{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3PZUOAWPFBANDHDDZMHTGOQKLK","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":"d32add5ea6ee8f1def10b8ba46e38a256d740ff48b2f541ce5ccfa3d154a5aac","cross_cats_sorted":["nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-08T05:37:15Z","title_canon_sha256":"f3abe96dba7afdc146aa11286def6d5c1023d954b441e2129c49e84d7fd75266"},"schema_version":"1.0","source":{"id":"1512.02335","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02335","created_at":"2026-05-18T01:10:32Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02335v2","created_at":"2026-05-18T01:10:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02335","created_at":"2026-05-18T01:10:32Z"},{"alias_kind":"pith_short_12","alias_value":"3PZUOAWPFBAN","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3PZUOAWPFBANDHDD","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3PZUOAWP","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:5387407b053cb760fce815d8fd8e92ba00280c25e37026662631cfbc0975f572","target":"graph","created_at":"2026-05-18T01:10:32Z","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 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","authors_text":"Bertrand Ottino-Loffler, Steven Strogatz","cross_cats":["nlin.AO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-08T05:37:15Z","title":"Frequency Spirals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02335","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":"sha256:26a0756b168011991d518572224bacae20bb70185a548b280479796fefbb8dc9","target":"record","created_at":"2026-05-18T01:10:32Z","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":"d32add5ea6ee8f1def10b8ba46e38a256d740ff48b2f541ce5ccfa3d154a5aac","cross_cats_sorted":["nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-08T05:37:15Z","title_canon_sha256":"f3abe96dba7afdc146aa11286def6d5c1023d954b441e2129c49e84d7fd75266"},"schema_version":"1.0","source":{"id":"1512.02335","kind":"arxiv","version":2}},"canonical_sha256":"dbf34702cf2840d19c63cb0f333a0a5aaa0719cad97ff7f725e86795960c91e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dbf34702cf2840d19c63cb0f333a0a5aaa0719cad97ff7f725e86795960c91e2","first_computed_at":"2026-05-18T01:10:32.888989Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:32.888989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"35MZuDXPghLOCQx4umMXZiEIKD8NPU/U6NJ/sIlq3mVprkjDXntP+XEXyDxdikatgPu6OvgoTb5bRgaNQFHuBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:32.889773Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.02335","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26a0756b168011991d518572224bacae20bb70185a548b280479796fefbb8dc9","sha256:5387407b053cb760fce815d8fd8e92ba00280c25e37026662631cfbc0975f572"],"state_sha256":"088d473858158403b46361e9f8e8a3ed6b2d2c031149cdf7baa33d10be002f19"}