\begin{document}$ e^+e^- \rightarrow \tau^+\tau^- $\end{document} process and optimize the analysis methodology for EDM extraction. Machine learning techniques are implemented to efficiently identify signal events (\begin{document}$ \tau^\pm\rightarrow \pi^\pm\pi^0\nu_\tau $\end{document}), which result in a significant improvement in signal-to-noise ratio. Our optimized event selection algorithm achieves 80.0% signal purity with 6.3% efficiency. We develop an analytical approach for τ lepton momentum reconstruction and derive the squared spin density matrix along with optimal observables, which maximize the sensitivity to \begin{document}$ d_\tau $\end{document}. The relationship between these observables and the EDM is established with the estimated sensitivity of \begin{document}$ |d_\tau| < 3.89\times 10^{-18}\,e\cdot\mathrm{cm} $\end{document} at a 68% confidence level. These results provide a foundation for future experimental measurements of the τ lepton EDM in STCF experiments."> Sensitivity study of the tau lepton electric dipole moment at the Super Tau-Charm Facility -
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