The $D^0 \to K_S^0 \pi^+ \pi^-$ decay channel plays a central role in precision studies of charm mixing and indirect CP violation.
The status of the time-dependent binned analysis of this decay is presented using data collected by the LHCb experiment during Run 3 in 2024.

This dataset benefits from the fully software-based trigger system introduced in Run 3, which significantly enhances the efficiency for reconstructing hadronic charm decays. In particular, the new GPU-accelerated HLT1 trigger selects tracks based on displacement and kinematic properties using a refined approach compared to the Run 2 hardware-based system, which relied heavily on calorimetry.

This results in a nearly threefold increase in signal yield per unit luminosity, as well as a substantial reduction in trigger-induced correlations between decay time and Dalitz plot position, which were previously a dominant source of systematic uncertainty.

The analysis strategy is presented, demonstrating improved sensitivity to the mixing and CP-violating parameters $x$ and $y$. The results highlight the impact of the upgraded LHCb trigger system in enabling more precise and robust charm physics measurements.