{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4FPQ63XYAF57QKYSBOIR7LZOBS","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":"4e880b477bd8d9a5d05833006c0137473ade7ca126860cdfd0d3c2bd406bf956","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2013-04-16T02:15:32Z","title_canon_sha256":"7fc0a26faf620f625c47473c3dde706373b5a08ead666c24b9562243382f2440"},"schema_version":"1.0","source":{"id":"1304.4310","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4310","created_at":"2026-05-18T03:16:19Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4310v2","created_at":"2026-05-18T03:16:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4310","created_at":"2026-05-18T03:16:19Z"},{"alias_kind":"pith_short_12","alias_value":"4FPQ63XYAF57","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4FPQ63XYAF57QKYS","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4FPQ63XY","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:53d1224e69c580eadacca95592c64a15f006f899fddb9359979132faad681857","target":"graph","created_at":"2026-05-18T03:16:19Z","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":"Infection dynamics have been studied extensively on complex networks, yielding insight into the effects of heterogeneity in contact patterns on disease spread. Somewhat separately, metapopulations have provided a paradigm for modeling systems with spatially extended and \"patchy\" organization. In this paper we expand on the use of multitype networks for combining these paradigms, such that simple contagion models can include complexity in the agent interactions and multiscale structure. We first present a generalization of the Volz-Miller mean-field approximation for Susceptible-Infected-Recove","authors_text":"Christopher R. Myers, David J. Schneider, Jason Hindes, Sarabjeet Singh","cross_cats":["q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2013-04-16T02:15:32Z","title":"Epidemic fronts in complex networks with metapopulation structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4310","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":"sha256:26eacddcf987f017c9a49ea9888e71cbd467bbca05eb1fb89acae84cf55706ae","target":"record","created_at":"2026-05-18T03:16:19Z","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":"4e880b477bd8d9a5d05833006c0137473ade7ca126860cdfd0d3c2bd406bf956","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2013-04-16T02:15:32Z","title_canon_sha256":"7fc0a26faf620f625c47473c3dde706373b5a08ead666c24b9562243382f2440"},"schema_version":"1.0","source":{"id":"1304.4310","kind":"arxiv","version":2}},"canonical_sha256":"e15f0f6ef8017bf82b120b911faf2e0c85213e56f80261afbbaa998a1100ab60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e15f0f6ef8017bf82b120b911faf2e0c85213e56f80261afbbaa998a1100ab60","first_computed_at":"2026-05-18T03:16:19.810105Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:19.810105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ftNJMB94ZjECCDKJewjORRJXrxJoVNqoFBiLMW3JaA8jcyM/wO153gZm0SCKViNyGyLCP7Nbh1OAq9GjTh5RCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:19.810618Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.4310","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26eacddcf987f017c9a49ea9888e71cbd467bbca05eb1fb89acae84cf55706ae","sha256:53d1224e69c580eadacca95592c64a15f006f899fddb9359979132faad681857"],"state_sha256":"a6cefdccf81ed374618237b2b78405eece985cffbda08cdffbc449de3275697d"}