Identifiability limits in rare network count processes: a simulation laboratory with empirical probes in crime, seismology and neural spike trains

<p>Rare network count data — panels with 90–99% zeros across nodes and time — are common in criminology, seismology and neuroscience, where a fitted Poisson, negative-binomial or zero-inflated model is often read as evidence about mechanism. Using a simulation laboratory of ten stress-test data-generating processes and semi-synthetic probes in UK Police, USGS and Allen Neuropixels data, this work shows that model fingerprints, dispersion, residual autocorrelation and intervention estimates can instead reflect sparsity, the observation operator and effect design. Identifiability is layered: a stable fingerprint is not a mechanism.</p>