{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PRWLD5VHBJYUDDZHLUXI4SW56W","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":"9f97d0f9817ed05a46768d32657e56e0cf9352587c45065a0fdbd4b167542242","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-17T14:45:07Z","title_canon_sha256":"27c766f90a9eee3467582d1b943582690f11edd67fb4776851a30e488acb5f28"},"schema_version":"1.0","source":{"id":"1703.06789","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.06789","created_at":"2026-05-18T00:48:21Z"},{"alias_kind":"arxiv_version","alias_value":"1703.06789v1","created_at":"2026-05-18T00:48:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06789","created_at":"2026-05-18T00:48:21Z"},{"alias_kind":"pith_short_12","alias_value":"PRWLD5VHBJYU","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PRWLD5VHBJYUDDZH","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PRWLD5VH","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:0ca62d2d1f0043edf4d97f07efa17f3f358dd438a673b16395d0baa7f72c7799","target":"graph","created_at":"2026-05-18T00:48:21Z","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":"A practical and accessible introduction to most probable phase portraits is given. The reader is assumed to be familiar with stochastic differential equations and Euler-Maruyama method in numerical simulation. The article first introduce the method to obtain most probable phase portraits and then give its numerical simulation which is based on Euler-Maruyama method. All of these are given by examples and easy to understand.","authors_text":"Bing Yang, Ling Wang, Zhu Zeng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-17T14:45:07Z","title":"Most Probable Phase Portraits of Stochastic Differential Equations and its Numerical Simulation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06789","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:fe5733b8ce8005e32ffe0d314861ac19de4e2f8a6a9dc532bc19da0a03fe656c","target":"record","created_at":"2026-05-18T00:48:21Z","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":"9f97d0f9817ed05a46768d32657e56e0cf9352587c45065a0fdbd4b167542242","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-17T14:45:07Z","title_canon_sha256":"27c766f90a9eee3467582d1b943582690f11edd67fb4776851a30e488acb5f28"},"schema_version":"1.0","source":{"id":"1703.06789","kind":"arxiv","version":1}},"canonical_sha256":"7c6cb1f6a70a71418f275d2e8e4addf5bacce9f05ccecaef448f0cc7d7a92239","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c6cb1f6a70a71418f275d2e8e4addf5bacce9f05ccecaef448f0cc7d7a92239","first_computed_at":"2026-05-18T00:48:21.719752Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:21.719752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"buul0fIs3nmRaldo/4d0o5r0m8yeJP6xwDQQKiSpKoRvedmeu3E6eNY/rcUe22smEj3TnKNHjoZWj3i1lSkQBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:21.720400Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.06789","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe5733b8ce8005e32ffe0d314861ac19de4e2f8a6a9dc532bc19da0a03fe656c","sha256:0ca62d2d1f0043edf4d97f07efa17f3f358dd438a673b16395d0baa7f72c7799"],"state_sha256":"5f9ffd5fbb5bbe71ec2e36d58810a4fd1845b3af49ba1425054b65152e5e1621"}