TIC 123951716's boundary mass is too small under the printed precession law and original stability fit over e=0–0.7 and mu=0.1–0.5

We test all 36 rows in Table 1 of Thornton et al. (2026). That study reports 27 candidate circumbinary planets. We combine its relativistic and third body precession laws with the original Holman and Wiegert (1999) stability fit. We eliminate the unknown binary mass. An exact proof gives a lower bound for the companion mass at the stability boundary. The bound applies over binary eccentricity 0–0.7 and secondary mass fraction 0.1–0.5. TIC 123951716 is the only central row that fails. Its reported boundary mass is 0.14 Jupiter masses; the model requires at least 0.312111. The mismatch remains when each input changes by up to three printed errors. This test includes rounding of values and errors. The boxes are sensitivity tests, not confidence intervals. We also reduce each stability radius by 6 percent as a control. The mismatch then remains through two errors, but this test no longer excludes a match at three. A missing mass factor in the printed stability equation is material. The literal printed version can match the central mass. We cannot identify which formula the authors used in code. The source table does not supply the actual binary eccentricity and mass fraction. We cannot establish that the real system is in the tested range. This is a conditional test of model consistency. It does not confirm or reject a planet. We preserve the source PDF, all input rows, provenance, exact calculations, independent checks, a reusable tool, and figures.

circumbinary planets · TESS · apsidal precession · eclipsing binaries · stability boundary · mass limits · model consistency · exact bound · reproducible research