Iterative TLS search, masking the signals already identified and rerunning the search (M. Hippke & R. Heller 2019, see R. Heller et al. 2019). The signal detection efficiency (SDE) is plotted against trial period on a logarithmic scale. Top: after masking the three validated planets, a significant peak appears at P = 19.742 days (SDE = 24.5), which we report as the candidate TOI-789.04. Middle: after additionally masking the candidate, the strongest remaining peak (P = 28.09 days) is spurious—it coincides with ∼2× the TESS orbital period and shows a 3.3σ odd–even mismatch—and is rejected. The top and middle panels share an identical period range (0.5–30 days). Bottom: the search extended to P = 290 days (masking all four objects); the only excesses are long-period artifacts, the strongest at P = 249.7 days (SDE =34.7, odd–even 6.0σ), all rejected as described in Section 4.4. Dashed lines mark the periods of interest.