Anisotropy Limits for a Nanohertz Background with a Bounce Contribution

This paper asks a single question: How anisotropic may a nanohertz background be before it conflicts with isotropy limits, and what dipole would a bounce contribution add? 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 spherical-harmonic decomposition of background intensity with a dipole term set by a fractional density contrast. The headline computed values are dipole_reference = 0.1, C1_C0_at_ref = 0.003333333333333334. 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.