{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:R4LCIWE6SZHARNIZ7UZUJAF3RB","short_pith_number":"pith:R4LCIWE6","schema_version":"1.0","canonical_sha256":"8f1624589e964e08b519fd334480bb8843ef47112000de5201027992c36d2c41","source":{"kind":"arxiv","id":"1808.07833","version":3},"attestation_state":"computed","paper":{"title":"Collective mode reductions for populations of coupled noisy oscillators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"nlin.AO","authors_text":"Arkady Pikovsky, Denis S. Goldobin, Irina V. Tyulkina, Lyudmila S. Klimenko","submitted_at":"2018-08-23T16:40:35Z","abstract_excerpt":"We analyze accuracy of different low-dimensional reductions of the collective dynamics in large populations of coupled phase oscillators with intrinsic noise. Three approximations are considered: (i) the Ott-Antonsen ansatz, (ii) the Gaussian ansatz, and (iii) a two-cumulant truncation of the circular cumulant representation of the original system's dynamics. For the latter we suggest a closure, which makes the truncation, for small noise, a rigorous first-order correction to the Ott-Antonsen ansatz, and simultaneously is a generalization of the Gaussian ansatz. The Kuramoto model with intrins"},"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":"1808.07833","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2018-08-23T16:40:35Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"d6a6fe2f318d92c10f59ba820daa534dacd5aa0d954138e41fefb399785be934","abstract_canon_sha256":"b080be00bef3252e59898e45c5d4dc099087e523098db2f96b11d7825b473d20"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:24.173049Z","signature_b64":"PDF8Amv8nVKOplHL/yNCW7vU+axbjXLykaNge6p3nM1nucJltAiJT4g6869LvzYknjGBactpWanVFE3QOYcGDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f1624589e964e08b519fd334480bb8843ef47112000de5201027992c36d2c41","last_reissued_at":"2026-05-18T00:03:24.172255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:24.172255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Collective mode reductions for populations of coupled noisy oscillators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"nlin.AO","authors_text":"Arkady Pikovsky, Denis S. Goldobin, Irina V. Tyulkina, Lyudmila S. Klimenko","submitted_at":"2018-08-23T16:40:35Z","abstract_excerpt":"We analyze accuracy of different low-dimensional reductions of the collective dynamics in large populations of coupled phase oscillators with intrinsic noise. Three approximations are considered: (i) the Ott-Antonsen ansatz, (ii) the Gaussian ansatz, and (iii) a two-cumulant truncation of the circular cumulant representation of the original system's dynamics. For the latter we suggest a closure, which makes the truncation, for small noise, a rigorous first-order correction to the Ott-Antonsen ansatz, and simultaneously is a generalization of the Gaussian ansatz. The Kuramoto model with intrins"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07833","kind":"arxiv","version":3},"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":"1808.07833","created_at":"2026-05-18T00:03:24.172377+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.07833v3","created_at":"2026-05-18T00:03:24.172377+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.07833","created_at":"2026-05-18T00:03:24.172377+00:00"},{"alias_kind":"pith_short_12","alias_value":"R4LCIWE6SZHA","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"R4LCIWE6SZHARNIZ","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"R4LCIWE6","created_at":"2026-05-18T12:32:50.500415+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/R4LCIWE6SZHARNIZ7UZUJAF3RB","json":"https://pith.science/pith/R4LCIWE6SZHARNIZ7UZUJAF3RB.json","graph_json":"https://pith.science/api/pith-number/R4LCIWE6SZHARNIZ7UZUJAF3RB/graph.json","events_json":"https://pith.science/api/pith-number/R4LCIWE6SZHARNIZ7UZUJAF3RB/events.json","paper":"https://pith.science/paper/R4LCIWE6"},"agent_actions":{"view_html":"https://pith.science/pith/R4LCIWE6SZHARNIZ7UZUJAF3RB","download_json":"https://pith.science/pith/R4LCIWE6SZHARNIZ7UZUJAF3RB.json","view_paper":"https://pith.science/paper/R4LCIWE6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.07833&json=true","fetch_graph":"https://pith.science/api/pith-number/R4LCIWE6SZHARNIZ7UZUJAF3RB/graph.json","fetch_events":"https://pith.science/api/pith-number/R4LCIWE6SZHARNIZ7UZUJAF3RB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R4LCIWE6SZHARNIZ7UZUJAF3RB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R4LCIWE6SZHARNIZ7UZUJAF3RB/action/storage_attestation","attest_author":"https://pith.science/pith/R4LCIWE6SZHARNIZ7UZUJAF3RB/action/author_attestation","sign_citation":"https://pith.science/pith/R4LCIWE6SZHARNIZ7UZUJAF3RB/action/citation_signature","submit_replication":"https://pith.science/pith/R4LCIWE6SZHARNIZ7UZUJAF3RB/action/replication_record"}},"created_at":"2026-05-18T00:03:24.172377+00:00","updated_at":"2026-05-18T00:03:24.172377+00:00"}