{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ZUUCZJPLHCVACDURIYTPUVRZQT","short_pith_number":"pith:ZUUCZJPL","canonical_record":{"source":{"id":"1207.1809","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-07-07T16:11:55Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","cs.SI"],"title_canon_sha256":"d1be22e88e2b4291f72210dd6d3e1246dca2e3b28d3dc9f2465ebf5aeb6e7af2","abstract_canon_sha256":"97f8a959e0e8e61f602a0cb0bad5f1c758bcd6bb712c64f289e827bb34e8d73d"},"schema_version":"1.0"},"canonical_sha256":"cd282ca5eb38aa010e914626fa563984c520e463f52f0080175fc31caa9be440","source":{"kind":"arxiv","id":"1207.1809","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1809","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1809v2","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1809","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"pith_short_12","alias_value":"ZUUCZJPLHCVA","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZUUCZJPLHCVACDUR","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZUUCZJPL","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ZUUCZJPLHCVACDURIYTPUVRZQT","target":"record","payload":{"canonical_record":{"source":{"id":"1207.1809","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-07-07T16:11:55Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","cs.SI"],"title_canon_sha256":"d1be22e88e2b4291f72210dd6d3e1246dca2e3b28d3dc9f2465ebf5aeb6e7af2","abstract_canon_sha256":"97f8a959e0e8e61f602a0cb0bad5f1c758bcd6bb712c64f289e827bb34e8d73d"},"schema_version":"1.0"},"canonical_sha256":"cd282ca5eb38aa010e914626fa563984c520e463f52f0080175fc31caa9be440","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:05.386673Z","signature_b64":"p2+mqadOcFCYralCtL4pH/bWl6c3pIpensvPWqYMnDJXer6K7WCSBlWc1MotzqueQu6nNOIo2X6w21IlOmYICw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd282ca5eb38aa010e914626fa563984c520e463f52f0080175fc31caa9be440","last_reissued_at":"2026-05-18T02:54:05.386059Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:05.386059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.1809","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":"2026-05-18T02:54:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GDXTDf3A6OWn4JOM3yOV4IKfVkNncixSR/1Os9YcdbDh8dYnx7qh5RzMg6o1OayT2wGFQgNCwMUkSILbyfqPBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T06:18:15.172111Z"},"content_sha256":"b72bba964ae20f5f81914f3d839b85f6593be101f34dcbc02eca51f77949302f","schema_version":"1.0","event_id":"sha256:b72bba964ae20f5f81914f3d839b85f6593be101f34dcbc02eca51f77949302f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ZUUCZJPLHCVACDURIYTPUVRZQT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamics on Modular Networks with Heterogeneous Correlations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"James P. Gleeson, Mason A. Porter, Peter J. Mucha, Sergey Melnik","submitted_at":"2012-07-07T16:11:55Z","abstract_excerpt":"We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules. We present an analytical approach that allows one to analyze several types of binary dynamics operating on such networks, and we illustrate our approach using bond percolation, site percolation, and the Watts threshold model. The new network ensemble generalizes existing models (e.g., the well-known configuration model and LFR networks) by allowing a heteroge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1809","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":"2026-05-18T02:54:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JA5hk69IjEqld0Yw14I4cFvi4v7FLl3pHLYNUN03EZwZ1FCKb6oJiCeGLdap0hd8JVKjenmPB0HoJPzDHQqGCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T06:18:15.172472Z"},"content_sha256":"35bc60747f1eb7bd70d70f600b2c02625601f2630025b26641bbb9f3d118f9cf","schema_version":"1.0","event_id":"sha256:35bc60747f1eb7bd70d70f600b2c02625601f2630025b26641bbb9f3d118f9cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZUUCZJPLHCVACDURIYTPUVRZQT/bundle.json","state_url":"https://pith.science/pith/ZUUCZJPLHCVACDURIYTPUVRZQT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZUUCZJPLHCVACDURIYTPUVRZQT/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":"2026-05-20T06:18:15Z","links":{"resolver":"https://pith.science/pith/ZUUCZJPLHCVACDURIYTPUVRZQT","bundle":"https://pith.science/pith/ZUUCZJPLHCVACDURIYTPUVRZQT/bundle.json","state":"https://pith.science/pith/ZUUCZJPLHCVACDURIYTPUVRZQT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZUUCZJPLHCVACDURIYTPUVRZQT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZUUCZJPLHCVACDURIYTPUVRZQT","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":"97f8a959e0e8e61f602a0cb0bad5f1c758bcd6bb712c64f289e827bb34e8d73d","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-07-07T16:11:55Z","title_canon_sha256":"d1be22e88e2b4291f72210dd6d3e1246dca2e3b28d3dc9f2465ebf5aeb6e7af2"},"schema_version":"1.0","source":{"id":"1207.1809","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1809","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1809v2","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1809","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"pith_short_12","alias_value":"ZUUCZJPLHCVA","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZUUCZJPLHCVACDUR","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZUUCZJPL","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:35bc60747f1eb7bd70d70f600b2c02625601f2630025b26641bbb9f3d118f9cf","target":"graph","created_at":"2026-05-18T02:54:05Z","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 develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules. We present an analytical approach that allows one to analyze several types of binary dynamics operating on such networks, and we illustrate our approach using bond percolation, site percolation, and the Watts threshold model. The new network ensemble generalizes existing models (e.g., the well-known configuration model and LFR networks) by allowing a heteroge","authors_text":"James P. Gleeson, Mason A. Porter, Peter J. Mucha, Sergey Melnik","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-07-07T16:11:55Z","title":"Dynamics on Modular Networks with Heterogeneous Correlations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1809","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:b72bba964ae20f5f81914f3d839b85f6593be101f34dcbc02eca51f77949302f","target":"record","created_at":"2026-05-18T02:54:05Z","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":"97f8a959e0e8e61f602a0cb0bad5f1c758bcd6bb712c64f289e827bb34e8d73d","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-07-07T16:11:55Z","title_canon_sha256":"d1be22e88e2b4291f72210dd6d3e1246dca2e3b28d3dc9f2465ebf5aeb6e7af2"},"schema_version":"1.0","source":{"id":"1207.1809","kind":"arxiv","version":2}},"canonical_sha256":"cd282ca5eb38aa010e914626fa563984c520e463f52f0080175fc31caa9be440","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd282ca5eb38aa010e914626fa563984c520e463f52f0080175fc31caa9be440","first_computed_at":"2026-05-18T02:54:05.386059Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:05.386059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p2+mqadOcFCYralCtL4pH/bWl6c3pIpensvPWqYMnDJXer6K7WCSBlWc1MotzqueQu6nNOIo2X6w21IlOmYICw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:05.386673Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.1809","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b72bba964ae20f5f81914f3d839b85f6593be101f34dcbc02eca51f77949302f","sha256:35bc60747f1eb7bd70d70f600b2c02625601f2630025b26641bbb9f3d118f9cf"],"state_sha256":"aa6f473341f516e267271b772d1414841cc1bb1990c3b03f002cd26d610531e6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rvmITc610nLmyrdM2LQacMQ2m3k/VAC63C/Vhy098BnWYFB81LTWFzsQ+bpA1PhgZD7ezzhubNCQhTFOtWS+Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T06:18:15.174827Z","bundle_sha256":"786f9db1521d8c67767a33e3033566bc04f60e99413262e4160c46ac57e3d937"}}