\begin{document}$ \hat{k} $\end{document}. We also examine the impact of quantum corrections on the properties of stable circular orbits (SCOs) around the polymerized black hole. We model the smaller object's trajectory as an adiabatic evolution along SCOs using a semi-relativistic approach. In this method, the motion of the object is described by relativistic geodesics, and changes in the object's energy and orbital angular momentum due to gravitational radiation are calculated using the mass quadrupole formula. The corresponding gravitational waveforms are generated using the numerical kludge method, revealing that quantum corrections cause phase advances in the gravitational waveforms. We further analyze the potential constraints on the quantum parameter \begin{document}$ \hat{k} $\end{document} from future space-based gravitational wave observations, concluding that the constraints on \begin{document}$ \hat{k} $\end{document} imposed by these observations will likely be stronger than those imposed by black hole shadow measurements."> Constraining polymerized black holes with quasi-circular extreme mass-ratio inspirals -
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