{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4SSUPURBWFDEREFJA7QTMI6WFE","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":"92c19debaa183568aa397accbdb8dda65dea386427ee94ffcce49d27f6d7d7d3","cross_cats_sorted":["math.MP","nlin.CD","q-bio.NC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-03T20:16:52Z","title_canon_sha256":"8b3bfbe6196b76d915d7d9cbfd8f3c1706aa028851ea3d225c8ded5e07ae860e"},"schema_version":"1.0","source":{"id":"1106.0758","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.0758","created_at":"2026-05-18T02:21:44Z"},{"alias_kind":"arxiv_version","alias_value":"1106.0758v2","created_at":"2026-05-18T02:21:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0758","created_at":"2026-05-18T02:21:44Z"},{"alias_kind":"pith_short_12","alias_value":"4SSUPURBWFDE","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4SSUPURBWFDEREFJ","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4SSUPURB","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:692f0c42ac8c0e35d1235cc02abce053ed7a0c5efcd4fa2c5a3bf085f8f3556c","target":"graph","created_at":"2026-05-18T02:21:44Z","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":"Our main focus is on a general class of active rotators with mean field interactions, that is globally coupled large families of dynamical systems on the unit circle with non-trivial stochastic dynamics. Each isolated system is a diffusion process on a circle, with drift -delta V', where V' is a periodic function and delta is an intensity parameter. It is well known that the interacting dynamics is accurately described, in the limit of infinitely many interacting components, by a Fokker-Planck PDE and the model reduces for delta=0 to a particular case of the Kuramoto synchronization model, for","authors_text":"Christophe Poquet, Giambattista Giacomin, Khashayar Pakdaman, Xavier Pellegrin","cross_cats":["math.MP","nlin.CD","q-bio.NC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-03T20:16:52Z","title":"Transitions in active rotator systems: invariant hyperbolic manifold approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0758","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:f68a009f566bdc6c8eb02067b88c9d8f2c6c0c0e6dffbf8b11da3a672a16f8fb","target":"record","created_at":"2026-05-18T02:21:44Z","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":"92c19debaa183568aa397accbdb8dda65dea386427ee94ffcce49d27f6d7d7d3","cross_cats_sorted":["math.MP","nlin.CD","q-bio.NC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-03T20:16:52Z","title_canon_sha256":"8b3bfbe6196b76d915d7d9cbfd8f3c1706aa028851ea3d225c8ded5e07ae860e"},"schema_version":"1.0","source":{"id":"1106.0758","kind":"arxiv","version":2}},"canonical_sha256":"e4a547d221b1464890a907e13623d62928c9d018b422361bd07ff8c68a3e1fdd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4a547d221b1464890a907e13623d62928c9d018b422361bd07ff8c68a3e1fdd","first_computed_at":"2026-05-18T02:21:44.209013Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:44.209013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7CUqVu5+FXQQWr3cMtaMfxMiD9Sogx4ULOD9i6aZt0oORKhvem87nV9ieUViQxkXrsOV6KBzU+etCq00jM1iCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:44.209493Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.0758","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f68a009f566bdc6c8eb02067b88c9d8f2c6c0c0e6dffbf8b11da3a672a16f8fb","sha256:692f0c42ac8c0e35d1235cc02abce053ed7a0c5efcd4fa2c5a3bf085f8f3556c"],"state_sha256":"02c6f1e6c105b35fdbd92cb7672528503e1d7e81130b7353ee2e2486ac5cb992"}