{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PRNBO55WGTT3MAFKEXGOI6Y6QD","short_pith_number":"pith:PRNBO55W","canonical_record":{"source":{"id":"1208.4561","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2012-08-22T17:13:29Z","cross_cats_sorted":["math.DS","nlin.CD","nlin.PS"],"title_canon_sha256":"01c969d2775684f09c3d3017584b8234270ae4fb19cc848cc3e6a6c266120e22","abstract_canon_sha256":"773d47eb3ef97da2bae555bb36fa69416979fa6447fa10aa6012b1f029b8745e"},"schema_version":"1.0"},"canonical_sha256":"7c5a1777b634e7b600aa25cce47b1e80e3de7660770cceed4f0d38d4c78a38cb","source":{"kind":"arxiv","id":"1208.4561","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.4561","created_at":"2026-05-18T01:54:59Z"},{"alias_kind":"arxiv_version","alias_value":"1208.4561v2","created_at":"2026-05-18T01:54:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4561","created_at":"2026-05-18T01:54:59Z"},{"alias_kind":"pith_short_12","alias_value":"PRNBO55WGTT3","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PRNBO55WGTT3MAFK","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PRNBO55W","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PRNBO55WGTT3MAFKEXGOI6Y6QD","target":"record","payload":{"canonical_record":{"source":{"id":"1208.4561","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2012-08-22T17:13:29Z","cross_cats_sorted":["math.DS","nlin.CD","nlin.PS"],"title_canon_sha256":"01c969d2775684f09c3d3017584b8234270ae4fb19cc848cc3e6a6c266120e22","abstract_canon_sha256":"773d47eb3ef97da2bae555bb36fa69416979fa6447fa10aa6012b1f029b8745e"},"schema_version":"1.0"},"canonical_sha256":"7c5a1777b634e7b600aa25cce47b1e80e3de7660770cceed4f0d38d4c78a38cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:54:59.523556Z","signature_b64":"U5MJ3OW8oa0BsmUiuK2DhiycIkWZ44g7MAfkW5rtYntgkuZCB77hzzCn7y6zQUTOxERkao1onfriGmIcBEtHBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c5a1777b634e7b600aa25cce47b1e80e3de7660770cceed4f0d38d4c78a38cb","last_reissued_at":"2026-05-18T01:54:59.522826Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:54:59.522826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.4561","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:54:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9s+53yw3NKK8OF25G9xUS5Ihxl4qCcyKjNGrEu92RtGNf/iP+EMqD+lezvzcOqOmpbAw+IxXiseGYhaTgvwrBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T12:39:28.842079Z"},"content_sha256":"0c1fb6725f221fa080c1c40e7d365a94482ed026d766ae20c8433689dd5c55e2","schema_version":"1.0","event_id":"sha256:0c1fb6725f221fa080c1c40e7d365a94482ed026d766ae20c8433689dd5c55e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PRNBO55WGTT3MAFKEXGOI6Y6QD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stationary and Traveling Wave States of the Kuramoto Model with an Arbitrary Distribution of Frequencies and Coupling Strengths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","nlin.CD","nlin.PS"],"primary_cat":"nlin.AO","authors_text":"Aneta Stefanovska, Dmytro Iatsenko, Peter V. E. McClintock, Spase Petkoski","submitted_at":"2012-08-22T17:13:29Z","abstract_excerpt":"We consider the Kuramoto model of an ensemble of interacting oscillators allowing for an arbitrary distribution of frequencies and coupling strengths. We define a family of traveling wave states as stationary in a rotating frame, and derive general equations for their parameters. We suggest empirical stability conditions which, for the case of incoherence, become exact. In addition to making new theoretical predictions, we show that many earlier results follow naturally from our general framework. The results are applicable in scientific contexts ranging from physics to biology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4561","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:54:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GLZSppWk0er2zOK9yx4c9CbU3ut5UtthyMZ+se3d/XAbG3/70PnpmEz73YRFkJM/WyKecCkT6T9ogc9/AjzmCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T12:39:28.842606Z"},"content_sha256":"40c4db6ea4dc8c1c3e62e10042bf9aa2629173aa31b7a8637bba1b9b72f3a371","schema_version":"1.0","event_id":"sha256:40c4db6ea4dc8c1c3e62e10042bf9aa2629173aa31b7a8637bba1b9b72f3a371"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PRNBO55WGTT3MAFKEXGOI6Y6QD/bundle.json","state_url":"https://pith.science/pith/PRNBO55WGTT3MAFKEXGOI6Y6QD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PRNBO55WGTT3MAFKEXGOI6Y6QD/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":"2026-06-23T12:39:28Z","links":{"resolver":"https://pith.science/pith/PRNBO55WGTT3MAFKEXGOI6Y6QD","bundle":"https://pith.science/pith/PRNBO55WGTT3MAFKEXGOI6Y6QD/bundle.json","state":"https://pith.science/pith/PRNBO55WGTT3MAFKEXGOI6Y6QD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PRNBO55WGTT3MAFKEXGOI6Y6QD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PRNBO55WGTT3MAFKEXGOI6Y6QD","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":"773d47eb3ef97da2bae555bb36fa69416979fa6447fa10aa6012b1f029b8745e","cross_cats_sorted":["math.DS","nlin.CD","nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2012-08-22T17:13:29Z","title_canon_sha256":"01c969d2775684f09c3d3017584b8234270ae4fb19cc848cc3e6a6c266120e22"},"schema_version":"1.0","source":{"id":"1208.4561","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.4561","created_at":"2026-05-18T01:54:59Z"},{"alias_kind":"arxiv_version","alias_value":"1208.4561v2","created_at":"2026-05-18T01:54:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4561","created_at":"2026-05-18T01:54:59Z"},{"alias_kind":"pith_short_12","alias_value":"PRNBO55WGTT3","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PRNBO55WGTT3MAFK","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PRNBO55W","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:40c4db6ea4dc8c1c3e62e10042bf9aa2629173aa31b7a8637bba1b9b72f3a371","target":"graph","created_at":"2026-05-18T01:54:59Z","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 consider the Kuramoto model of an ensemble of interacting oscillators allowing for an arbitrary distribution of frequencies and coupling strengths. We define a family of traveling wave states as stationary in a rotating frame, and derive general equations for their parameters. We suggest empirical stability conditions which, for the case of incoherence, become exact. In addition to making new theoretical predictions, we show that many earlier results follow naturally from our general framework. The results are applicable in scientific contexts ranging from physics to biology.","authors_text":"Aneta Stefanovska, Dmytro Iatsenko, Peter V. E. McClintock, Spase Petkoski","cross_cats":["math.DS","nlin.CD","nlin.PS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2012-08-22T17:13:29Z","title":"Stationary and Traveling Wave States of the Kuramoto Model with an Arbitrary Distribution of Frequencies and Coupling Strengths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4561","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":"sha256:0c1fb6725f221fa080c1c40e7d365a94482ed026d766ae20c8433689dd5c55e2","target":"record","created_at":"2026-05-18T01:54:59Z","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":"773d47eb3ef97da2bae555bb36fa69416979fa6447fa10aa6012b1f029b8745e","cross_cats_sorted":["math.DS","nlin.CD","nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2012-08-22T17:13:29Z","title_canon_sha256":"01c969d2775684f09c3d3017584b8234270ae4fb19cc848cc3e6a6c266120e22"},"schema_version":"1.0","source":{"id":"1208.4561","kind":"arxiv","version":2}},"canonical_sha256":"7c5a1777b634e7b600aa25cce47b1e80e3de7660770cceed4f0d38d4c78a38cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c5a1777b634e7b600aa25cce47b1e80e3de7660770cceed4f0d38d4c78a38cb","first_computed_at":"2026-05-18T01:54:59.522826Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:54:59.522826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U5MJ3OW8oa0BsmUiuK2DhiycIkWZ44g7MAfkW5rtYntgkuZCB77hzzCn7y6zQUTOxERkao1onfriGmIcBEtHBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:54:59.523556Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.4561","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c1fb6725f221fa080c1c40e7d365a94482ed026d766ae20c8433689dd5c55e2","sha256:40c4db6ea4dc8c1c3e62e10042bf9aa2629173aa31b7a8637bba1b9b72f3a371"],"state_sha256":"64791f6e1f3e21f510c31f662bc54d84c52b4182f217217f54cc780e2d0790d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sZdN0gpia5N2Eet7X5tE0FAkXEh3f5ZhVPqvS9SMKsG7ieuz5mXCaDo9XS9Gup9jAPXRomlzm5M45QcVVXgiBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T12:39:28.845222Z","bundle_sha256":"7e303c8d94da150b5e5524064f1b0406aea1f24de5a7ea1f62769a6ac523fe37"}}