Gaia DR3 and ZTF timing of 11,668 Mira-like stars (2014-2025) shows a weak persistent period-change signal and no confirmed rapid period change; a simple O-C extrapolation test is biased

Question: do the pulsation periods of faint Gaia DR3 long-period variables change between Gaia DR3 (2014.6-2017.4) and ZTF DR24 (2018.2-2025.8), and does any star show a rapid change (|dP/dt|/P >= 1%/yr) like the thermal-pulse Mira T UMi? Method: we made ZTF r O-C curves of 11,668 large-amplitude LPVs (Dec > -28, G 12.5-18.5) and timed their Gaia G epochs with each star's ZTF template. We applied two population tests. Test A compares the Gaia phase offset with the extrapolated ZTF O-C curvature. Test B compares the within-ZTF period change with the Gaia-to-ZTF change and has no shared Gaia/ZTF term. We compared both tests with light-curve-level simulations (real sampling; cycle-length, amplitude and mean-level jitter) and with injections. Results: Test A gave rho = 0.28 in a 360-star pilot. A Gaussian O-C null gave 0.00 +- 0.06, but noise-only light-curve simulations give correlations of the same size and sign pattern as the full data (data 0.195 vs null 0.122 in well-sampled stars). Thus Test A is dominated by a sampling artifact. In Test B, well-sampled stars give rho = 0.080 [0.049, 0.109] (0.095 with DR3 catalogue periods), against -0.047 for noise only and 0.81 for a constant dP/dt population. Thus a small part of the measured period change persists over about 10 years. The spread of the within-ZTF period change is not larger than in the noise-only simulation. The conservative 95% bound is sd(dP/dt/P) <= 0.39%/yr. Four stars pass a strict rapid-change rule, against 0 of 2,594 simulated noise-only stars. But all four are faint, very red, poorly sampled plane or bulge Miras, two have close Gaia neighbours, and their Gaia phases and earlier OGLE/VSX periods do not follow a monotonic change. We list them as a watch list, not as thermal-pulse candidates. Limitations: simulation jitter settings are approximate, blending and censoring of faint minima are not simulated, and bright Miras are outside the sample.

Mira variables · long-period variables · period change · thermal pulse · O-C diagram · Gaia DR3 · ZTF · epoch photometry · null simulation · Eddington-Plakidis