{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WWRP6HGAEYPAWWTI2FR64OONCF","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":"61b0c173473e8a42c5db90abf42669218ed6f2ccfebe4ef348e1d5e4d0504f70","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2013-12-03T04:01:51Z","title_canon_sha256":"1c548579a3b5d9515f43bbe11476c73356c0ba163cb1ea39e650b69905b15a60"},"schema_version":"1.0","source":{"id":"1312.0938","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0938","created_at":"2026-05-18T03:05:36Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0938v1","created_at":"2026-05-18T03:05:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0938","created_at":"2026-05-18T03:05:36Z"},{"alias_kind":"pith_short_12","alias_value":"WWRP6HGAEYPA","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"WWRP6HGAEYPAWWTI","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"WWRP6HGA","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:0d02fe3e3250c73d6f19882c4c573bad1b1786ccb44c0780cbfcb6171572aa16","target":"graph","created_at":"2026-05-18T03:05:36Z","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 study the effect of external infection sources on phase transitions in epidemic processes. In particular, we consider an epidemic spreading on a network via the SIS/SIR dynamics, which in addition is aided by external agents - sources unconstrained by the graph, but possessing a limited infection rate or virulence. Such a model captures many existing models of externally aided epidemics, and finds use in many settings - epidemiology, marketing and advertising, network robustness, etc. We provide a detailed characterization of the impact of external agents on epidemic thresholds. In particul","authors_text":"Avhishek Chatterjee, Sanjay Shakkottai, Siddhartha Banerjee","cross_cats":["physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2013-12-03T04:01:51Z","title":"Epidemic Thresholds with External Agents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0938","kind":"arxiv","version":1},"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:fbabb4eba2fe521be531fca108e769fe283cd9bdcdf2ea2cccb9c3256c5f0317","target":"record","created_at":"2026-05-18T03:05:36Z","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":"61b0c173473e8a42c5db90abf42669218ed6f2ccfebe4ef348e1d5e4d0504f70","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2013-12-03T04:01:51Z","title_canon_sha256":"1c548579a3b5d9515f43bbe11476c73356c0ba163cb1ea39e650b69905b15a60"},"schema_version":"1.0","source":{"id":"1312.0938","kind":"arxiv","version":1}},"canonical_sha256":"b5a2ff1cc0261e0b5a68d163ee39cd115776db4d2d7a62bb3067bd0873d848c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5a2ff1cc0261e0b5a68d163ee39cd115776db4d2d7a62bb3067bd0873d848c5","first_computed_at":"2026-05-18T03:05:36.191779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:36.191779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ShcLd5yBeCSY1ZwSZDgb/Minqq7yCZEG8SJ8ovJsbUvjDvobxKdIy/mmReboCPmDJKrIIaiTQ2uw1KuD1ATrDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:36.192297Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.0938","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbabb4eba2fe521be531fca108e769fe283cd9bdcdf2ea2cccb9c3256c5f0317","sha256:0d02fe3e3250c73d6f19882c4c573bad1b1786ccb44c0780cbfcb6171572aa16"],"state_sha256":"b48da366a7001edfea55b563668cfcb552cf5f6d0ca82a93b897decfc1f8abe7"}