{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:AUSFMSRBNS2L6QBYH3PZCAWGWQ","short_pith_number":"pith:AUSFMSRB","canonical_record":{"source":{"id":"2001.06469","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2020-01-17T18:43:11Z","cross_cats_sorted":["gr-qc","hep-th"],"title_canon_sha256":"44e248c5607c99c80e46c5fd6f96b4720b202ef5e1fe40f22d5eae2013079a39","abstract_canon_sha256":"1d236354802d64b821b5867109d2eb3367018d1b4cfc9dd2a1e55331f4cb478e"},"schema_version":"1.0"},"canonical_sha256":"0524564a216cb4bf40383edf9102c6b41292c07f7c9b416c92ecc68eaa1d2aba","source":{"kind":"arxiv","id":"2001.06469","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2001.06469","created_at":"2026-07-05T03:26:12Z"},{"alias_kind":"arxiv_version","alias_value":"2001.06469v1","created_at":"2026-07-05T03:26:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.06469","created_at":"2026-07-05T03:26:12Z"},{"alias_kind":"pith_short_12","alias_value":"AUSFMSRBNS2L","created_at":"2026-07-05T03:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"AUSFMSRBNS2L6QBY","created_at":"2026-07-05T03:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"AUSFMSRB","created_at":"2026-07-05T03:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:AUSFMSRBNS2L6QBYH3PZCAWGWQ","target":"record","payload":{"canonical_record":{"source":{"id":"2001.06469","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2020-01-17T18:43:11Z","cross_cats_sorted":["gr-qc","hep-th"],"title_canon_sha256":"44e248c5607c99c80e46c5fd6f96b4720b202ef5e1fe40f22d5eae2013079a39","abstract_canon_sha256":"1d236354802d64b821b5867109d2eb3367018d1b4cfc9dd2a1e55331f4cb478e"},"schema_version":"1.0"},"canonical_sha256":"0524564a216cb4bf40383edf9102c6b41292c07f7c9b416c92ecc68eaa1d2aba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:26:12.403648Z","signature_b64":"iDGrjcZIAc1w4+zzVihrySyhUR1etN0VobDSWGZ4d4Y0LhsAQPis67HT3XaQoRIPILecaIFcR3pN3PgZsZfHBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0524564a216cb4bf40383edf9102c6b41292c07f7c9b416c92ecc68eaa1d2aba","last_reissued_at":"2026-07-05T03:26:12.403154Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:26:12.403154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2001.06469","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:26:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qje0Cd3XIfomcPIZVA58n09zoOZifpMZFn/NIYZzT56H8eVH3Di7D4YdJxNa3mA3id8Lm8yAWQut4l0vaNmqBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:28:38.268231Z"},"content_sha256":"7293ab174b40f83f15a233ee455b5dec8be65618aedcfb8af171babf019926d8","schema_version":"1.0","event_id":"sha256:7293ab174b40f83f15a233ee455b5dec8be65618aedcfb8af171babf019926d8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:AUSFMSRBNS2L6QBYH3PZCAWGWQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Application of peaks theory to the abundance of primordial black holes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-th"],"primary_cat":"astro-ph.CO","authors_text":"Marcello Musso, Sam Young","submitted_at":"2020-01-17T18:43:11Z","abstract_excerpt":"We consider the application of peaks theory to the calculation of the number density of peaks relevant for primordial black hole (PBH) formation. For PBHs, the final mass is related to the amplitude and scale of the perturbation from which it forms, where the scale is defined as the scale at which the compaction function peaks. We therefore extend peaks theory to calculate not only the abundance of peaks of a given amplitude, but peaks of a given amplitude and scale. A simple fitting formula is given in the high-peak limit relevant for PBH formation. We also adapt the calculation to use a Gaus"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.06469","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2001.06469/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:26:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VK1KHSvaZ6dYjqAidyv6PP2gT7pW9psAnOKbJnAvJ3SYZMy027+HtpmddCQm3Kw+wtdu7iXizFQKIQ1MPgKwDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:28:38.268755Z"},"content_sha256":"3de85cc73195e9cf9c0b13f0886eca986f3fbe6be4cfc99c315efb8db462eadd","schema_version":"1.0","event_id":"sha256:3de85cc73195e9cf9c0b13f0886eca986f3fbe6be4cfc99c315efb8db462eadd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AUSFMSRBNS2L6QBYH3PZCAWGWQ/bundle.json","state_url":"https://pith.science