Recovering the Hellings-Downs Curve with a Finite Pulsar Array

This paper asks a single question: How well can the Hellings-Downs angular correlation be recovered with the pulsar counts and sky coverage of present and near-future arrays? Working from the published common-process amplitude of 2.4e-15 in characteristic strain at one cycle per year and the standard binary spectral index of thirteen thirds, the study computes the relevant quantities by the angular correlation between pulsar pairs averaged into angular bins, with pair-count noise scaling as the inverse square root of pairs per bin. The headline computed values are hd_at_90deg = -0.14486038541995894, pair_noise = 0.08408749651825217. These values are compared throughout with the published pulsar-timing values from the North American, European, Parkes and Chinese arrays. The calculation is fully reproducible from the deposited code, and every headline number appears in the accompanying results file. This study is simulated and computed from stated assumptions; it is not a measurement, and no new timing data are presented.