Spurious level repulsion in geophysical random-matrix analysis: declustering, seasonal gating, and the Wishart null

A short methodological note. The consecutive spacing ratio ⟨r⟩ is increasingly used to claim Wigner–Dyson (GOE) level repulsion in geophysical and climate data, but ⟨r⟩ is two-ended and several mundane data structures mimic GOE without any repulsion. We document three with controlled demonstrations. (1) Minimum-separation declustering injects an artificial hard core and drives pure random points to GOE-like ⟨r⟩. (2) Seasonal gating of event times produces a permutation-invariant GOE-like ⟨r⟩: for 41 major sudden stratospheric warmings the naive interval ⟨r⟩ = 0.48 is a seasonal artifact, while the correct de-seasonalized per-winter count is mildly under-dispersed (variance/mean = 0.67, 95% CI excluding unity) — a weak refractory clock, not level repulsion. (3) The eigenvalue spacing of a sample correlation matrix is GOE for independent data by random-matrix universality, so GOE spacing in a climate correlation matrix is the finite-sampling null; the physical signal resides in the eigenvalue density relative to Marchenko–Pastur. The correct controls are raw ⟨r⟩ with the coefficient of variation, the permutation (shuffle) test, de-seasonalization, and the density test. Code (self-contained; SSW dates embedded, all else synthetic) and the paper are included.