A coherent fit to TESS Sector 80 gives two HAT-P-57 frequencies that differ from exact orbital harmonics

We test an exact frequency relation for two known light variations in the unresolved HAT-P-57 system. We use public TESS Sector 80 data and a model with constant sinusoid frequencies, amplitudes, and phases. The two fitted frequencies are 8.093877 and 20.316756 cycles per day. They differ from orbital harmonics 20 and 50 by -0.018743 and +0.035207 cycles per day. The comparison uses 9,319 two-minute samples, separate slow trends across large gaps, and six other fitted waves. Tests with other flux extractions and model settings check the result. For three residual block sizes, the local 95% quantile envelopes are 8.089419 to 8.098571 and 20.311800 to 20.320339 cycles per day. These ranges do not include uncertainty from the selection of other signals. Injection tests check recovery of exact harmonics on the observed time grid. A separate prediction test fails: waves fitted on earlier data give 1,690 ppm error on later data, compared with 1,518 ppm for a slow baseline alone. Thus the frequency comparison describes the full-record coherent fit. It does not establish a stable physical mode model. The signals were reported before; this work adds a test of the exact relation and its limits. It does not identify the emitting star or exclude other tidal effects. The package contains original FITS inputs, source records, code, numerical results, and figures.

HAT-P-57 · TESS Sector 80 · stellar light variations · orbital harmonics · frequency estimation · residual block tests · waveform prediction · reproducible astronomy