Testing the Nanohertz Spectral Index Against the Binary Prediction

This paper asks a single question: Is the measured spectral slope of the common process consistent with the minus thirteen thirds law expected for circular binaries evolving by gravitational radiation alone? 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 a power-law fit in log strain against log frequency, compared bin by bin with the reference slope. The headline computed values are A_ref = 2.4e-15, h_c_at_10nHz = 5.177760169452975e-15, omega_at_10nHz = 3.4232658889151874e-09, ratio_bounce_to_ref = 1.1. 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.