{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:5GE426S6SVCWNQ5GEXMYB3WG63","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":"49ad153ce90dd7f5d16951ae1d801d59dd9705296bbc38e6e7fb33b0cd0cb23d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.soc-ph","submitted_at":"2021-07-21T15:09:03Z","title_canon_sha256":"dc8c781d17ba864c5d82a9eee725484ac8dd067fcd79c97a78350c474f4d4f2f"},"schema_version":"1.0","source":{"id":"2107.10134","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.10134","created_at":"2026-07-05T04:11:47Z"},{"alias_kind":"arxiv_version","alias_value":"2107.10134v3","created_at":"2026-07-05T04:11:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.10134","created_at":"2026-07-05T04:11:47Z"},{"alias_kind":"pith_short_12","alias_value":"5GE426S6SVCW","created_at":"2026-07-05T04:11:47Z"},{"alias_kind":"pith_short_16","alias_value":"5GE426S6SVCWNQ5G","created_at":"2026-07-05T04:11:47Z"},{"alias_kind":"pith_short_8","alias_value":"5GE426S6","created_at":"2026-07-05T04:11:47Z"}],"graph_snapshots":[{"event_id":"sha256:9ae7834f3bfb066a80e27f7b60ec873ad9204d4fd25ac4ab7dd0c3a6ad273368","target":"graph","created_at":"2026-07-05T04:11:47Z","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/2107.10134/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Complex contagion adoption dynamics are characterised by a node being more likely to adopt after multiple network neighbours have adopted. We show how to construct multi-type branching processes to approximate complex contagion adoption dynamics on networks with clique-based clustering. This involves tracking the evolution of a cascade via different classes of clique motifs that account for the different numbers of active, inactive and removed nodes. This discrete-time model assumes that active nodes become immediately and certainly removed in the next time step. This description allows for ex","authors_text":"David J.P. O'Sullivan, James P. Gleeson, Leah A. Keating","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.soc-ph","submitted_at":"2021-07-21T15:09:03Z","title":"A multi-type branching process method for modelling complex contagion on clustered networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.10134","kind":"arxiv","version":3},"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":"sha256:482dcb4390ef7032fd073e9fd2f2df7a0fc6a034d8eac58c628f1da151ad77b4","target":"record","created_at":"2026-07-05T04:11:47Z","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":"49ad153ce90dd7f5d16951ae1d801d59dd9705296bbc38e6e7fb33b0cd0cb23d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.soc-ph","submitted_at":"2021-07-21T15:09:03Z","title_canon_sha256":"dc8c781d17ba864c5d82a9eee725484ac8dd067fcd79c97a78350c474f4d4f2f"},"schema_version":"1.0","source":{"id":"2107.10134","kind":"arxiv","version":3}},"canonical_sha256":"e989cd7a5e954566c3a625d980eec6f6f487e9113c6e6ad5450a9ce917ce4a91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e989cd7a5e954566c3a625d980eec6f6f487e9113c6e6ad5450a9ce917ce4a91","first_computed_at":"2026-07-05T04:11:47.426257Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:11:47.426257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8YYfdeh+t/jkJe7ZYTJoRIvVVyCvRDXOuAeWkNQ4G6GdlYCUryjYMwZLo6+2QkBNbEC/Nw3lhOz0r0XN67bODQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:11:47.426674Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.10134","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:482dcb4390ef7032fd073e9fd2f2df7a0fc6a034d8eac58c628f1da151ad77b4","sha256:9ae7834f3bfb066a80e27f7b60ec873ad9204d4fd25ac4ab7dd0c3a6ad273368"],"state_sha256":"12191f6d6b1aa4e7c3970ed159da1b4f9c24e3c6da9253e63b1fa9c2e8ccaa75"}