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Measurement of the branching fraction of leptonic decay <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mrow><mml:mi>τ</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msub><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mi>τ</mml:mi></…

By analyzing $6.32\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of ${e}^{+}{e}^{\ensuremath{-}}$ annihilation data collected at the center-of-mass energies between 4.178 and 4.226 GeV with the BESIII detector, we determine the branching fraction of the leptonic decay ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\nu}}_{\ensuremath{\tau}}$, with ${\ensuremath{\tau}}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}{\overline{\ensuremath{\nu}}}_{\ensuremath{\tau}}$, to be ${\mathcal{B}}_{{D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\nu}}_{\ensuremath{\tau}}}=(5.29\ifmmode\pm\else\textpm\fi{}{0.25}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{0.20}_{\mathrm{syst}})%$. We estimate the product of the Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{cs}|$ and the …