{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:7MGD73ZOEWMWIUJMXKTOLVGHJV","short_pith_number":"pith:7MGD73ZO","schema_version":"1.0","canonical_sha256":"fb0c3fef2e259964512cbaa6e5d4c74d4e39d7daae5733b946cdc12b744e96fb","source":{"kind":"arxiv","id":"0904.1680","version":2},"attestation_state":"computed","paper":{"title":"Phase oscillators with global sinusoidal coupling evolve by Mobius group action","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Renato E. Mirollo, Seth A. Marvel, Steven H. Strogatz","submitted_at":"2009-04-10T11:39:38Z","abstract_excerpt":"Systems of N identical phase oscillators with global sinusoidal coupling are known to display low-dimensional dynamics. Although this phenomenon was first observed about 20 years ago, its underlying cause has remained a puzzle. Here we expose the structure working behind the scenes of these systems, by proving that the governing equations are generated by the action of the Mobius group, a three-parameter subgroup of fractional linear transformations that map the unit disc to itself. When there are no auxiliary state variables, the group action partitions the N-dimensional state space into thre"},"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":"0904.1680","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2009-04-10T11:39:38Z","cross_cats_sorted":[],"title_canon_sha256":"53da4dbbab47e6186df82b730f1a1e08d4f5425fdbcd7e2f24afa0f9bd9cb5f4","abstract_canon_sha256":"8441872eeb510c7de999ffefddee5881ec9479e5e5b886abff44b1c949a2b4fb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:14:06.556497Z","signature_b64":"qAWP42j4v3dlA16UOincIzcHjpvSDmiwXVBWRMf5z0MWv8sbjGBHcjuzIA7bG0rRA+xCv1qvU6tsaG4Bs1vqDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb0c3fef2e259964512cbaa6e5d4c74d4e39d7daae5733b946cdc12b744e96fb","last_reissued_at":"2026-05-18T02:14:06.555944Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:14:06.555944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Phase oscillators with global sinusoidal coupling evolve by Mobius group action","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Renato E. Mirollo, Seth A. Marvel, Steven H. Strogatz","submitted_at":"2009-04-10T11:39:38Z","abstract_excerpt":"Systems of N identical phase oscillators with global sinusoidal coupling are known to display low-dimensional dynamics. Although this phenomenon was first observed about 20 years ago, its underlying cause has remained a puzzle. Here we expose the structure working behind the scenes of these systems, by proving that the governing equations are generated by the action of the Mobius group, a three-parameter subgroup of fractional linear transformations that map the unit disc to itself. When there are no auxiliary state variables, the group action partitions the N-dimensional state space into thre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.1680","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":"0904.1680","created_at":"2026-05-18T02:14:06.556043+00:00"},{"alias_kind":"arxiv_version","alias_value":"0904.1680v2","created_at":"2026-05-18T02:14:06.556043+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.1680","created_at":"2026-05-18T02:14:06.556043+00:00"},{"alias_kind":"pith_short_12","alias_value":"7MGD73ZOEWMW","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"7MGD73ZOEWMWIUJM","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"7MGD73ZO","created_at":"2026-05-18T12:25:58.837520+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/7MGD73ZOEWMWIUJMXKTOLVGHJV","json":"https://pith.science/pith/7MGD73ZOEWMWIUJMXKTOLVGHJV.json","graph_json":"https://pith.science/api/pith-number/7MGD73ZOEWMWIUJMXKTOLVGHJV/graph.json","events_json":"https://pith.science/api/pith-number/7MGD73ZOEWMWIUJMXKTOLVGHJV/events.json","paper":"https://pith.science/paper/7MGD73ZO"},"agent_actions":{"view_html":"https://pith.science/pith/7MGD73ZOEWMWIUJMXKTOLVGHJV","download_json":"https://pith.science/pith/7MGD73ZOEWMWIUJMXKTOLVGHJV.json","view_paper":"https://pith.science/paper/7MGD73ZO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0904.1680&json=true","fetch_graph":"https://pith.science/api/pith-number/7MGD73ZOEWMWIUJMXKTOLVGHJV/graph.json","fetch_events":"https://pith.science/api/pith-number/7MGD73ZOEWMWIUJMXKTOLVGHJV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7MGD73ZOEWMWIUJMXKTOLVGHJV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7MGD73ZOEWMWIUJMXKTOLVGHJV/action/storage_attestation","attest_author":"https://pith.science/pith/7MGD73ZOEWMWIUJMXKTOLVGHJV/action/author_attestation","sign_citation":"https://pith.science/pith/7MGD73ZOEWMWIUJMXKTOLVGHJV/action/citation_signature","submit_replication":"https://pith.science/pith/7MGD73ZOEWMWIUJMXKTOLVGHJV/action/replication_record"}},"created_at":"2026-05-18T02:14:06.556043+00:00","updated_at":"2026-05-18T02:14:06.556043+00:00"}