The unit of analysis in two claimed detections of open-cluster tidal-tail asymmetry

Two recent results are read as evidence that the tidal tails of nearby open clusters are asymmetrically populated, with more stars in the leading tail than in the trailing one. Kroupa et al. (2024) combine six teams' member catalogues for four clusters and report an 8.99σ falsification of leading–trailing symmetry. Jadhav et al. (2025) grade 122 published catalogues covering 58 clusters and report that among their higher-quality entries "the majority of catalogues (38:31) have more populated leading tails". This note re-examines both at the level of the statistic. It contains no new observation, no simulation and no astrophysical model; every number is recomputed from published tables. The 8.99σ is reproduced exactly (pooled n_l = 762, n_t = 449, n = 1211, ε = +0.2585). It is a single Bernoulli test over 1211 individual stars, and its authors state its precondition themselves: that the clusters are "unperturbed", so that one Bernoulli description covers them all. They also ask, in the same section, whether the membership methods could instead be producing the asymmetry. Both questions have an answer in their own collaboration's published numbers. Pflamm-Altenburg et al. (2023) — with Kroupa as an author — tabulate three of the same four clusters on compact-convergent-point tails covering a different radial window, and the two sets of ε disagree at χ² = 42.3 for 3 degrees of freedom, p = 3.4 × 10⁻⁹, with Praesepe changing sign (−0.078 against +0.266). The implied per-measurement scatter is τ ≈ 0.18, measured on the very clusters in dispute and requiring no external sample. Four qualifications belong with that figure, and the first is the most serious: two of the three CCP member lists are unpublished ("Jerabkova et al. in prep."), and they supply 77% of the χ². On the one published list alone τ = 0.129, which gives 4.0σ rather than 3.0σ. Kroupa et al. also exclude the CCP data deliberately and say why; any evidence that τ ≠ 0 is itself evidence against the Newtonian stochastic model, which predicts τ = 0 exactly; and the 0.18 is measured across a longer lever arm in tail length than separates their six catalogues, so it bounds the relevant scatter rather than measuring it. The argument below is that the quoted confidence is unsupportable, not that the data are unremarkable. Carrying that scatter, the four clusters give ε = +0.293 ± 0.096, or 3.0σ — with a defensible range of about 2.3–4.0σ across the estimators and provenances examined in §2.4 — and — this is the part that matters, and that an earlier draft of this note missed — the per-cluster figures deflate too, because they are computed against the same τ = 0 null: COIN-Gaia13's 8.39σ becomes 2.6–3.4σ across the same range. The distinction must be kept sharp: this is the right correction for the claim actually made, that a universal law produces the asymmetry, and the wrong one for the narrower claim that a particular cluster's tails are lopsided, which stands untouched. The 38:31 was never significant as published — a binomial test gives p = 0.47, and its authors claim no significance for it. It is also a catalogue-multiplicity effect. Those non-bronze entries cover 40 distinct clusters, and the Hyades alone is counted seven times. Collapsed to one value per cluster the population tally becomes consistent with 50:50 under all six collapse rules tried, with a mean consistent with zero throughout and a Wilcoxon p = 0.85. It disappears rather than reversing. Their companion span tally does survive the same treatment in direction if not in significance — 43:28 on the deposited table, one-sided p = 0.048, falling to 23:17 and 0.63σ per cluster without changing sign — and is the one published number here that is not disposed of.