/pith/AUSFMSRBNS2L6QBYH3PZCAWGWQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AUSFMSRBNS2L6QBYH3PZCAWGWQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-03T16:28:38Z","links":{"resolver":"https://pith.science/pith/AUSFMSRBNS2L6QBYH3PZCAWGWQ","bundle":"https://pith.science/pith/AUSFMSRBNS2L6QBYH3PZCAWGWQ/bundle.json","state":"https://pith.science/pith/AUSFMSRBNS2L6QBYH3PZCAWGWQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AUSFMSRBNS2L6QBYH3PZCAWGWQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:AUSFMSRBNS2L6QBYH3PZCAWGWQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1d236354802d64b821b5867109d2eb3367018d1b4cfc9dd2a1e55331f4cb478e","cross_cats_sorted":["gr-qc","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2020-01-17T18:43:11Z","title_canon_sha256":"44e248c5607c99c80e46c5fd6f96b4720b202ef5e1fe40f22d5eae2013079a39"},"schema_version":"1.0","source":{"id":"2001.06469","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2001.06469","created_at":"2026-07-05T03:26:12Z"},{"alias_kind":"arxiv_version","alias_value":"2001.06469v1","created_at":"2026-07-05T03:26:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.06469","created_at":"2026-07-05T03:26:12Z"},{"alias_kind":"pith_short_12","alias_value":"AUSFMSRBNS2L","created_at":"2026-07-05T03:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"AUSFMSRBNS2L6QBY","created_at":"2026-07-05T03:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"AUSFMSRB","created_at":"2026-07-05T03:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:3de85cc73195e9cf9c0b13f0886eca986f3fbe6be4cfc99c315efb8db462eadd","target":"graph","created_at":"2026-07-05T03:26:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2001.06469/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the application of peaks theory to the calculation of the number density of peaks relevant for primordial black hole (PBH) formation. For PBHs, the final mass is related to the amplitude and scale of the perturbation from which it forms, where the scale is defined as the scale at which the compaction function peaks. We therefore extend peaks theory to calculate not only the abundance of peaks of a given amplitude, but peaks of a given amplitude and scale. A simple fitting formula is given in the high-peak limit relevant for PBH formation. We also adapt the calculation to use a Gaus","authors_text":"Marcello Musso, Sam Young","cross_cats":["gr-qc","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2020-01-17T18:43:11Z","title":"Application of peaks theory to the abundance of primordial black holes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.06469","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7293ab174b40f83f15a233ee455b5dec8be65618aedcfb8af171babf019926d8","target":"record","created_at":"2026-07-05T03:26:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1d236354802d64b821b5867109d2eb3367018d1b4cfc9dd2a1e55331f4cb478e","cross_cats_sorted":["gr-qc","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2020-01-17T18:43:11Z","title_canon_sha256":"44e248c5607c99c80e46c5fd6f96b4720b202ef5e1fe40f22d5eae2013079a39"},"schema_version":"1.0","source":{"id":"2001.06469","kind":"arxiv","version":1}},"canonical_sha256":"0524564a216cb4bf40383edf9102c6b41292c07f7c9b416c92ecc68eaa1d2aba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0524564a216cb4bf40383edf9102c6b41292c07f7c9b416c92ecc68eaa1d2aba","first_computed_at":"2026-07-05T03:26:12.403154Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:26:12.403154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iDGrjcZIAc1w4+zzVihrySyhUR1etN0VobDSWGZ4d4Y0LhsAQPis67HT3XaQoRIPILecaIFcR3pN3PgZsZfHBg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:26:12.403648Z","signed_message":"canonical_sha256_bytes"},"source_id":"2001.06469","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7293ab174b40f83f15a233ee455b5dec8be65618aedcfb8af171babf019926d8","sha256:3de85cc73195e9cf9c0b13f0886eca986f3fbe6be4cfc99c315efb8db462eadd"],"state_sha256":"ef59f9dc3ae623654ccb6bd2a43290e188a2a10bef92694ae34326d35f645d48"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WqO0fC/YxaDgs0zW4ye5jm2c12ut9eN70W+lRWjkaY9wy+44gX5Ij86KZE00GREN+eqLap2EDpfz+UBwNOW1CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T16:28:38.272365Z","bundle_sha256":"8afe093b459a564b77e2b22bf49d6b45ff63c38f8b5675e314442eadbf34e575"}}