{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:B6KQQID2GUB3ETWA4VCXA2IPWG","short_pith_number":"pith:B6KQQID2","canonical_record":{"source":{"id":"0907.3509","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2009-07-20T22:44:30Z","cross_cats_sorted":[],"title_canon_sha256":"9f4ce61389f7831d4bdd67f39e7df2cd300d5b6ea70ab459d182fab3348289ff","abstract_canon_sha256":"36a0fd22c4960c5768996f847abd464d56069d8d91d1decf54c814fcd849b3d9"},"schema_version":"1.0"},"canonical_sha256":"0f9508207a3503b24ec0e54570690fb195dd07a08280b05a2a37f6e20140dbdc","source":{"kind":"arxiv","id":"0907.3509","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.3509","created_at":"2026-05-18T04:17:03Z"},{"alias_kind":"arxiv_version","alias_value":"0907.3509v3","created_at":"2026-05-18T04:17:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.3509","created_at":"2026-05-18T04:17:03Z"},{"alias_kind":"pith_short_12","alias_value":"B6KQQID2GUB3","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"B6KQQID2GUB3ETWA","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"B6KQQID2","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:B6KQQID2GUB3ETWA4VCXA2IPWG","target":"record","payload":{"canonical_record":{"source":{"id":"0907.3509","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2009-07-20T22:44:30Z","cross_cats_sorted":[],"title_canon_sha256":"9f4ce61389f7831d4bdd67f39e7df2cd300d5b6ea70ab459d182fab3348289ff","abstract_canon_sha256":"36a0fd22c4960c5768996f847abd464d56069d8d91d1decf54c814fcd849b3d9"},"schema_version":"1.0"},"canonical_sha256":"0f9508207a3503b24ec0e54570690fb195dd07a08280b05a2a37f6e20140dbdc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:17:03.512003Z","signature_b64":"73cFvXt8gRN5Vs+6Gv5ROBbMef/HL/w5y6aaN78ditp22QXqF305Op2Eo1GAAmt+IT1R5wK0rkVIP54V+TcrCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f9508207a3503b24ec0e54570690fb195dd07a08280b05a2a37f6e20140dbdc","last_reissued_at":"2026-05-18T04:17:03.511230Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:17:03.511230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0907.3509","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:17:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+PiKzVay2+XGeKBYPM7GlFWQ/CPzSybum47U1nhfVt8S9k+RE5l0m+ErvR9iOA0W6p61JfM6oJredcn9fXleAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T05:33:21.569525Z"},"content_sha256":"a90e5ff80578c18c3c246eb81b7b21fb3b08b1d3426b355dce303b80fda27558","schema_version":"1.0","event_id":"sha256:a90e5ff80578c18c3c246eb81b7b21fb3b08b1d3426b355dce303b80fda27558"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:B6KQQID2GUB3ETWA4VCXA2IPWG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Party Polarization in Congress: A Network Science Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.soc-ph","authors_text":"Andrew Scott Waugh, James H. Fowler, Liuyi Pei, Mason A. Porter, Peter J. Mucha","submitted_at":"2009-07-20T22:44:30Z","abstract_excerpt":"We measure polarization in the United States Congress using the network science concept of modularity. Modularity provides a conceptually-clear measure of polarization that reveals both the number of relevant groups and the strength of inter-group divisions without making restrictive assumptions about the structure of the party system or the shape of legislator utilities. We show that party influence on Congressional blocs varies widely throughout history, and that existing measures underestimate polarization in periods with weak party structures. We demonstrate that modularity is a significan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.3509","kind":"arxiv","version":3},"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":"2026-05-18T04:17:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1PiICWkURWniYIQ2qlyxgEVNbWp8534J5vTjeKD/KuCCqamM+qUpi5B2AJuJYI2Q21PVpMa1fbu4ETO4VjUZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T05:33:21.569885Z"},"content_sha256":"dba02032526bd8f054fb6205cd3c352fdc030328bb08d3b9812801e77cdb96df","schema_version":"1.0","event_id":"sha256:dba02032526bd8f054fb6205cd3c352fdc030328bb08d3b9812801e77cdb96df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B6KQQID2GUB3ETWA4VCXA2IPWG/bundle.json","state_