{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:3PZUOAWPFBANDHDDZMHTGOQKLK","short_pith_number":"pith:3PZUOAWP","schema_version":"1.0","canonical_sha256":"dbf34702cf2840d19c63cb0f333a0a5aaa0719cad97ff7f725e86795960c91e2","source":{"kind":"arxiv","id":"1512.02335","version":2},"attestation_state":"computed","paper":{"title":"Frequency Spirals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.AO"],"primary_cat":"math.DS","authors_text":"Bertrand Ottino-Loffler, Steven Strogatz","submitted_at":"2015-12-08T05:37:15Z","abstract_excerpt":"We study the dynamics of coupled phase oscillators on a two-dimensional Kuramoto lattice with periodic boundary conditions. For coupling strengths just below the transition to global phase-locking, we find localized spatiotemporal patterns that we call \"frequency spirals.\" These patterns cannot be seen under time averaging; they become visible only when we examine the spatial variation of the oscillators' instantaneous frequencies, where they manifest themselves as two-armed rotating spirals. In the more familiar phase representation, they appear as wobbly periodic patterns surrounding a phase"},"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":"1512.02335","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-08T05:37:15Z","cross_cats_sorted":["nlin.AO"],"title_canon_sha256":"f3abe96dba7afdc146aa11286def6d5c1023d954b441e2129c49e84d7fd75266","abstract_canon_sha256":"d32add5ea6ee8f1def10b8ba46e38a256d740ff48b2f541ce5ccfa3d154a5aac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:32.889773Z","signature_b64":"35MZuDXPghLOCQx4umMXZiEIKD8NPU/U6NJ/sIlq3mVprkjDXntP+XEXyDxdikatgPu6OvgoTb5bRgaNQFHuBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dbf34702cf2840d19c63cb0f333a0a5aaa0719cad97ff7f725e86795960c91e2","last_reissued_at":"2026-05-18T01:10:32.888989Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:32.888989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Frequency Spirals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.AO"],"primary_cat":"math.DS","authors_text":"Bertrand Ottino-Loffler, Steven Strogatz","submitted_at":"2015-12-08T05:37:15Z","abstract_excerpt":"We study the dynamics of coupled phase oscillators on a two-dimensional Kuramoto lattice with periodic boundary conditions. For coupling strengths just below the transition to global phase-locking, we find localized spatiotemporal patterns that we call \"frequency spirals.\" These patterns cannot be seen under time averaging; they become visible only when we examine the spatial variation of the oscillators' instantaneous frequencies, where they manifest themselves as two-armed rotating spirals. In the more familiar phase representation, they appear as wobbly periodic patterns surrounding a phase"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02335","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":"1512.02335","created_at":"2026-05-18T01:10:32.889114+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.02335v2","created_at":"2026-05-18T01:10:32.889114+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02335","created_at":"2026-05-18T01:10:32.889114+00:00"},{"alias_kind":"pith_short_12","alias_value":"3PZUOAWPFBAN","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"3PZUOAWPFBANDHDD","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"3PZUOAWP","created_at":"2026-05-18T12:29:02.477457+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/3PZUOAWPFBANDHDDZMHTGOQKLK","json":"https://pith.science/pith/3PZUOAWPFBANDHDDZMHTGOQKLK.json","graph_json":"https://pith.science/api/pith-number/3PZUOAWPFBANDHDDZMHTGOQKLK/graph.json","events_json":"https://pith.science/api/pith-number/3PZUOAWPFBANDHDDZMHTGOQKLK/events.json","paper":"https://pith.science/paper/3PZUOAWP"},"agent_actions":{"view_html":"https://pith.science/pith/3PZUOAWPFBANDHDDZMHTGOQKLK","download_json":"https://pith.science/pith/3PZUOAWPFBANDHDDZMHTGOQKLK.json","view_paper":"https://pith.science/paper/3PZUOAWP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.02335&json=true","fetch_graph":"https://pith.science/api/pith-number/3PZUOAWPFBANDHDDZMHTGOQKLK/graph.json","fetch_events":"https://pith.science/api/pith-number/3PZUOAWPFBANDHDDZMHTGOQKLK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3PZUOAWPFBANDHDDZMHTGOQKLK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3PZUOAWPFBANDHDDZMHTGOQKLK/action/storage_attestation","attest_author":"https://pith.science/pith/3PZUOAWPFBANDHDDZMHTGOQKLK/action/author_attestation","sign_citation":"https://pith.science/pith/3PZUOAWPFBANDHDDZMHTGOQKLK/action/citation_signature","submit_replication":"https://pith.science/pith/3PZUOAWPFBANDHDDZMHTGOQKLK/action/replication_record"}},"created_at":"2026-05-18T01:10:32.889114+00:00","updated_at":"2026-05-18T01:10:32.889114+00:00"}