\begin{document}$ v_2 $\end{document} relative to the participant plane (PP) and reaction plane (RP) in Au+Au collisions at \begin{document}$ \sqrt{s_{NN}} = 7.7 $\end{document}−200 GeV using the AMPT model (string melting version). The ratio \begin{document}$ v_{2}^{\text{PP}} $\end{document}/\begin{document}$ v_{2}^{\text{RP}} $\end{document} is investigated under different hadronic cascade times (0.6 fm/c, 10 fm/c, and the maximum evolution time) and across various collision centralities. The results show that, at a fixed collision energy, the ratio exhibits negligible sensitivity to the duration of the hadronic rescattering stage, indicating that hadronic interactions have a minimal effect on the relative difference generated by initial-state fluctuations. However, a strong energy dependence is observed: the ratio increases with beam energy and saturates above \begin{document}$ \sqrt{s_{NN}} \approx 62.4 $\end{document} GeV, a trend that persists across all centralities. These findings highlight the dominant role of the partonic phase in converting initial-state geometry fluctuations into final-state momentum anisotropy. Conversely, at lower energies, the reduced partonic interaction strength limits the efficiency of this conversion, weakening the system’s ability to preserve the initial geometric information. Our results suggest that the conversion of initial geometric fluctuations into final momentum anisotropy requires sufficient partonic interactions."> Energy dependence of the elliptic flow ratio <i>v</i><sub>2</sub><sup>PP</sup>/<i>v</i><sub>2</sub><sup>RP</sup> in heavy-ion collisions using the AMPT model -
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