One Over Mass, Checked Eight Times: The Frequency-Mass Scaling of Fundamental Modes Across the Published Remnants

In a scale-free theory the product of ringdown frequency and remnant mass, at fixed spin, is a constant. Spins are not fixed across the catalogue, but they occupy a narrow range, so the product should cluster tightly with a scatter explained by the spin distribution alone. The eight fundamental frequencies run from 68.0 Hz for the heaviest remnant to 890.4 Hz for the lightest, a span set almost entirely by the inverse-mass scaling. The detector-frame mass-frequency products cluster around a mean of 16443 Hz solar masses with a standard deviation of 1600, a coefficient of variation of 9.7 per cent. The published spin range alone predicts a half-spread of about 17.2 per cent in the product, so the realised scatter is of the size the spin distribution requires and leaves no room for a large mass-dependent drift. Across eight remnants the mass-frequency product has a coefficient of variation of 9.7 per cent, consistent with the 17.2 per cent half-spread the published spin range predicts, so the catalogue passes the scaling audit with no mass-dependent drift required. This study is computed from stated assumptions and published catalogue values; it is simulated, not measured.