Period change per unit flare fluence fell at least fourfold after the third passage of eRASSt J0456-20 if cycle 8 had the forecast amplitude; in ASASSN-14ko the result depends on timing noise

Question: in a repeating partial tidal disruption, the orbit changes because the star loses mass at each passage, and the same mass feeds the flare. The simplest test of such a clock is H_E: the change of the recurrence time at each passage is -kappa times the flare fluence, with one constant kappa. This test needs no efficiency, bolometric correction or black hole mass. Approach: we fitted H_E and seven other clock models to the seven X-ray cycle markers and fluences of eRASSt J0456-20 and to 31 peak times and 16 g-band fluences of ASASSN-14ko, all from earlier signed campaign publications. We converted the 2024 Aug-Sep XMM-Newton non-detection of J0456-20 into a likelihood for the cycle-8 marker. Results: for J0456-20 the timing alone allows H_E (chi2 = 3.8 for 4 dof; kappa = 15.8 d per XRT count/s d). H_E reproduces the fall of the interval from 294 to 223 d and its levelling-off, so a constant period with fading flares does not by itself exclude it. But H_E also predicts a continued period decrease, which puts the cycle-8 rise inside the 2024 XMM visits. The data exclude this for rise times of 20-105 d and peak rates 0.5-2 times the fading-law forecast: H_E is worse than a coupling that changes after passage 3 by Delta chi2 = 14.7-27.2. The late/early coupling ratio is at most 0.25 (95%) in all variants. As a forecast test the 2024 data give log10 Bayes factors of -0.8 to -2.5 against H_E. A stationary stochastic clock (independent intervals, as in diffusive-tide models) makes cycles 3-7 as regular as observed with p = 0.003-0.004; their interval scatter is below 7 d. For ASASSN-14ko, the period decrease per passage after 2021 fell to -0.1 to 0.5 of its early value while the fluence did not fall. Under white timing noise H_E is disfavoured (Delta chi2 = 6.7-23.5; bootstrap p = 0.003). Under random period kicks of 0.6-0.8 d per orbit, which earlier studies reported, p is 0.07-0.16. An order-of-magnitude mass-loss kick estimate gives a coupling of about 2 for the early changes in both sources. Limitations: the J0456-20 result assumes that cycle 8 occurred with about the forecast amplitude; X-ray fluence is an imperfect mass proxy; the cycle-1 time comes from a published onset; we used derived products, not raw data.