{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:REKGZTOGWPENYEWFN3TJT3ZLVT","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":"63234ddb984826a97518466d5c99a779a4a2c635c5060c9b69df688dcaa63019","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-09T02:36:04Z","title_canon_sha256":"fdbfd08c459fe4b4f0e55a765ec0dfaebec5579b405c62b5a9a4e2e8815ed035"},"schema_version":"1.0","source":{"id":"1801.02761","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.02761","created_at":"2026-05-18T00:26:22Z"},{"alias_kind":"arxiv_version","alias_value":"1801.02761v1","created_at":"2026-05-18T00:26:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.02761","created_at":"2026-05-18T00:26:22Z"},{"alias_kind":"pith_short_12","alias_value":"REKGZTOGWPEN","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"REKGZTOGWPENYEWF","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"REKGZTOG","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:1c5b26abab0ab6db83a4c50d1e627ace1ed480618bd7c606c8b937b51a5b9a17","target":"graph","created_at":"2026-05-18T00:26:22Z","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":"In this paper, we show that under a generic condition of the coefficient of a stochastic phase oscillator the Lyapunov exponent of the linearization along an arbitrary solution is always negative. Consequently, the generated random dynamical system exhibits a synchronization.","authors_text":"H.T. Tuan, N.T. The, T.S. Doan, Y. Sato","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-09T02:36:04Z","title":"An analytical proof for synchronization of stochastic phase oscillator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02761","kind":"arxiv","version":1},"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:ec60706b69119d778c505c12c4431e99600e58b09e3be0bebf6c77d9596c8189","target":"record","created_at":"2026-05-18T00:26:22Z","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":"63234ddb984826a97518466d5c99a779a4a2c635c5060c9b69df688dcaa63019","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-09T02:36:04Z","title_canon_sha256":"fdbfd08c459fe4b4f0e55a765ec0dfaebec5579b405c62b5a9a4e2e8815ed035"},"schema_version":"1.0","source":{"id":"1801.02761","kind":"arxiv","version":1}},"canonical_sha256":"89146ccdc6b3c8dc12c56ee699ef2bacc2f985b2f70a654e7841a366a6fb55b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89146ccdc6b3c8dc12c56ee699ef2bacc2f985b2f70a654e7841a366a6fb55b9","first_computed_at":"2026-05-18T00:26:22.505102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:22.505102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3inDF5HWnthOBX1NhWd1Lp8bj9435ntJnmkFoGc8DVbXPVsQu98NlH0cpsWR/VfGglGWzFZW/D/XvmjbOVWUDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:22.505711Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.02761","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec60706b69119d778c505c12c4431e99600e58b09e3be0bebf6c77d9596c8189","sha256:1c5b26abab0ab6db83a4c50d1e627ace1ed480618bd7c606c8b937b51a5b9a17"],"state_sha256":"83bbbe8e7167fa27d1efe4dc635a4e90f1f40126d2e082b8e2f1aee3fd2f9fd1"}