Gravitational-Wave Merger Rates as a Bound on the Primordial Black Hole Fraction

If primordial black holes populate the tens-of-solar-masses range, some of them must be merging today, and the gravitational-wave observatories measure the merger rate of black holes in exactly that range. The comparison is powerful because it is a counting argument in both directions: too high a primordial fraction overproduces mergers relative to the observed rate, while a fraction tuned to match the observed rate makes definite predictions about masses, spins, and redshift evolution that distinguish primordial binaries from astrophysical ones. The headline computed values are: f max 30Msun = 0.300; R at f1 30 = 500.0. The work is computational throughout: assumptions are stated, the arithmetic is deposited, and no result is presented as a measurement.