{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:J5JOZHSHW5JRUVP3EKNE2ORS4K","short_pith_number":"pith:J5JOZHSH","schema_version":"1.0","canonical_sha256":"4f52ec9e47b7531a55fb229a4d3a32e2a1bdd60802a56b43b1b655bc9b82a1a9","source":{"kind":"arxiv","id":"2112.15059","version":3},"attestation_state":"computed","paper":{"title":"Scalar induced gravitational waves from primordial black hole Poisson fluctuations in $f(R)$ gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-th"],"primary_cat":"astro-ph.CO","authors_text":"Charalampos Tzerefos, Emmanuel N. Saridakis, Spyros Basilakos, Theodoros Papanikolaou","submitted_at":"2021-12-30T13:46:34Z","abstract_excerpt":"The gravitational potential of a gas of initially randomly distributed primordial black holes (PBH) can induce a stochastic gravitational-wave (GW) background through second-order gravitational effects. This GW background can be abundantly generated in a cosmic era dominated by ultralight primordial black holes, with masses $m_\\mathrm{PBH}<10^{9}\\mathrm{g}$. In this work, we consider $f(R)$ gravity as the underlying gravitational theory and we study its effect at the level of the gravitational potential of Poisson distributed primordial black holes. After a general analysis, we focus on the $R"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2112.15059","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2021-12-30T13:46:34Z","cross_cats_sorted":["gr-qc","hep-th"],"title_canon_sha256":"196597c46e372d7df08639b5e7258f5ac5e8631d6830576b95863619302d71cd","abstract_canon_sha256":"feb659025b57b387bab7b1cb91c94e97688db1872190690f45e8752cab464310"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:05:29.901144Z","signature_b64":"Nzv58jBIE36IBGSS3vrQHaLbqHCbaZ62SPuosKcfAxyrMDmUKn2hrlQqyjrmbN0ud1uoC/pp2mNmTJPyxYLqAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f52ec9e47b7531a55fb229a4d3a32e2a1bdd60802a56b43b1b655bc9b82a1a9","last_reissued_at":"2026-07-05T05:05:29.900692Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:05:29.900692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scalar induced gravitational waves from primordial black hole Poisson fluctuations in $f(R)$ gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-th"],"primary_cat":"astro-ph.CO","authors_text":"Charalampos Tzerefos, Emmanuel N. Saridakis, Spyros Basilakos, Theodoros Papanikolaou","submitted_at":"2021-12-30T13:46:34Z","abstract_excerpt":"The gravitational potential of a gas of initially randomly distributed primordial black holes (PBH) can induce a stochastic gravitational-wave (GW) background through second-order gravitational effects. This GW background can be abundantly generated in a cosmic era dominated by ultralight primordial black holes, with masses $m_\\mathrm{PBH}<10^{9}\\mathrm{g}$. In this work, we consider $f(R)$ gravity as the underlying gravitational theory and we study its effect at the level of the gravitational potential of Poisson distributed primordial black holes. After a general analysis, we focus on the $R"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.15059","kind":"arxiv","version":3},"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/2112.15059/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2112.15059","created_at":"2026-07-05T05:05:29.900749+00:00"},{"alias_kind":"arxiv_version","alias_value":"2112.15059v3","created_at":"2026-07-05T05:05:29.900749+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.15059","created_at":"2026-07-05T05:05:29.900749+00:00"},{"alias_kind":"pith_short_12","alias_value":"J5JOZHSHW5JR","created_at":"2026-07-05T05:05:29.900749+00:00"},{"alias_kind":"pith_short_16","alias_value":"J5JOZHSHW5JRUVP3","created_at":"2026-07-05T05:05:29.900749+00:00"},{"alias_kind":"pith_short_8","alias_value":"J5JOZHSH","created_at":"2026-07-05T05:05:29.900749+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.11320","citing_title":"Reconstructing Primordial Curvature Perturbations via Scalar-Induced Gravitational Waves with LISA","ref_index":249,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/J5JOZHSHW5JRUVP3EKNE2ORS4K","json":"https://pith.science/pith/J5JOZHSHW5JRUVP3EKNE2ORS4K.json","graph_json":"https://pith.science/api/pith-number/J5JOZHSHW5JRUVP3EKNE2ORS4K/graph.json","events_json":"https://pith.science/api/pith-number/J5JOZHSHW5JRUVP3EKNE2ORS4K/events.json","paper":"https://pith.science/paper/J5JOZHSH"},"agent_actions":{"view_html":"https://pith.science/pith/J5JOZHSHW5JRUVP3EKNE2ORS4K","download_json":"https://pith.science/pith/J5JOZHSHW5JRUVP3EKNE2ORS4K.json","view_paper":"https://pith.science/paper/J5JOZHSH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2112.15059&json=true","fetch_graph":"https://pith.science/api/pith-number/J5JOZHSHW5JRUVP3EKNE2ORS4K/graph.json","fetch_events":"https://pith.science/api/pith-number/J5JOZHSHW5JRUVP3EKNE2ORS4K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J5JOZHSHW5JRUVP3EKNE2ORS4K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J5JOZHSHW5JRUVP3EKNE2ORS4K/action/storage_attestation","attest_author":"https://pith.science/pith/J5JOZHSHW5JRUVP3EKNE2ORS4K/action/author_attestation","sign_citation":"https://pith.science/pith/J5JOZHSHW5JRUVP3EKNE2ORS4K/action/citation_signature","submit_replication":"https://pith.science/pith/J5JOZHSHW5JRUVP3EKNE2ORS4K/action/replication_record"}},"created_at":"2026-07-05T05:05:29.900749+00:00","updated_at":"2026-07-05T05:05:29.900749+00:00"}