Period recovery from a real survey cadence is an inverse problem whose posterior is genuinely multimodal. Drive the survey window below — how many real ATLAS epochs survive, and what shape the star actually has — and watch distinct periods appear with nearly equal data fidelity. Lomb–Scargle reports the single tallest peak and no error bar.
Two measures on different scales get two panels sharing one period axis — never
a twinned y-axis. Faint vertical lines are the survey's own alias lattice,
f = a·f_sid + (b/4)·f_sol, measured independently from 24 real ATLAS
cadences. Circles mark extracted modes; click one to highlight its fold below.
| Mode | Period (d) | Ratio to true | Lattice / harmonic | reduced χ² | Δχ²tot | two-sided χ² | phase coverage |
|---|
Δχ²tot is the gap to the best mode in total χ²
— the statistic that actually decides degeneracy. A gap of 10% in reduced
χ² would be a gap of ~60 in total χ² over 600 epochs, i.e. decisive; only gaps
of a few units are genuine ties. The two-sided statistic is
χ² if χ² ≥ 1 else 1/χ² (InverseBench Eq. 10), so over- and
under-fitting are penalised symmetrically. χ² is per measurement, and the unknown
has 128 free phase bins, so values below 1 are absorbing noise, not succeeding.
Folds are drawn at 32 display bins because at these SNRs 128 bins render as noise.
The score prior is a 2.42 M-parameter 1-D circular UNet with EDM preconditioning, trained on five analytic morphology classes — — on 128 phase bins with random phase rolls. It has never seen a real light curve. The signals here are synthetic; the cadence and the per-epoch uncertainties are real ATLAS forced photometry. Modes are basins of the data-fit landscape, which needs no prior normalisation; the mode weights reported in the paper require a variational evidence estimate and are reported there with a sensitivity sweep.