A Brownian pulsar glitch model permits size–wait rank correlations near zero at finite drift with nonzero diffusion and narrow continuous size laws

A 2020 study states that a Brownian pulsar glitch model requires a size–next-wait Spearman correlation above 0.25. We show that this bound does not hold over the permitted continuous reset size distributions. We fix any finite nonnegative drift ratio and keep diffusion nonzero. Independent uniform reset laws give correlations that approach zero as their width decreases around an interior size. Larger resets have longer waits in stochastic order. Thus correlations are nonnegative, and their infimum over continuous size laws is zero. A Gaussian reset law centered at 0.5, with width parameter 0.05 and truncation to (0,1), gives correlation 0.1233927784 at drift ratio 1. A uniform law on [0.45,0.55] gives 0.0731524242. A separate grid method agrees within 1.9e-7 at 1024 intervals. We also form three hypothetical reset laws from 26 public Vela glitch sizes. At a fixed largest reset of 0.9 and drift ratio 0.05, the model correlations range from 0.2353 to 0.6599. These examples show dependence on the assumed size law. They do not fit Vela or identify its physical trigger. The result corrects the universal correlation claim. The package contains the proof, code, numeric source facts, provenance, results, figures, and offline reproduction instructions.

pulsar glitches · Brownian motion · first-passage time · Spearman correlation · reset distributions · Vela pulsar · model falsification · reproducible research