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The Solar Neighborhood LV: Spectral Characterization of an Equatorial Sample of 580 K Dwarfs

We present a spectroscopic characterization of 580 K dwarfs within 33 pc, observed with the CHIRON echelle spectrograph (R=80,000) on the SMARTS 1.5m telescope. This volume-limited sample is part of the RKSTAR survey of $\sim$4400 K dwarf primaries within 50 pc. Using Empirical SpecMatch and the diagnostic lines H-alpha (6562.8 Angstrom) and Li I (6707.8 Angstrom), we derive stellar properties, activity status, and age indicators calibrated against 35 benchmark K dwarfs with ages from 20 Myr to 5 Gyr. We find that 7.4% (43 stars) exhibit signatures of youth and/or chromospheric activity: 19 stars show lithium absorption indicating ages $<$1 Gyr, and 36 display H$α$ emission. Kinematic analysis using BANYAN $Σ$ identifies 8 additional young stars through membership in the AB Doradus moving group and the Hyades cluster, bringing the total young/active population to 8.8% (51 stars). Stellar parameters span 3600--5500 K in \teff, $-$0.60 to $+$0.55 dex in [Fe/H], and $<$10 to $>$25 km s$^{-1}$ in $v\sin i$. A metal-poor population ([Fe/H] $\leq -$0.50 dex) comprises 4\% of the sample. Galactic kinematics place 80% in the thin disk and 18.4% in the thick disk, with one halo member (HD 134439). Young and active stars are predominantly thin disk members, with two thick disk exceptions. Cross-matching with NASA's Exoplanet Archive reveals only 7.5% (44 stars) host confirmed planets as of July 2025. Our results identify 529 mature, inactive K dwarfs as prime targets for terrestrial planet searches, providing a crucial resource for exoplanet habitability studies in the solar neighborhood.