${V}_{us}$

We determine the decay constants of the $$\pi${}$ and $K$ mesons on gluon field configurations from the MILC Collaboration including $u$, $d$, $s$, and $c$ quarks. We use three values of the lattice spacing and $u/d$ quark masses going down to the physical value. We use the ${w}_{0}$ parameter to fix the relative lattice spacing and ${f}_{$\pi${}}$ to fix the overall scale. This allows us to obtain a value for ${f}_{{K}^{+}}/{f}_{{$\pi${}}^{+}}=1.1916(21)$. Comparing to the ratio of experimental leptonic decay rates gives $|{V}_{us}|=0.22564(28{)}_{\mathrm{Br}({K}^{+})}(20{)}_{\mathrm{EM}}(40{)}_{\mathrm{latt}}(5{)}_{{V}_{ud}}$ and the test of unitarity of the first row of the Cabibbo-Kobayashi-Maskawa matrix: $|{V}_{ud}{|}^{2}+|{V}_{us}{|}^{2}+|{V}_{ub}{|}^{2}-1=0.000\text{ }09(51)$.