A Note on QPE Timing: False Alarms in O-C

O-C timing analysis is a useful diagnostic tool for quasi-periodic eruptions (QPEs), but their interpretation depends sensitively on the integer cycle number assigned to each eruption. In this note, we show that even a small mismatch in the cycle number, $N_{\rm cyc}$, can produce large false signals in O-C diagrams, and \emph{a universal feature of these false signals is a large in-phase sinusoidal modulation between even and odd eruptions.} Therefore, uncertainties in $N_{\rm cyc}$ must be inferred or marginalized over before physical interpretations are attached to O-C. We then apply both O-C and EMRI+disk to GSN 069 and eRO-QPE2. For GSN 069, the timing data favor an anti-phase modulation in even and odd eruptions, consistent with apsidal precession in a low-eccetricity EMRI crossing an equatorial disk. For eRO-QPE2, the data are well described by a near-circular EMRI and a precessing disk.