How the Optimal-Statistic Signal-to-Noise Scales with Pulsars, Span and Cadence

This paper asks a single question: How fast does detection significance grow when an array adds pulsars, extends its span, or observes more often? 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 cross-correlation signal-to-noise integral for the optimal statistic under weak-signal conditions. The headline computed values are snr_largest_array = 546.3515351859095, snr_reference_array = 28.317838900594094, gain_factor = 19.29354627320969. 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.