{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:DVE7O52F4U3QQV7UEAXYTXGAGW","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":"c4ebd02ca21b006bdff27fb9052e6a1e456df083e9b88a8c50c39fc25bc4900f","cross_cats_sorted":["physics.bio-ph"],"license":"","primary_cat":"physics.soc-ph","submitted_at":"2006-09-17T19:37:05Z","title_canon_sha256":"77debda5bec73f86b3967ef2b28132a5ccf8c0cb0c94aea3b55726c9dfdb959d"},"schema_version":"1.0","source":{"id":"physics/0609150","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"physics/0609150","created_at":"2026-07-04T15:01:10Z"},{"alias_kind":"arxiv_version","alias_value":"physics/0609150v1","created_at":"2026-07-04T15:01:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.physics/0609150","created_at":"2026-07-04T15:01:10Z"},{"alias_kind":"pith_short_12","alias_value":"DVE7O52F4U3Q","created_at":"2026-07-04T15:01:10Z"},{"alias_kind":"pith_short_16","alias_value":"DVE7O52F4U3QQV7U","created_at":"2026-07-04T15:01:10Z"},{"alias_kind":"pith_short_8","alias_value":"DVE7O52F","created_at":"2026-07-04T15:01:10Z"}],"graph_snapshots":[{"event_id":"sha256:19907585b732bb510e2f933d0d5a2c553816ef2c91bb47e63df8a1fb7c7eed19","target":"graph","created_at":"2026-07-04T15:01:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/physics/0609150/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we propose a modified susceptible-infected-recovered (SIR) model, in which each node is assigned with an identical capability of active contacts, $A$, at each time step. In contrast to the previous studies, we find that on scale-free networks, the density of the recovered individuals in the present model shows a threshold behavior. We obtain the analytical results using the mean-field theory and find that the threshold value equals 1/A, indicating that the threshold value is independent of the topology of the underlying network. The simulations agree well with the analytic resul","authors_text":"Bing-Hong Wang, Jie Ren, Rui Yang, Tao Zhou, Wen-Jie Bai, Wen-Xu Wang, Zhi-Wen Shi","cross_cats":["physics.bio-ph"],"headline":"","license":"","primary_cat":"physics.soc-ph","submitted_at":"2006-09-17T19:37:05Z","title":"Epidemic spreading on heterogeneous networks with identical infectivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"physics/0609150","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":"sha256:3e5a3f40a2ab2756a50257b52ca682c1d079589d75455a3f56ae91c207e539cf","target":"record","created_at":"2026-07-04T15:01:10Z","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":"c4ebd02ca21b006bdff27fb9052e6a1e456df083e9b88a8c50c39fc25bc4900f","cross_cats_sorted":["physics.bio-ph"],"license":"","primary_cat":"physics.soc-ph","submitted_at":"2006-09-17T19:37:05Z","title_canon_sha256":"77debda5bec73f86b3967ef2b28132a5ccf8c0cb0c94aea3b55726c9dfdb959d"},"schema_version":"1.0","source":{"id":"physics/0609150","kind":"arxiv","version":1}},"canonical_sha256":"1d49f77745e5370857f4202f89dcc035a67023ab0509456e16eaef178c98cdc4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d49f77745e5370857f4202f89dcc035a67023ab0509456e16eaef178c98cdc4","first_computed_at":"2026-07-04T15:01:10.807507Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:01:10.807507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wwTri4fkuW1yHhze70d/cSst4wZa4JOfKrwXae3I8RROJjxrpsDwPZhhkCiKmnUmm5dVVHRSRqO2XVc2Q77jBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:01:10.807871Z","signed_message":"canonical_sha256_bytes"},"source_id":"physics/0609150","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e5a3f40a2ab2756a50257b52ca682c1d079589d75455a3f56ae91c207e539cf","sha256:19907585b732bb510e2f933d0d5a2c553816ef2c91bb47e63df8a1fb7c7eed19"],"state_sha256":"71e63b014006eeb54c4e3ec482b7980605d0cdb4e8544cc577093b412c3f166c"}