A negative Delta-BIC is not a detection: calibrating an orbit-versus-noise test on 87 RR Lyrae binary candidates

Binary companions to RR Lyrae stars are sought through the light-travel-time effect (LTTE) in O−C pulsation timing. The same stars show stochastic period fluctuations, which produce O−C excursions of similar size and timescale. This note measures what an information-criterion comparison between an orbital and a noise-only model family establishes for the 87 candidates of Hajdu et al. (2021, ApJ 915, 50). The O−C curves are rebuilt from public OGLE photometry (4,947 timing points; baselines 7.1–20.3 yr) with a procedure checked on synthetic light curves. The noise family follows Koen's (2006, MNRAS 365, 489) covariance model; each orbital model adds an LTTE term. A negative ΔBIC is not a detection. On 3,480 curves simulated from each star's own fitted noise model on its own cadence, the orbital family has the lower BIC in 72.4% of cases (95% interval over stars 68.8–75.9%), and, a post-hoc finding, more often for stars with fewer timing points. A calibrated per-star test. A parametric-bootstrap tail probability (40 null curves per star) rejects 4 of 87 synthetic noise-only stars at a nominal 2.4% threshold (95% interval 1–11%); at both thresholds used the point estimates are about twice nominal, significantly so (in a post-hoc test) only at the second. Against synthetic stars carrying each candidate's own fitted orbit, its power at that threshold is 32% or 94% under two assumptions about the noise under the orbit, both injecting the orbits fitted to the real curves; the second arm was added after the first had been seen. The catalogue. At that threshold 68 of 87 candidates, including all 25 of Hajdu et al.'s best-quality class (an agreement that is not independent evidence), have O−C curves that the fitted noise family does not describe. That rejects the noise family for those stars; it does not establish orbits. The candidates were chosen by eye from 27,480 O−C diagrams for LTTE-like shapes, with earlier-announced candidates added, so the measured false-positive rate is for the wrong population, and the noise family omits other structure such as Blazhko modulation. No candidate is confirmed and none is refuted. Note on versions. Version 2 supersedes version 1, which stays available. The analysis was redone from the OGLE photometry up, with new O−C and model code, and every result was recomputed. Withdrawn from version 1: its conclusion that the sign rule fires on roughly half of pure noise (72.4% here, against 52.4%); its statement that the pass fraction cannot be reconciled with the measured power (that rested on one power estimate from injections that did not cover the sample's amplitudes; the power here is 32% or 94% depending on the noise assumed under the orbit); its estimate that a noise population of the size searched contains stars as orbit-like as the median candidate in numbers of order tens; its claims that the method had never had a calibration, that Koen's procedure was never accompanied by a null distribution, and that the null was measured for the first time; its approximate bootstrap-correction experiment and conclusions; its accounts of its own earlier drafts and analysis history; and its statement that its allocation of draws was decided before any was looked at. Its description of Protassov et al. (2002) and its count of stars whose published period exceeds the baseline are corrected. Full list in the note's Note on versions. Files: the note (PDF) and the analysis bundle (OGLE photometry and catalogue files as used, with checksums and download script; O−C construction and its synthetic test; model code; campaign protocol and post-hoc log; all per-star outputs; summary, claim-verification and self-check scripts; README). Computations and drafting were assisted by an AI system (Claude).