{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YKELTXJZ23JZJQAMR77WEFA45M","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":"fc14555b631bc061d3fe6628f98c6e19a79307e469395c117f04887280abd6fd","cross_cats_sorted":["cond-mat.stat-mech","cs.SI","q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-03-21T15:42:20Z","title_canon_sha256":"43fc5e725c55fbcb186c842295a10e7400ae83a9d1b28a2849a1275195a6040e"},"schema_version":"1.0","source":{"id":"1103.4059","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4059","created_at":"2026-05-18T02:22:17Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4059v2","created_at":"2026-05-18T02:22:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4059","created_at":"2026-05-18T02:22:17Z"},{"alias_kind":"pith_short_12","alias_value":"YKELTXJZ23JZ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YKELTXJZ23JZJQAM","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YKELTXJZ","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:1aab19b4281c4eaa914410b4ae8ff2ad5dc56ea2eb70e256bbfec6541fd84742","target":"graph","created_at":"2026-05-18T02:22:17Z","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":"Epidemics seldom occur as isolated phenomena. Typically, two or more viral agents spread within the same host population and may interact dynamically with each other. We present a general model where two viral agents interact via an immunity mechanism as they propagate simultaneously on two networks connecting the same set of nodes. Exploiting a correspondence between the propagation dynamics and a dynamical process performing progressive network generation, we develop an analytic approach that accurately captures the dynamical interaction between epidemics on overlay networks. The formalism a","authors_text":"Antoine Allard, Laurent H\\'ebert-Dufresne, Louis J. Dub\\'e, Pierre-Andr\\'e No\\\"el, Vincent Marceau","cross_cats":["cond-mat.stat-mech","cs.SI","q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-03-21T15:42:20Z","title":"Modeling the dynamical interaction between epidemics on overlay networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4059","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":"sha256:2d40baa4095483ddff2a3ba3bd176edc364878fc762ada329fba0673e807872e","target":"record","created_at":"2026-05-18T02:22:17Z","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":"fc14555b631bc061d3fe6628f98c6e19a79307e469395c117f04887280abd6fd","cross_cats_sorted":["cond-mat.stat-mech","cs.SI","q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-03-21T15:42:20Z","title_canon_sha256":"43fc5e725c55fbcb186c842295a10e7400ae83a9d1b28a2849a1275195a6040e"},"schema_version":"1.0","source":{"id":"1103.4059","kind":"arxiv","version":2}},"canonical_sha256":"c288b9dd39d6d394c00c8fff62141ceb18c4782f59052710e759e8fe8cfcf1a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c288b9dd39d6d394c00c8fff62141ceb18c4782f59052710e759e8fe8cfcf1a2","first_computed_at":"2026-05-18T02:22:17.839709Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:17.839709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2WRPbPIZfoQ4zeb1ys9yvfMDa0S5XEHui4hrI7OBD7P6H1IJJhySlSeUERYqf81uqJRzsUoP9Lxsp9AxQdqqCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:17.840475Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.4059","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d40baa4095483ddff2a3ba3bd176edc364878fc762ada329fba0673e807872e","sha256:1aab19b4281c4eaa914410b4ae8ff2ad5dc56ea2eb70e256bbfec6541fd84742"],"state_sha256":"4e293fef358fb6fb9d60c84e57b3bebbe14b865e20f8902b287618dab0ad46f8"}