{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AKDL2WIMERMAH2Z34Z22QRVVGF","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":"e7bd6029b40fb337ff60227636b93f0c53bfb04df685f0d3f0ca085d85ed20ce","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2013-05-22T14:42:12Z","title_canon_sha256":"f9b8d550746f1fa4a7820cf0f1f75258be34331c70501cd984e84d27dec120a4"},"schema_version":"1.0","source":{"id":"1305.5153","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.5153","created_at":"2026-05-18T03:13:45Z"},{"alias_kind":"arxiv_version","alias_value":"1305.5153v2","created_at":"2026-05-18T03:13:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5153","created_at":"2026-05-18T03:13:45Z"},{"alias_kind":"pith_short_12","alias_value":"AKDL2WIMERMA","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AKDL2WIMERMAH2Z3","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AKDL2WIM","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:9484d753ed6460e2bc9c7abd334208afb7a5f60c541c7aa53921582c1ee0d348","target":"graph","created_at":"2026-05-18T03:13:45Z","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":"We present a quenched mean-field (QMF) theory for the dynamics of the susceptible-infected-susceptible (SIS) epidemic model on complex networks where dynamical correlations between connected vertices are taken into account by means of a pair approximation. We present analytical expressions of the epidemic thresholds in the star and wheel graphs and in random regular networks. For random networks with a power law degree distribution, the thresholds are numerically determined via an eigenvalue problem. The pair and one-vertex QMF theories yield the same scaling for the thresholds as functions of","authors_text":"Ang\\'elica S. Mata, Silvio C. Ferreira","cross_cats":["cond-mat.stat-mech","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2013-05-22T14:42:12Z","title":"Pair quenched mean-field theory for the susceptible-infected-susceptible model on complex networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5153","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":"sha256:14fb144ee8a45d7d5009ab640acb5a80e41d47bf6cddec54c586ab766d2278ca","target":"record","created_at":"2026-05-18T03:13:45Z","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":"e7bd6029b40fb337ff60227636b93f0c53bfb04df685f0d3f0ca085d85ed20ce","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2013-05-22T14:42:12Z","title_canon_sha256":"f9b8d550746f1fa4a7820cf0f1f75258be34331c70501cd984e84d27dec120a4"},"schema_version":"1.0","source":{"id":"1305.5153","kind":"arxiv","version":2}},"canonical_sha256":"0286bd590c245803eb3be675a846b531709ab2636cae927a135206e1eba41986","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0286bd590c245803eb3be675a846b531709ab2636cae927a135206e1eba41986","first_computed_at":"2026-05-18T03:13:45.707566Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:45.707566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sncpWA6eINt3YToItbRSNmBAwcUCZw2j48AqwfAf2HCbXaqm/05s63n7u5G1zjapoS+eNU8p8VQE0zFxwp7hAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:45.708251Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.5153","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14fb144ee8a45d7d5009ab640acb5a80e41d47bf6cddec54c586ab766d2278ca","sha256:9484d753ed6460e2bc9c7abd334208afb7a5f60c541c7aa53921582c1ee0d348"],"state_sha256":"1004981d70e0b6919ce1cf24b82a8af53b68a4a9cfb6f7d9a81cf5312ff8eb1f"}