Amplitude analysis of the decay<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>D</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:mo>→</mml:mo><mml:msup><mml:mi>K</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:msup><mml:mi>K</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup></mml:math>

Using $385\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of ${e}^{+}{e}^{\ensuremath{-}}$ collisions, we study the amplitudes of the singly Cabibbo-suppressed decay ${D}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{K}^{+}{\ensuremath{\pi}}^{0}$. We measure the strong phase difference between the ${\overline{D}}^{0}$ and ${D}^{0}$ decays to ${K}^{*}(892{)}^{+}{K}^{\ensuremath{-}}$ to be $\ensuremath{-}35.5\ifmmode^\circ\else\textdegree\fi{}\ifmmode\pm\else\textpm\fi{}1.9\ifmmode^\circ\else\textdegree\fi{}(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}2.2\ifmmode^\circ\else\textdegree\fi{}(\mathrm{syst})$, and their amplitude ratio to be $0.599\ifmmode\pm\else\textpm\fi{}0.013(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.011(\mathrm{syst})$. We observe contributions from the $K\ensuremath{\pi}$ and ${K}^{\ensuremath{-}}{K}^{+}$ scalar and vector amplitudes, and analyze their angular moments. We find no evidence for charged $\ensuremath{\kappa}$, nor for higher spin states. We also perform a partial-wave analysis of the ${K}^{\ensuremath{-}}{K}^{+}$ system in a limited mass range.

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