FAST Polarization Catalog of FRB 20240114A
Polarization measurements of fast radio bursts (FRBs) probe the magnetized plasma surrounding their central engines. FRB~20240114A is an exceptionally active repeating source, with 17,356 bursts detected between 2024 January 28 and 2025 May 30 by FAST, enabling time-resolved polarimetric studies. In this work, we present a polarimetric catalog of 6,131 bright bursts (with a signal-to-noise ratio S/N $\geq$ 20, 35.3% of the total sample), including arrival time (MJD$_{\text{topo}}$), dispersion measure (DM), burst width (W$_{\text{eff}}$), bandwidth, Faraday rotation measure (RM), linear and circular polarization degrees (DOL, DOC), and intrinsic polarization angle (PA$_0$). We detect a clear temporal evolution of RM: after an initial stable phase, it decreases linearly by $\sim$200 $\rm rad\ m^{-2}$ over 200 days, forming a bimodal distribution, whereas DM remains stable at 528.9 $\rm pc\ cm^{-3}$. The linear polarization fraction is generally high, with the 3$\sigma$ lower bound around 76%, while circular polarization is low, with 1,157 of 17,356 bursts (6.67%) having DOC $\geq$10%. We perform a power-law fit between $|\textrm{V}|$/I and $|\textrm{RM}|$, which yields an index of $-2.98 \pm 0.80$. It is found that the combined 2D distribution of L/I versus V/I remains stable, implying that the emission mechanism is largely invariant. Our PA$_0$ measurements show a broad, non-uniform distribution, implying a complex emission geometry. These results suggest that FRB~20240114A resides in a dynamically evolving magneto-ionic environment. This catalog provides a foundation for studies of repeating FRB progenitors and their environments.