The Energy-Density Budget of the Nanohertz Background

This paper asks a single question: What fraction of the critical density does the measured nanohertz background carry, and what room remains for an additional bounce-frame component? 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 conversion from characteristic strain to fractional energy density per logarithmic frequency interval. 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.