Working Commensurate Ephemerides for the Sparse TESS Events in TIC 768070

Long-period planets can be difficult to recover with TESS because a typical ∼27-d sector may contain only one or no transit. Here, we analyze three transit-like events identified in the TESS light curves of TIC 768070 at BTJD 1446.202, 2176.188, and 4001.434, in Sectors 5, 32, and 98. Their timings admit three simple commensurate cycle-count solutions corresponding to periods of 365.036 ± 0.012, 182.518 ± 0.006, and 73.007 ± 0.002 d for cycle assignments [0, 2, 7], [0, 4, 14], and [0, 10, 35], respectively, without breaking the degeneracy among the three ephemerides. Only the 73-d ephemeris predicts an event near BTJD 4293.45 during the forthcoming TESS Sector 108 coverage, providing a prospective discriminant against the 182.5- and 365-d alternatives. In fully blind searches over 0.5–2607.7 d, the TLS periodogram contains peaks consistent with all three timing-derived ephemerides, whereas BLS provides a clear counterpart only near 182.5 d; a MonoTools analysis restricted to the three period hypotheses conditionally favors the 73-d solution. TIC 768070 remains an unresolved sparse-transit system for which future time-domain coverage can directly discriminate between the current timing solutions. Version note: This version supersedes the erroneous previous version and provides a revised interpretation of the candidate periodicities.