{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:REKGZTOGWPENYEWFN3TJT3ZLVT","short_pith_number":"pith:REKGZTOG","canonical_record":{"source":{"id":"1801.02761","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-09T02:36:04Z","cross_cats_sorted":[],"title_canon_sha256":"fdbfd08c459fe4b4f0e55a765ec0dfaebec5579b405c62b5a9a4e2e8815ed035","abstract_canon_sha256":"63234ddb984826a97518466d5c99a779a4a2c635c5060c9b69df688dcaa63019"},"schema_version":"1.0"},"canonical_sha256":"89146ccdc6b3c8dc12c56ee699ef2bacc2f985b2f70a654e7841a366a6fb55b9","source":{"kind":"arxiv","id":"1801.02761","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:REKGZTOGWPENYEWFN3TJT3ZLVT","target":"record","payload":{"canonical_record":{"source":{"id":"1801.02761","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-09T02:36:04Z","cross_cats_sorted":[],"title_canon_sha256":"fdbfd08c459fe4b4f0e55a765ec0dfaebec5579b405c62b5a9a4e2e8815ed035","abstract_canon_sha256":"63234ddb984826a97518466d5c99a779a4a2c635c5060c9b69df688dcaa63019"},"schema_version":"1.0"},"canonical_sha256":"89146ccdc6b3c8dc12c56ee699ef2bacc2f985b2f70a654e7841a366a6fb55b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:22.505711Z","signature_b64":"3inDF5HWnthOBX1NhWd1Lp8bj9435ntJnmkFoGc8DVbXPVsQu98NlH0cpsWR/VfGglGWzFZW/D/XvmjbOVWUDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89146ccdc6b3c8dc12c56ee699ef2bacc2f985b2f70a654e7841a366a6fb55b9","last_reissued_at":"2026-05-18T00:26:22.505102Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:22.505102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.02761","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:26:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EntXF4DzRG2XRvOy0Q3nX6bYbEcxuH5nzKo3H72ZFMQeR8hkYTGJ3Y/C7KSxPwB9NWg/oliiQKzN7KFNiHbUAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T04:38:32.420977Z"},"content_sha256":"ec60706b69119d778c505c12c4431e99600e58b09e3be0bebf6c77d9596c8189","schema_version":"1.0","event_id":"sha256:ec60706b69119d778c505c12c4431e99600e58b09e3be0bebf6c77d9596c8189"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:REKGZTOGWPENYEWFN3TJT3ZLVT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An analytical proof for synchronization of stochastic phase oscillator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"H.T. Tuan, N.T. The, T.S. Doan, Y. Sato","submitted_at":"2018-01-09T02:36:04Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02761","kind":"arxiv","version":1},"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":"2026-05-18T00:26:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z6c258y9GNr2e1ueLwQD4xBazohinz+W/MtN2oU2yri5kZooLYGRFLuodoZbVncXdznJfcD1w2Tpx5vOM5BdCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T04:38:32.421332Z"},"content_sha256":"1c5b26abab0ab6db83a4c50d1e627ace1ed480618bd7c606c8b937b51a5b9a17","schema_version":"1.0","event_id":"sha256:1c5b26abab0ab6db83a4c50d1e627ace1ed480618bd7c606c8b937b51a5b9a17"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/REKGZTOGWPENYEWFN3TJT3ZLVT/bundle.json","state_url":"https://pith.science/pith/REKGZTOGWPENYEWFN3TJT3ZLVT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/REKGZTOGWPENYEWFN3TJT3ZLVT/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":"2026-06-12T04:38:32Z","links":{"resolver":"https://pith.science/pith/REKGZTOGWPENYEWFN3TJT3ZLVT","bundle":"https://pith.science/pith/REKGZTOGWPENYEWFN3TJT3ZLVT/bundle.json","state":"https://pith.science/pith/REKGZTOGWPENYEWFN3TJT3ZLVT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/REKGZTOGWPENYEWFN3TJT3ZLVT/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IukxXVdWIODT2hsqN98tQav17XRqXH4FeBkteFTJauKc59t+hT8r/vRwXbImpiE5s3wB9n6Z5xl0DAmvDImqBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T04:38:32.423367Z","bundle_sha256":"84f1529feb17c5c3b1112af83cfd56a4d9584d449652b48f86b7ee3caeb74919"}}