{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:EONMQ36XKHXVWPFOI5S3VFSMM2","short_pith_number":"pith:EONMQ36X","schema_version":"1.0","canonical_sha256":"239ac86fd751ef5b3cae4765ba964c669f98e81871f7f54ab3db44bdeb168980","source":{"kind":"arxiv","id":"1308.5493","version":3},"attestation_state":"computed","paper":{"title":"Law of large numbers for the SIR epidemic on a random graph with given degrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Malwina Luczak, Peter Windridge, Svante Janson","submitted_at":"2013-08-26T06:20:13Z","abstract_excerpt":"We study the susceptible-infective-recovered (SIR) epidemic on a random graph chosen uniformly subject to having given vertex degrees. In this model infective vertices infect each of their susceptible neighbours, and recover, at a constant rate.\n  Suppose that initially there are only a few infective vertices. We prove there is a threshold for a parameter involving the rates and vertex degrees below which only a small number of infections occur. Above the threshold a large outbreak occurs with probability bounded away from zero. Our main result is that, conditional on a large outbreak, the evo"},"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":"1308.5493","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-26T06:20:13Z","cross_cats_sorted":[],"title_canon_sha256":"c38554f6f27cf7aa869734165d6b494ffdd85c3472959f1797a4ab1848d419f8","abstract_canon_sha256":"b4ee3ea540343bbf19fc5198abe7603f88c1ad8655c37886a4b7cfbaacd5a8de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:13.135932Z","signature_b64":"b+8DH0ChQtmJtyDRg94E4gA8qSrqP20uNquEK+8GWZNJDWjzpEfbf5+Rtkzd28fYPo6Ax0tnjhKQSkCL9H6JCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"239ac86fd751ef5b3cae4765ba964c669f98e81871f7f54ab3db44bdeb168980","last_reissued_at":"2026-05-18T02:42:13.135478Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:13.135478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Law of large numbers for the SIR epidemic on a random graph with given degrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Malwina Luczak, Peter Windridge, Svante Janson","submitted_at":"2013-08-26T06:20:13Z","abstract_excerpt":"We study the susceptible-infective-recovered (SIR) epidemic on a random graph chosen uniformly subject to having given vertex degrees. In this model infective vertices infect each of their susceptible neighbours, and recover, at a constant rate.\n  Suppose that initially there are only a few infective vertices. We prove there is a threshold for a parameter involving the rates and vertex degrees below which only a small number of infections occur. Above the threshold a large outbreak occurs with probability bounded away from zero. Our main result is that, conditional on a large outbreak, the evo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5493","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":""},"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":"1308.5493","created_at":"2026-05-18T02:42:13.135552+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.5493v3","created_at":"2026-05-18T02:42:13.135552+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5493","created_at":"2026-05-18T02:42:13.135552+00:00"},{"alias_kind":"pith_short_12","alias_value":"EONMQ36XKHXV","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"EONMQ36XKHXVWPFO","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"EONMQ36X","created_at":"2026-05-18T12:27:43.054852+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EONMQ36XKHXVWPFOI5S3VFSMM2","json":"https://pith.science/pith/EONMQ36XKHXVWPFOI5S3VFSMM2.json","graph_json":"https://pith.science/api/pith-number/EONMQ36XKHXVWPFOI5S3VFSMM2/graph.json","events_json":"https://pith.science/api/pith-number/EONMQ36XKHXVWPFOI5S3VFSMM2/events.json","paper":"https://pith.science/paper/EONMQ36X"},"agent_actions":{"view_html":"https://pith.science/pith/EONMQ36XKHXVWPFOI5S3VFSMM2","download_json":"https://pith.science/pith/EONMQ36XKHXVWPFOI5S3VFSMM2.json","view_paper":"https://pith.science/paper/EONMQ36X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.5493&json=true","fetch_graph":"https://pith.science/api/pith-number/EONMQ36XKHXVWPFOI5S3VFSMM2/graph.json","fetch_events":"https://pith.science/api/pith-number/EONMQ36XKHXVWPFOI5S3VFSMM2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EONMQ36XKHXVWPFOI5S3VFSMM2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EONMQ36XKHXVWPFOI5S3VFSMM2/action/storage_attestation","attest_author":"https://pith.science/pith/EONMQ36XKHXVWPFOI5S3VFSMM2/action/author_attestation","sign_citation":"https://pith.science/pith/EONMQ36XKHXVWPFOI5S3VFSMM2/action/citation_signature","submit_replication":"https://pith.science/pith/EONMQ36XKHXVWPFOI5S3VFSMM2/action/replication_record"}},"created_at":"2026-05-18T02:42:13.135552+00:00","updated_at":"2026-05-18T02:42:13.135552+00:00"}