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One of the main scientific goals of the TESS mission is the discovery of transiting small planets around the closest and brightest stars in the sky. Here, using data from the CARMENES, MAROON-X, and HIRES spectrographs together with TESS, we report the discovery and mass determination of aplanetary system around the M1.5 V star GJ 806 (TOI-4481). GJ 806 is a bright (V≈ 10.8mag,J≈ 7.3 mag) and nearby (d= 12 pc) M dwarf that hosts at least two planets. The innermost planet, GJ 806 b, is transiting and has an ultra-short orbital period of 0.93 d, a radius of 1.331 ± 0.023R_⊕, a mass of 1.90 ± 0.17M_⊕, a mean density of 4.40 ± 0.45 g cm⁻³, and an equilibrium temperature of 940 ± 10 K. We detect a second, non-transiting, super-Earth planet in the system, GJ 806 c, with an orbital period of 6.6 d, a minimum mass of 5.80 ± 0.30M_⊕, and an equilibrium temperature of 490 ± 5 K. The radial velocity data also shows evidence for a third periodicity at 13.6 d, although the current dataset does not provide sufficient evidence to unambiguously distinguish between a third super-Earth mass (Msini= 8.50 ± 0.45M_⊕) planet or stellar activity. Additionally, we report one transit observation of GJ 806 b taken with CARMENES in search of a possible extended atmosphere of H or He, but we can only place upper limits to its existence. This is not surprising as our evolutionary models support the idea that any possible primordial H/He atmosphere that GJ 806 b might have had would be long lost. However, the bulk density of GJ 806 b makes it likely that the planet hosts some type of volatile atmosphere. With transmission spectroscopy metrics (TSM) of 44 and emission spectroscopy metrics (ESM) of 24, GJ 806 b is to date the third-ranked terrestrial planet around an M dwarf suitable for transmission spectroscopy studies using JWST, and the most promising terrestrial planet for emission spectroscopy studies. GJ 806b is also an excellent target for the detection of radio emission via star-planet interactions. 

We validate the Transiting Exoplanet Survey Satellite (TESS) object of interest TOI-2266.01 (TIC 8348911) as a small transiting planet (most likely a super-Earth) orbiting a faint M5 dwarf (V= 16.54) on a 2.33 d orbit. The validation is based on an approach where multicolour transit light curves are used to robustly estimate the upper limit of the transiting object's radius. Our analysis uses SPOC-pipeline TESS light curves from Sectors 24, 25, 51, and 52, simultaneous multicolour transit photometry observed with MuSCAT2, MuSCAT3' and HiPERCAM, and additional transit photometry observed with the LCOGT telescopes. TOI-2266 b is found to be a planet with a radius of 1.54 ± 0.09R_⊕, which locates it at the edge of the transition zone between rocky planets, water-rich planets, and sub-Neptunes (the so-called M dwarf radius valley). The planet is amenable to ground-based radial velocity mass measurement with red-sensitive spectrographs installed in large telescopes, such as MAROON-X and Keck Planet Finder (KPF), which makes it a valuable addition to a relatively small population of planets that can be used to probe the physics of the transition zone. Further, the planet's orbital period of 2.33 days places it inside a ‘keystone planet’ wedge in the period-radius plane where competing planet formation scenarios make conflicting predictions on how the radius valley depends on the orbital period. This makes the planet also a welcome addition to the small population of planets that can be used to test small-planet formation scenarios around M dwarfs.