ZTF data from 2022 to 2025 and Gaia DR3 data from 2014 to 2017 do not follow the published sinusoids of 36 periodic-quasar binary black-hole candidates; at most 3 to 7 can have a coherent period

Question: Foustoul et al. (2025) report 36 quasars with sinusoidal optical variation over 3-5 cycles in CRTS and ZTF data (to mid 2022) and propose them as sub-parsec binary black-hole candidates. Do their sinusoids predict data that the selection did not use? Method: For each candidate we fit a sinusoid at the published period plus a damped random walk (DRW) to ZTF DR24 r data up to MJD 59800, and a DRW-only model to the same data. We score the log predictive density of two hold-outs: Gaia DR3 G epochs from 2014.6 to 2017.4 (31 candidates, in the CRTS-ZTF gap) and ZTF r and g data from August 2022 to October 2025 (36 candidates). Nulls: 200 random periods per source, and simulations on the real sampling of DRW with a period search (also with a CRTS+ZTF sinusoid selection) and of injected sinusoids at the fitted and half amplitude. Results: The sinusoid beats DRW alone in the forward ZTF r data for 3 of 36 candidates (all by less than 1 nat; sum -804 nats; g band 2 of 36). This agrees with the DRW nulls (0.07-0.15) and not with injected sinusoids (0.64-0.72). In Gaia the sinusoid wins for 9 of 31 (median -1.6 nats), close to the null with CRTS-based selection (0.18; binomial p = 0.10) and far from injected sinusoids (0.60-0.73; p < 0.0001). No candidate wins in both hold-outs (expected 0.43-0.56 for a coherent sinusoid). The published periods rank below the median of random periods in the forward data (mean percentile 0.26), as red noise with a period search predicts. A mixture fit gives a periodic fraction of 0 with a 95% upper limit of 0.08-0.19 (3-7 of 36). For the 111 Graham et al. (2015) CRTS candidates at their own periods, no source passes strict criteria; the 26 that Foustoul et al. kept predict worse than the rejected ones because their larger fitted amplitudes extrapolate badly. HS 2219+1944 has large positive scores but sparse ZTF data, an amplitude of 0.08 +/- 0.08 mag and an insignificant period rank. Limitations: CRTS data were not available, so the phase comes from ZTF alone at the published period; the end of the published ZTF data is estimated from figures; the DRW is a simple red-noise model; Gaia G and ZTF r amplitudes are assumed equal; 6 simulations per source and scenario.

binary supermassive black holes · periodic quasars · quasar variability · damped random walk · red noise · out-of-sample test · hold-out prediction · ZTF DR24 · Gaia DR3 epoch photometry · CRTS · Foustoul 2025 · Graham 2015 · HS 2219+1944 · null result · Gaussian process · celerite