{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:W7I52PIIOJJDL44J34CDPFIJCG","short_pith_number":"pith:W7I52PII","schema_version":"1.0","canonical_sha256":"b7d1dd3d08725235f389df04379509118348aef5f2dacf5077f8da2dd0056ecb","source":{"kind":"arxiv","id":"0904.3735","version":2},"attestation_state":"computed","paper":{"title":"Existence of hysteresis in the Kuramoto model with bimodal frequency distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.AO","authors_text":"Diego Paz\\'o, Ernest Montbri\\'o","submitted_at":"2009-04-23T17:33:37Z","abstract_excerpt":"We investigate the transition to synchronization in the Kuramoto model with bimodal distributions of the natural frequencies. Previous studies have concluded that the model exhibits a hysteretic phase transition if the bimodal distribution is close to a unimodal one, due to the shallowness the central dip. Here we show that proximity to the unimodal-bimodal border does not necessarily imply hysteresis when the width, but not the depth, of the central dip tends to zero. We draw this conclusion from a detailed study of the Kuramoto model with a suitable family of bimodal distributions."},"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":"0904.3735","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2009-04-23T17:33:37Z","cross_cats_sorted":[],"title_canon_sha256":"42f2a292537fe621d74b95be6f463f0f84a1dcc5f0ba3217e2750df86f7c0406","abstract_canon_sha256":"ae82a1ec3575768bfcb4f66cc2b76a7a382a85f63635aa0880956003c2fb8a01"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:57.720747Z","signature_b64":"fnz/bI066a+l/yiTZDEz28ozKsjSq/AC6iYC7SFXAwzF0/Ah51/DYGODqXr7Em9qwSmfmKaCAUIefLtEUqjNAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7d1dd3d08725235f389df04379509118348aef5f2dacf5077f8da2dd0056ecb","last_reissued_at":"2026-05-18T02:13:57.720242Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:57.720242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of hysteresis in the Kuramoto model with bimodal frequency distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.AO","authors_text":"Diego Paz\\'o, Ernest Montbri\\'o","submitted_at":"2009-04-23T17:33:37Z","abstract_excerpt":"We investigate the transition to synchronization in the Kuramoto model with bimodal distributions of the natural frequencies. Previous studies have concluded that the model exhibits a hysteretic phase transition if the bimodal distribution is close to a unimodal one, due to the shallowness the central dip. Here we show that proximity to the unimodal-bimodal border does not necessarily imply hysteresis when the width, but not the depth, of the central dip tends to zero. We draw this conclusion from a detailed study of the Kuramoto model with a suitable family of bimodal distributions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.3735","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":"0904.3735","created_at":"2026-05-18T02:13:57.720329+00:00"},{"alias_kind":"arxiv_version","alias_value":"0904.3735v2","created_at":"2026-05-18T02:13:57.720329+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.3735","created_at":"2026-05-18T02:13:57.720329+00:00"},{"alias_kind":"pith_short_12","alias_value":"W7I52PIIOJJD","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"W7I52PIIOJJDL44J","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"W7I52PII","created_at":"2026-05-18T12:26:02.257875+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/W7I52PIIOJJDL44J34CDPFIJCG","json":"https://pith.science/pith/W7I52PIIOJJDL44J34CDPFIJCG.json","graph_json":"https://pith.science/api/pith-number/W7I52PIIOJJDL44J34CDPFIJCG/graph.json","events_json":"https://pith.science/api/pith-number/W7I52PIIOJJDL44J34CDPFIJCG/events.json","paper":"https://pith.science/paper/W7I52PII"},"agent_actions":{"view_html":"https://pith.science/pith/W7I52PIIOJJDL44J34CDPFIJCG","download_json":"https://pith.science/pith/W7I52PIIOJJDL44J34CDPFIJCG.json","view_paper":"https://pith.science/paper/W7I52PII","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0904.3735&json=true","fetch_graph":"https://pith.science/api/pith-number/W7I52PIIOJJDL44J34CDPFIJCG/graph.json","fetch_events":"https://pith.science/api/pith-number/W7I52PIIOJJDL44J34CDPFIJCG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W7I52PIIOJJDL44J34CDPFIJCG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W7I52PIIOJJDL44J34CDPFIJCG/action/storage_attestation","attest_author":"https://pith.science/pith/W7I52PIIOJJDL44J34CDPFIJCG/action/author_attestation","sign_citation":"https://pith.science/pith/W7I52PIIOJJDL44J34CDPFIJCG/action/citation_signature","submit_replication":"https://pith.science/pith/W7I52PIIOJJDL44J34CDPFIJCG/action/replication_record"}},"created_at":"2026-05-18T02:13:57.720329+00:00","updated_at":"2026-05-18T02:13:57.720329+00:00"}