{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6AVT6CASBK5S545S6SUXBK76K7","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":"7ed8a919fb3afe4de3396a7ee87b10733113147d11b78406cd6a260654a58aa7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-23T13:35:06Z","title_canon_sha256":"2874a274c7b8d4d5725af022759d6dbf741b1482624d071a190a34b841d059b7"},"schema_version":"1.0","source":{"id":"1501.05798","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05798","created_at":"2026-05-18T01:23:58Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05798v2","created_at":"2026-05-18T01:23:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05798","created_at":"2026-05-18T01:23:58Z"},{"alias_kind":"pith_short_12","alias_value":"6AVT6CASBK5S","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6AVT6CASBK5S545S","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6AVT6CAS","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:ba9f9ee48c633a9e24b173f96cee6fdfec03af4319f76daba5a8925b6ca9edb1","target":"graph","created_at":"2026-05-18T01:23:58Z","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"},"paper":{"abstract_excerpt":"Emergence of new diseases and elimination of existing diseases is a key public health issue. In mathematical models of epidemics, such phenomena involve the process of infections and recoveries passing through a critical threshold where the basic reproductive ratio is 1.\n  In this paper, we study near-critical behaviour in the context of a susceptible-infective-recovered (SIR) epidemic on a random (multi)graph on $n$ vertices with a given degree sequence. We concentrate on the regime just above the threshold for the emergence of a large epidemic, where the basic reproductive ratio is $1 + \\ome","authors_text":"Malwina Luczak, Peter Windridge, Svante Janson, Thomas House","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-23T13:35:06Z","title":"Near-critical SIR epidemic on a random graph with given degrees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05798","kind":"arxiv","version":2},"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":"sha256:250bc699731dd7c1c2a57ea975877aacd7e1b149f5ea3b6fafb804fefaf62b26","target":"record","created_at":"2026-05-18T01:23:58Z","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":"7ed8a919fb3afe4de3396a7ee87b10733113147d11b78406cd6a260654a58aa7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-23T13:35:06Z","title_canon_sha256":"2874a274c7b8d4d5725af022759d6dbf741b1482624d071a190a34b841d059b7"},"schema_version":"1.0","source":{"id":"1501.05798","kind":"arxiv","version":2}},"canonical_sha256":"f02b3f08120abb2ef3b2f4a970abfe57f02c7c699f512a4ed44bac01580e883f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f02b3f08120abb2ef3b2f4a970abfe57f02c7c699f512a4ed44bac01580e883f","first_computed_at":"2026-05-18T01:23:58.659456Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:58.659456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q8jS6hTdj5gjuyA53PatMg9bAdRfdKAY+0ujv+3faM2IGaj1PJ1MuFAOBR03rXh98ZxtHpn/+b8luozSkMU6AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:58.660161Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.05798","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:250bc699731dd7c1c2a57ea975877aacd7e1b149f5ea3b6fafb804fefaf62b26","sha256:ba9f9ee48c633a9e24b173f96cee6fdfec03af4319f76daba5a8925b6ca9edb1"],"state_sha256":"193cb0d3ac06cd50d155c78829c8ecc4657d89226d1d62ee111a5629f366f0b7"}