url":"https://pith.science/pith/B6KQQID2GUB3ETWA4VCXA2IPWG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B6KQQID2GUB3ETWA4VCXA2IPWG/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":"2026-05-21T05:33:21Z","links":{"resolver":"https://pith.science/pith/B6KQQID2GUB3ETWA4VCXA2IPWG","bundle":"https://pith.science/pith/B6KQQID2GUB3ETWA4VCXA2IPWG/bundle.json","state":"https://pith.science/pith/B6KQQID2GUB3ETWA4VCXA2IPWG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B6KQQID2GUB3ETWA4VCXA2IPWG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:B6KQQID2GUB3ETWA4VCXA2IPWG","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":"36a0fd22c4960c5768996f847abd464d56069d8d91d1decf54c814fcd849b3d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2009-07-20T22:44:30Z","title_canon_sha256":"9f4ce61389f7831d4bdd67f39e7df2cd300d5b6ea70ab459d182fab3348289ff"},"schema_version":"1.0","source":{"id":"0907.3509","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.3509","created_at":"2026-05-18T04:17:03Z"},{"alias_kind":"arxiv_version","alias_value":"0907.3509v3","created_at":"2026-05-18T04:17:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.3509","created_at":"2026-05-18T04:17:03Z"},{"alias_kind":"pith_short_12","alias_value":"B6KQQID2GUB3","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"B6KQQID2GUB3ETWA","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"B6KQQID2","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:dba02032526bd8f054fb6205cd3c352fdc030328bb08d3b9812801e77cdb96df","target":"graph","created_at":"2026-05-18T04:17:03Z","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 measure polarization in the United States Congress using the network science concept of modularity. Modularity provides a conceptually-clear measure of polarization that reveals both the number of relevant groups and the strength of inter-group divisions without making restrictive assumptions about the structure of the party system or the shape of legislator utilities. We show that party influence on Congressional blocs varies widely throughout history, and that existing measures underestimate polarization in periods with weak party structures. We demonstrate that modularity is a significan","authors_text":"Andrew Scott Waugh, James H. Fowler, Liuyi Pei, Mason A. Porter, Peter J. Mucha","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2009-07-20T22:44:30Z","title":"Party Polarization in Congress: A Network Science Approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.3509","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:a90e5ff80578c18c3c246eb81b7b21fb3b08b1d3426b355dce303b80fda27558","target":"record","created_at":"2026-05-18T04:17:03Z","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":"36a0fd22c4960c5768996f847abd464d56069d8d91d1decf54c814fcd849b3d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2009-07-20T22:44:30Z","title_canon_sha256":"9f4ce61389f7831d4bdd67f39e7df2cd300d5b6ea70ab459d182fab3348289ff"},"schema_version":"1.0","source":{"id":"0907.3509","kind":"arxiv","version":3}},"canonical_sha256":"0f9508207a3503b24ec0e54570690fb195dd07a08280b05a2a37f6e20140dbdc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f9508207a3503b24ec0e54570690fb195dd07a08280b05a2a37f6e20140dbdc","first_computed_at":"2026-05-18T04:17:03.511230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:03.511230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"73cFvXt8gRN5Vs+6Gv5ROBbMef/HL/w5y6aaN78ditp22QXqF305Op2Eo1GAAmt+IT1R5wK0rkVIP54V+TcrCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:03.512003Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.3509","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a90e5ff80578c18c3c246eb81b7b21fb3b08b1d3426b355dce303b80fda27558","sha256:dba02032526bd8f054fb6205cd3c352fdc030328bb08d3b9812801e77cdb96df"],"state_sha256":"0de7b41bf1a2c71ceb3856723e609fbd85b69af9e7b5e11efc6ae63d59799464"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C+d+UIk0l1O4OS6yU2gQ+loKea7aSl5VDXrY8v/HnACpWllE8UH/P+TB1mrPwjZuHoTO+9Y8tgDeLyjPT5BlDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T05:33:21.572102Z","bundle_sha256":"1cdd3d3ce4a7905e35a53ac57aee43c2e87c2215e225e802ab1dfb513dd789e5"}}