The Timing-Residual Budget Implied by the Nanohertz Common Process

This paper asks a single question: What root-mean-square timing residual does the published background amplitude imply over a fifteen-year baseline, and how does that budget divide among frequency bins? 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 residual power spectrum obtained by integrating the strain spectrum through the timing response over the observing span. The headline computed values are rms_ns_15yr = 654.4911671445291, rms_ns_25yr = 1533.3867486698969. 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.