic stable homotopy theory. Over base fields of
characteristic not two, we prove that the $n$-th stable homotopy group of
motivic spheres is detected in the first $n$ lines of the $kq$-resolution,
thereby reinterpreting results of Morel and R{\"o}ndigs-Spitzweck-{\O}stv{\ae}r
in terms of $kq$ and $kq$-cooperations. Over algebraically closed fields of
characteristic 0, we compute the ring of $kq$-cooperations modulo
$v_1$-torsion, establish a vanishing line of slope $1/5$ in the $E_2$-page, and
completely determine the $0$- and $1$- lines of the $kq$-resolution. This gives
a full computation of the $v_1$-periodic motivic stable stems and recovers
Andrews and Miller's calculation of the $\eta$-periodic $\mathbb{C}$-motivic
stable stems. We also construct a motivic connective $j$ spectrum and identify
its homotopy groups with the $v_1$-periodic motivic stable stems. Finally, we
propose motivic analogs of Ravenel's Telescope and Smashing Conjectures and
present evidence for both.
