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 identified from the light-travel-time effect in observed-minus-calculated (O−C) pulsation timing. The same stars undergo stochastic period fluctuation, which produces O−C excursions of comparable amplitude and timescale. Koen (2006, MNRAS 365, 489) gave the covariance framework for that noise and proposed choosing between models by information criterion. This note measures what such a comparison establishes, using the 87 candidates of Hajdu et al. (2021, ApJ 915, 50) and O−C curves rebuilt from public OGLE photometry (doi:10.5281/zenodo.22748783). A negative ΔBIC is not a detection. Across 8,700 noise-only curves simulated on the real cadences — a flat 100 per star — the orbital family is favoured on 52.4% of curves containing no orbit (95% CI over stars 46.9–57.9%). Against injected orbits the same rule fires on 79.2%, so the sign carries weak information (likelihood ratio ≈ 1.5, Fisher p = 0.019), but a rule with a false-positive rate near one half cannot select a candidate list. The per-star bootstrap behaves, and cannot be certified at this scale. On 90 synthetic noise-only stars the tail probabilities are close to uniform (mean 0.472 where 0.512 is correct, KS p = 0.22 against the discrete null they actually have); a nominal 5% threshold fires on 8.9%. The known repair for a plug-in bootstrap (Protassov et al. 2002), implemented in approximate form, changes nothing that separates the two arms on 90 stars. The catalogue is neither supported nor undermined. Hajdu et al. report no significance test — no information criterion, no false-alarm rate, no p-value — so this supplies a calibration the method has never had rather than correcting one. At a threshold whose measured false-positive rate is 6.7%, 58 of 87 candidates pass. That count is not a detection count and the number of false positives within it is not estimated anywhere: the candidates were screened by eye out of 27,480 O−C diagrams, so the measured rate is for the wrong population; and the pass fraction cannot be reconciled with the measured power of 20.8%, itself measured over an amplitude band covering only the lower two-thirds of the sample. No candidate is confirmed and none is refuted. Note on an earlier version of this analysis. A previous draft reported badly non-uniform bootstrap p-values, “anti-conservative by a factor of three”, and built a section of argument on it. That was an artefact of synthetic stars sharing random-number streams across resumed invocations in the validation harness. All three simulation campaigns were re-run from empty checkpoints under per-star seeding, and the claim is withdrawn. §5 of the note records the episode, because a simulation-based calibration is only as trustworthy as its simulation and nothing in the original output looked anomalous. The deposit contains the model family and comparison code, all three simulation campaigns with their unedited logs, per-star results for all 87 candidates under two scorings, and a script that checks every quantitative claim in the note against the deposited files. Limitations are stated in the note's §7 and in the deposit README.