Sensitivity study of <inline-formula><tex-math id="M1">\begin{document}${\bar{K}_1(1270)}$\end{document}</tex-math></inline-formula> decay dynamics using four <inline-formula><tex-math id="M2">\begin{document}${D\to \bar{K}_1(1270)(\to \bar K\pi\pi)e^+\nu_e}$\end{document}</tex-math></inline-formula> decay channels

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