A 1.6 R_Earth Transiting Planet Candidate on a 5.31-day Orbit around the Nearby M4.5 Dwarf G 249-11 (TIC 417732194)

Preprint (Research Note format) with the vetting record, photometry, figures and code. We report a transit-like signal on G 249-11 (TIC 417732194), an M4.5 dwarf at 29 pc that is not a TOI, CTOI or SPOC threshold-crossing event. A box least squares search of TESS full-frame-image light curves of 7,474 nearby M dwarfs identified the signal. An ephemeris fitted to Sectors 59-60 alone predicted transits that appear in Sectors 73 and 86, which were not used for selection. End-to-end null simulations give a false-alarm probability of about 0.002 (3 sigma) for that prediction. A transit fit to all five TESS sectors with a stellar-density prior yields P = 5.307425 +- 0.000008 d, T0 = 2459912.3151 +- 0.0008 BJD_TDB, depth 3.0 ppt and Rp = 1.61 +- 0.09 R_Earth (Teq ~ 410 K). The signal passes standard photometric vetting, but a bound eclipsing companion and a G = 17.2 neighbour 20 arcsec away remain viable false positives. The candidate is unconfirmed. Predicted transit times for follow-up are included. Files: the note (PDF + LaTeX + figure); the full vetting report; transit-fit posteriors; the 400-realisation null test; stellar parameters; the extracted TESS photometry (SPOC 2-min, QLP, TESScut apertures) with its provenance; figures (fold, blind prediction, difference image); predicted transit windows; analysis code; SHA-256 sums.