{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:E34ORTOKU7ROVIOEW5ZXDM66CT","short_pith_number":"pith:E34ORTOK","canonical_record":{"source":{"id":"1105.5849","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-05-30T02:32:36Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"5663bbaeca1f8ecd3642dc33d78f9862f431cf2e54fa6995767bf5e89ee2e035","abstract_canon_sha256":"6a1700cdb55a5a10fcdb3ae2314e51a9cc3b860452d0c5d6990176da28cd4ceb"},"schema_version":"1.0"},"canonical_sha256":"26f8e8cdcaa7e2eaa1c4b77371b3de14f9e41960baa4b314b5811b7e13bf6292","source":{"kind":"arxiv","id":"1105.5849","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.5849","created_at":"2026-05-18T02:21:49Z"},{"alias_kind":"arxiv_version","alias_value":"1105.5849v2","created_at":"2026-05-18T02:21:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5849","created_at":"2026-05-18T02:21:49Z"},{"alias_kind":"pith_short_12","alias_value":"E34ORTOKU7RO","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"E34ORTOKU7ROVIOE","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"E34ORTOK","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:E34ORTOKU7ROVIOEW5ZXDM66CT","target":"record","payload":{"canonical_record":{"source":{"id":"1105.5849","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-05-30T02:32:36Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"5663bbaeca1f8ecd3642dc33d78f9862f431cf2e54fa6995767bf5e89ee2e035","abstract_canon_sha256":"6a1700cdb55a5a10fcdb3ae2314e51a9cc3b860452d0c5d6990176da28cd4ceb"},"schema_version":"1.0"},"canonical_sha256":"26f8e8cdcaa7e2eaa1c4b77371b3de14f9e41960baa4b314b5811b7e13bf6292","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:49.434881Z","signature_b64":"3oNlvoFr7zveWls5Kk7wZbbH4IVl7pyUNCM+bkzDzqMVKRmk5QTSU8OpLPwznSx0h0seLoW8/w9rJqThYcH+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26f8e8cdcaa7e2eaa1c4b77371b3de14f9e41960baa4b314b5811b7e13bf6292","last_reissued_at":"2026-05-18T02:21:49.434408Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:49.434408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.5849","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:21:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vVziFrQjkJ+gfP71Kw7xoFEo5X04/CDjzU1KetCCerRWs20Xp9Zu1zspuG3FpSxhMnHuc9f1cODmjxjuGh/ZAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T22:23:21.086297Z"},"content_sha256":"6393bfed73fa38bfcc1976ab82bfd291f53cf8ca51a8e333c585ec3c12366853","schema_version":"1.0","event_id":"sha256:6393bfed73fa38bfcc1976ab82bfd291f53cf8ca51a8e333c585ec3c12366853"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:E34ORTOKU7ROVIOEW5ZXDM66CT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diffusion in Networks With Overlapping Community Structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"Fergal Reid, Neil Hurley","submitted_at":"2011-05-30T02:32:36Z","abstract_excerpt":"In this work we study diffusion in networks with community structure. We first replicate and extend work on networks with non-overlapping community structure. We then study diffusion on network models that have overlapping community structure. We study contagions in the standard SIR model, and complex contagions thought to be better models of some social diffusion processes. Finally, we investigate diffusion on empirical networks with known overlapping community structure, by analysing the structure of such networks, and by simulating contagion on them. We find that simple and complex contagio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5849","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:21:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uSkE4DTY+AeylC8n1cqnDgxaX0A4pC2T150gNAiF7z/A86wBMlq5PEUOsP7/Aj9My6tfBVnFOnBieeDBxvSkDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T22:23:21.086813Z"},"content_sha256":"3b874ffeccb1b24d57773f624a0327a13ebec01ca62bbf3383b9e1739b0ee42c","schema_version":"1.0","event_id":"sha256:3b874ffeccb1b24d57773f624a0327a13ebec01ca62bbf3383b9e1739b0ee42c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E34ORTOKU7ROVIOEW5ZXDM66CT/bundle.json","state_url":"https://pith.science/pith/E34ORTOKU7ROVIOEW5ZXDM66CT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E34ORTOKU7ROVIOEW5ZXDM66CT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T22:23:21Z","links":{"resolver":"https://pith.science/pith/E34ORTOKU7ROVIOEW5ZXDM66CT","bundle":"https://pith.science/pith/E34ORTOKU7ROVIOEW5ZXDM66CT/bundle.json","state":"https://pith.science/pith/E34ORTOKU7ROVIOEW5ZXDM66CT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E34ORTOKU7ROVIOEW5ZXDM66CT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:E34ORTOKU7ROVIOEW5ZXDM66CT","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":"6a1700cdb55a5a10fcdb3ae2314e51a9cc3b860452d0c5d6990176da28cd4ceb","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-05-30T02:32:36Z","title_canon_sha256":"5663bbaeca1f8ecd3642dc33d78f9862f431cf2e54fa6995767bf5e89ee2e035"},"schema_version":"1.0","source":{"id":"1105.5849","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.5849","created_at":"2026-05-18T02:21:49Z"},{"alias_kind":"arxiv_version","alias_value":"1105.5849v2","created_at":"2026-05-18T02:21:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5849","created_at":"2026-05-18T02:21:49Z"},{"alias_kind":"pith_short_12","alias_value":"E34ORTOKU7RO","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"E34ORTOKU7ROVIOE","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"E34ORTOK","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:3b874ffeccb1b24d57773f624a0327a13ebec01ca62bbf3383b9e1739b0ee42c","target":"graph","created_at":"2026-05-18T02:21:49Z","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":"In this work we study diffusion in networks with community structure. We first replicate and extend work on networks with non-overlapping community structure. We then study diffusion on network models that have overlapping community structure. We study contagions in the standard SIR model, and complex contagions thought to be better models of some social diffusion processes. Finally, we investigate diffusion on empirical networks with known overlapping community structure, by analysing the structure of such networks, and by simulating contagion on them. We find that simple and complex contagio","authors_text":"Fergal Reid, Neil Hurley","cross_cats":["cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-05-30T02:32:36Z","title":"Diffusion in Networks With Overlapping Community Structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5849","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":"sha256:6393bfed73fa38bfcc1976ab82bfd291f53cf8ca51a8e333c585ec3c12366853","target":"record","created_at":"2026-05-18T02:21:49Z","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":"6a1700cdb55a5a10fcdb3ae2314e51a9cc3b860452d0c5d6990176da28cd4ceb","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-05-30T02:32:36Z","title_canon_sha256":"5663bbaeca1f8ecd3642dc33d78f9862f431cf2e54fa6995767bf5e89ee2e035"},"schema_version":"1.0","source":{"id":"1105.5849","kind":"arxiv","version":2}},"canonical_sha256":"26f8e8cdcaa7e2eaa1c4b77371b3de14f9e41960baa4b314b5811b7e13bf6292","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26f8e8cdcaa7e2eaa1c4b77371b3de14f9e41960baa4b314b5811b7e13bf6292","first_computed_at":"2026-05-18T02:21:49.434408Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:49.434408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3oNlvoFr7zveWls5Kk7wZbbH4IVl7pyUNCM+bkzDzqMVKRmk5QTSU8OpLPwznSx0h0seLoW8/w9rJqThYcH+BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:49.434881Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.5849","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6393bfed73fa38bfcc1976ab82bfd291f53cf8ca51a8e333c585ec3c12366853","sha256:3b874ffeccb1b24d57773f624a0327a13ebec01ca62bbf3383b9e1739b0ee42c"],"state_sha256":"551269a0c4d852f329150e932baf145cb9edff243acfbe5e4d3d508b398abdc2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7/EtSlXCMFivYiq3D0knRbrwBqqtgy719LwMr6dhKAVbqnHB8g/QZ06KKu23pqUIik5b2oP3wXoq4yVMIyfoAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T22:23:21.091053Z","bundle_sha256":"ecbfb8259f7b5d96b08df98174d13c428d0a803552b635377f352c18d6c32e73"}}