Amplitude analysis and branching fraction measurement of the Cabibbo-favored decay $\textit{D}$

An amplitude analysis of the Cabibbo-favored decay $\textit{D}$ → $\textit{K}$ $\textit{π}$ $\textit{π}$ $\textit{π}$ is performed, using 7.93 fb of $\textit{e}$ $\textit{e}$ collision data collected with the BESIII detector at the center-of-mass energy of 3.773 GeV. The branching fractions of the intermediate processes are measured, with the dominant contribution observed to have a branching fraction of (4.35 $\textit{±}$ 0.07 $\textit{±}$ 0.17 )%. With the detection efficiency derived from the amplitude analysis, the absolute branching fraction of $\textit{D}$ $\textit{→ K}$ $\textit{π}$ $\textit{π}$ $\textit{π}$ is measured to be (6.35 $\textit{±}$ 0.04 $\textit{±}$ 0.07 )%.