TOI-712: a system of adolescent mini-Neptunes extending to the habitable zone

As an all-sky survey, NASA's $TESS$ mission is able to detect the brightest and rarest types of transiting planetary systems, including young planets that enable study of the evolutionary processes that occur within the first billion years. Here, we report the discovery of a young, multi-planet system orbiting the bright K4.5V star, TOI-712 ($V = 10.838$, $M_\star = 0.733_{-0.025}^{+0.026} M_\odot$, $R_\star = 0.674\pm0.016 R_\odot$, $T_{\rm eff} = 4622_{-60}^{+61}$ K). From the $TESS$ light curve, we measure a rotation period of 12.48 days, and derive an age between about $500$ Myr and 1.1 Gyr. The photometric observations reveal three transiting mini-Neptunes ($R_b = 2.049^{+0.12}_{-0.080} R_\oplus$, $R_c = 2.701^{+0.092}_{-0.082} R_\oplus$, $R_d = 2.474^{+0.090}_{-0.082} R_\oplus $), with orbital periods of $P_b = 9.531$ days, $P_c = 51.699$ days, and $P_d = 84.839$ days. After modeling the three-planet system, an additional Earth-sized candidate is identified, TOI-712.05 ($P = 4.32$ days, $R_P = 0.81 \pm 0.11 R_\oplus$). We calculate that the habitable zone falls between 0.339 and 0.844 au (82.7 and 325.3 days), placing TOI-712 d near its inner edge. Among planetary systems harboring temperate planets, TOI-712 ($T = 9.9$) stands out as a relatively young star bright enough to motivate further characterization.