How many black holes does a given primordial spectrum produce?

For a curvature spectrum $P_{\zeta}(k)$ peaked at $k_p$, compute the mass fraction $\beta(M)$ collapsing into PBHs at horizon entry, including the profile-dependent collapse threshold $\delta_c$ (about 0.4 to 0.67), critical-collapse scaling M = K (delta - delta_c)^0.36 $M_H$ with M_H the horizon mass, the nonlinear relation between $\zeta$ and the density contrast, and non-Gaussian tails (including exponential tails from stochastic inflation). An answer is $\beta(M)$ with theoretical uncertainty below a factor of 10 for a benchmark spectrum, agreed between independent methods (peak theory, threshold statistics, numerical relativity).

A benchmark comparison in which peak-theory, threshold-statistics and numerical-relativity calculations of $\beta(M)$ for the same spectrum agree within a factor of 10.