{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"06bb31aca38dddbdf80659a2d7b0311ef7556017ba91cc6115c50e98558d9d80","created":"2026-10-03T07:18:02Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"90bdda13effc263cd950faa5c10358bfb889aba55c4efd24923304d2eb7d857f","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"cosmo.primordial-black-holes.abundance-from-spectrum","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"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.","posed_since":"","precise":"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).","problem_ref":null,"references":"","settled_by":"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.","status_note":"","title":"How many black holes does a given primordial spectrum produce?","topic_ref":"9ab792b7e278762046677161a5c3d97a4c12042fe341bebc00b0f937c2c50d7a"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"dce530dc3e4d40f2169c17f87243c5588ca09f9d5860c18c8f6abf50881375fd","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"1bc692e6c2d95d4ed9fcab5ea20c6251d00a83f87014adf9f7f725190d36af6b","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"-3EPBnD4Re6j3y6gm4C2-meBtNSdYhH0tI6Wjp4z16HEC2ltqYt5KPkcK1Ml8qVHYgahnHhP0qm9TZfM8c7DAg"},"schema":"pubphys.envelope/1"},"record_hash":"dce530dc3e4d40f2169c17f87243c5588ca09f9d5860c18c8f6abf50881375fd","leaf_index":1269}