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Kaon semileptonic decays with $N_f=2+1+1$ HISQ fermions and physical light-quark masses

We discuss the reduction of errors in the calculation of the form factor $f_+^{K π}(0)$ with HISQ fermions on the $N_f=2+1+1$ MILC configurations from increased statistics on some key ensembles, new data on ensembles with lattice spacings down to 0.042 fm and the study of finite-volume effects within staggered ChPT. We also study the implications for the unitarity of the CKM matrix in the first row and for current tensions with leptonic determinations of $\vert V_{us}\vert$.