Two Earth-size Planets and an Earth-size Candidate Transiting the Nearby Star HD 101581

We report the validation of multiple planets transiting the nearby ($d = 12.8$ pc) K5V dwarf HD 101581 (GJ 435, TOI-6276, TIC 397362481). The system consists of at least two Earth-size planets whose orbits are near a mutual 4:3 mean-motion resonance, HD 101581 b ($R_{p} = 0.956_{-0.061}^{+0.063}~R_{\oplus}$, $P = 4.47$ days) and HD 101581 c ($R_{p} = 0.990_{-0.070}^{+0.070}~R_{\oplus}$, $P = 6.21$ days). Both planets were discovered in Sectors 63 and 64 TESS observations and statistically validated with supporting ground-based follow-up. We also identify a signal that probably originates from a third transiting planet, TOI-6276.03 ($R_{p} = 0.982_{-0.098}^{+0.114}~R_{\oplus}$, $P = 7.87$ days). These planets are remarkably uniform in size and their orbits are evenly spaced, representing a prime example of the "peas-in-a-pod" architecture seen in other compact multi-planet systems. At $V = 7.77$, HD 101581 is the brightest star known to host multiple transiting planets smaller than $1.5~R_{\oplus}$. HD 101581 is a promising system for atmospheric characterization and comparative planetology of small planets.