Higher-order statistics could fingerprint the black hole binary hum

Pulsar Timing Arrays detect a hum of gravitational waves likely produced by millions of inspiraling supermassive black hole binaries, but standard analyses extract only the spectral shape. By introducing a physically motivated lower redshift cutoff tied to single-source detectability, higher-order statistical moments — previously plagued by divergences — become tractable. These moments turn out to depend on the binary mass function only through a single chirp-mass average, and the variance-to-mean ratio isolates that average independently of the total merger rate. A consistency relation between kurtosis and squared skewness also offers a direct test of whether binaries truly dominate the background.