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We discuss the reduction of errors in the calculation of the form factor$f_+^{K \pi}(0)$ with HISQ fermions on the $N_f=2+1+1$ MILC configurations fromincreased statistics on some key ensembles, new data on ensembles with latticespacings down to 0.042 fm and the study of finite-volume effects withinstaggered ChPT. We also study the implications for the unitarity of the CKMmatrix in the first row and for current tensions with leptonic determinationsof $\vert V_{us}\vert$.

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