  We present for the first time the exact NLO QCD corrections to the
light-quark part of the mixed QCD-EW contributions to Higgs production via
gluon fusion at LHC13, with exact EW-boson mass dependence. The relevant
two-loop real-emission matrix element is computed using a dynamic
one-dimensional series expansion strategy whose stability and speed allows for
a numerical phase-space integration using local IR subtraction counterterms.
For $\mu_R=\mu_F=M_H$, we find:
\begin{equation}\sigma^{(\alpha_s^2\alpha^2+\alpha_s^3\alpha^2)}_{g
g\rightarrow H+X} = 1.467(2)^{\;+18.7\%}_{\;-14.6\%}\;(\mu_R\;\text{var.})\;\pm
2\%\;(\text{PDF}) \ \textrm{pb},\end{equation} which we use to provide the best
result including an estimate of suppressed contributions:
\begin{equation}\sigma^{(\text{EW},\textrm{best})}_{p p\rightarrow H+X} = 2.11
\pm 0.28 \ (\textrm{theory}) \ \mathrm{pb}.\end{equation}
