  We report the first lattice QCD computation of pion and kaon electromagnetic
form factors, $F_M(Q^2)$, at large momentum transfer up to 10 and 28
$\mathrm{GeV}^2$, respectively. Utilizing physical masses and two fine
lattices, we achieve good agreement with JLab experimental results at $Q^2
\lesssim 4~\mathrm{GeV}^2$. For $Q^2 \gtrsim 4~\mathrm{GeV}^2$, our results
provide $\textit{ab-initio}$ QCD benchmarks for the forthcoming experiments at
JLab 12 GeV and future electron-ion colliders. We also test the QCD collinear
factorization framework utilizing our high-$Q^2$ form factors at
next-to-next-to-leading order in perturbation theory, which relates the form
factors to the leading Fock-state meson distribution amplitudes. Comparisons
with independent lattice QCD calculations using the same framework demonstrate,
within estimated uncertainties, the universality of these nonperturbative
quantities.
