Rare Common-Shock Detection from Binary Snapshots: Minimum Cover Order and Optimal Inspection

This preprint studies when to inspect a system to distinguish two specified global shock rates. Each independently restarted replicate gives one complete binary snapshot. The candidate models have the same one-dimensional margins and share the known background shocks. In fixed dimension, when the minimum nonglobal cover has order at least three and its leading coefficient is bounded away from zero, we give a uniform limiting Hellinger profile, its maximum in closed form and all first-order optimal inspection times. At cover order two, the leading coefficient is determined by a baseline Fisher information curve. For two overlapping backgrounds in growing dimension, reallocating blocks among the regions can change the separation exponent at matched rates and margins. The deposit includes the preprint and a reproducibility archive containing the LaTeX source, vector figures, Python code and build instructions.