How many black holes does a given primordial spectrum produce?
In plain words
The number of primordial black holes depends on the rarest, most extreme ripples, so small changes in the assumed statistics change the prediction by huge factors. A reliable calculation is still missing.
Precise statement
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).
What would settle it
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.