A 36.34-day Sub-Neptune Candidate Transiting the Nearby K Dwarf TIC 402710280

We report a transiting sub-Neptune candidate with a period of 36.34 days around TIC 402710280 (TYC 9041-03677-1), a K dwarf of TESS magnitude 9.24 at 66.8 pc that the Transiting Exoplanet Survey Satellite (TESS) has observed only in full-frame images. Four transits, recorded between 2021 and 2026 in Sectors 39, 93, 100 and 102 and reduced by three independent pipelines, share a depth of 2092 plus or minus 47 ppm and a duration of 5.27 plus or minus 0.05 h. Two of them fall on consecutive cycles, and every shorter period predicts transits in covered data that are absent at at least 18.6σ; the period is P = 36.33986 plus or minus 0.00051 d. A transit model gives R p/R = 0.0421+0.0007-0.0005 and a stellar density consistent with the host's. The candidate has a radius of 3.75 plus or minus 0.22 R and an equilibrium temperature of 498 plus or minus 21 K. Difference-image centroids place the signal 1.5'' plus or minus 1.3'' from the target. The only catalogued star close enough to contribute, a background star 3.5'' away, would have to host an eclipsing binary whose eclipse shape is disfavoured for any main-sequence pair (Δχ squared at least 142). No secondary eclipse is detected, and TRICERATOPS gives a false-positive probability of 0.003 plus or minus 0.004. No high-resolution imaging exists, so companions within about 1'' are constrained only by Gaia astrometry. The mid-times scatter about a linear ephemeris by 21.8 min (rms). Quick-Look Pipeline light curves reproduce the 29-min excess in the interval between the two 2026 transits, so it does not arise in our photometry; we report the scatter without choosing between an instrumental and a dynamical origin. The light curve also contains a 407 plus or minus 26 ppm signal with a period of 3.78 days whose source, the target or the background star, the present data cannot identify. We predict transit times, including one in TESS Sector 114 on 2027 February 19.