{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:QIOXB5M73XZ76DAJNE5WA2BEAY","short_pith_number":"pith:QIOXB5M7","schema_version":"1.0","canonical_sha256":"821d70f59fddf3ff0c09693b606824060a36eaa31b34cd8bbe79585e464b2a3a","source":{"kind":"arxiv","id":"1111.0921","version":2},"attestation_state":"computed","paper":{"title":"Hierarchical Synchrony of Phase Oscillators in Modular Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","nlin.AO","nlin.PS","nlin.SI"],"primary_cat":"nlin.CD","authors_text":"Juan G. Restrepo, Per Sebastian Skardal","submitted_at":"2011-11-03T17:23:35Z","abstract_excerpt":"We study synchronization of sinusoidally coupled phase oscillators on networks with modular structure and a large number of oscillators in each community. Of particular interest is the hierarchy of local and global synchrony, i.e., synchrony within and between communities, respectively. Using the recent ansatz of Ott and Antonsen, we find that the degree of local synchrony can be determined from a set of coupled low-dimensional equations. If the number of communities in the network is large, a low-dimensional description of global synchrony can be also found. Using these results, we study bifu"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1111.0921","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-11-03T17:23:35Z","cross_cats_sorted":["math.DS","nlin.AO","nlin.PS","nlin.SI"],"title_canon_sha256":"8de577f511c4425278b73c1fca6d7ce01df8a99c7b3b68531fd2ab5dd86a304c","abstract_canon_sha256":"0d0802a5db9f7e1f9ac8a9d7b697ffcfecc74a7efecfc02b3522ebd2a58704b7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:18.689465Z","signature_b64":"17JL7m9WRltN2OC2z/Oa4adRB1IoXuGniY15a+DHnuYM00PxzEX4Zr/UhGt2DbBzJF1am0AH4X3qpd9hO8msBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"821d70f59fddf3ff0c09693b606824060a36eaa31b34cd8bbe79585e464b2a3a","last_reissued_at":"2026-05-18T04:04:18.688890Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:18.688890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hierarchical Synchrony of Phase Oscillators in Modular Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","nlin.AO","nlin.PS","nlin.SI"],"primary_cat":"nlin.CD","authors_text":"Juan G. Restrepo, Per Sebastian Skardal","submitted_at":"2011-11-03T17:23:35Z","abstract_excerpt":"We study synchronization of sinusoidally coupled phase oscillators on networks with modular structure and a large number of oscillators in each community. Of particular interest is the hierarchy of local and global synchrony, i.e., synchrony within and between communities, respectively. Using the recent ansatz of Ott and Antonsen, we find that the degree of local synchrony can be determined from a set of coupled low-dimensional equations. If the number of communities in the network is large, a low-dimensional description of global synchrony can be also found. Using these results, we study bifu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0921","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1111.0921","created_at":"2026-05-18T04:04:18.688978+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.0921v2","created_at":"2026-05-18T04:04:18.688978+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0921","created_at":"2026-05-18T04:04:18.688978+00:00"},{"alias_kind":"pith_short_12","alias_value":"QIOXB5M73XZ7","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"QIOXB5M73XZ76DAJ","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"QIOXB5M7","created_at":"2026-05-18T12:26:39.201973+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QIOXB5M73XZ76DAJNE5WA2BEAY","json":"https://pith.science/pith/QIOXB5M73XZ76DAJNE5WA2BEAY.json","graph_json":"https://pith.science/api/pith-number/QIOXB5M73XZ76DAJNE5WA2BEAY/graph.json","events_json":"https://pith.science/api/pith-number/QIOXB5M73XZ76DAJNE5WA2BEAY/events.json","paper":"https://pith.science/paper/QIOXB5M7"},"agent_actions":{"view_html":"https://pith.science/pith/QIOXB5M73XZ76DAJNE5WA2BEAY","download_json":"https://pith.science/pith/QIOXB5M73XZ76DAJNE5WA2BEAY.json","view_paper":"https://pith.science/paper/QIOXB5M7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.0921&json=true","fetch_graph":"https://pith.science/api/pith-number/QIOXB5M73XZ76DAJNE5WA2BEAY/graph.json","fetch_events":"https://pith.science/api/pith-number/QIOXB5M73XZ76DAJNE5WA2BEAY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QIOXB5M73XZ76DAJNE5WA2BEAY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QIOXB5M73XZ76DAJNE5WA2BEAY/action/storage_attestation","attest_author":"https://pith.science/pith/QIOXB5M73XZ76DAJNE5WA2BEAY/action/author_attestation","sign_citation":"https://pith.science/pith/QIOXB5M73XZ76DAJNE5WA2BEAY/action/citation_signature","submit_replication":"https://pith.science/pith/QIOXB5M73XZ76DAJNE5WA2BEAY/action/replication_record"}},"created_at":"2026-05-18T04:04:18.688978+00:00","updated_at":"2026-05-18T04:04:18.688978+00:00"}