Incorporating BESIII measurements in the Updated $K^0_S$ Fragmentation Functions

We revisit the extraction of parton-to-$K^0_S$ fragmentation functions (FF24-$K^0_S$) at next-to-leading-order (NLO) and next-to-next-to-leading-order (NNLO) accuracy in a QCD analysis, using single inclusive electron-positron annihilation (SIA) data. Key improvements include incorporating new BESIII data and adopting Neural Networks in the fitting process. We also discuss the impact of hadron mass corrections, particularly at small z. Our NLO and NNLO predictions show good agreement with experimental data, accounting for uncertainties via the Monte Carlo method.