{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3MBHWADKK4PYNVF63MD3KPQGQV","short_pith_number":"pith:3MBHWADK","canonical_record":{"source":{"id":"1305.6747","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-29T10:03:58Z","cross_cats_sorted":[],"title_canon_sha256":"df7290f5f83730a95001f1c2a693f7128d0b3543de36e2293bd6bd4f5d608e2b","abstract_canon_sha256":"cf8c1e03a1b1dfce09c302d93040c40174c0d4af8630721b9a664fe37e66d8df"},"schema_version":"1.0"},"canonical_sha256":"db027b006a571f86d4bedb07b53e0685798e840b598d2856d9db77d87a3bf07f","source":{"kind":"arxiv","id":"1305.6747","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6747","created_at":"2026-05-18T02:57:43Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6747v2","created_at":"2026-05-18T02:57:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6747","created_at":"2026-05-18T02:57:43Z"},{"alias_kind":"pith_short_12","alias_value":"3MBHWADKK4PY","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3MBHWADKK4PYNVF6","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3MBHWADK","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3MBHWADKK4PYNVF63MD3KPQGQV","target":"record","payload":{"canonical_record":{"source":{"id":"1305.6747","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-29T10:03:58Z","cross_cats_sorted":[],"title_canon_sha256":"df7290f5f83730a95001f1c2a693f7128d0b3543de36e2293bd6bd4f5d608e2b","abstract_canon_sha256":"cf8c1e03a1b1dfce09c302d93040c40174c0d4af8630721b9a664fe37e66d8df"},"schema_version":"1.0"},"canonical_sha256":"db027b006a571f86d4bedb07b53e0685798e840b598d2856d9db77d87a3bf07f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:43.598715Z","signature_b64":"1KkYqZP169UQ4vlFcFOu/Hyjo03QYxfVV+gFgVr5EjtL9PgNYUDsqglgUMobyVC9vbqYs6rGaJIqbcSO78T4BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db027b006a571f86d4bedb07b53e0685798e840b598d2856d9db77d87a3bf07f","last_reissued_at":"2026-05-18T02:57:43.598098Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:43.598098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.6747","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:57:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"db4jzzk2/WGNlqPHejxyne47JKZLrpC9U3+PP9F8/ndwaxJcUbjw67XEI03BWjmyfGra+ugHQv9gmmYUrnT+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T02:48:37.002492Z"},"content_sha256":"b72d7b9892ca71860a87c99b2120d091e0e5df766d611f8512b38b45795685d6","schema_version":"1.0","event_id":"sha256:b72d7b9892ca71860a87c99b2120d091e0e5df766d611f8512b38b45795685d6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3MBHWADKK4PYNVF63MD3KPQGQV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weak and strong solutions of general stochastic models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Thomas G. Kurtz","submitted_at":"2013-05-29T10:03:58Z","abstract_excerpt":"Typically, a stochastic model relates stochastic \"inputs\" and, perhaps, controls to stochastic \"outputs\". A general version of the Yamada-Watanabe and Engelbert theorems relating existence and uniqueness of weak and strong solutions of stochastic equations is given in this context. A notion of {\\em compatibility} between inputs and outputs is critical in relating the general result to its classical forebears. The relationship between the compatibility condition and the usual formulation of stochastic differential equations driven by semimartingales is discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6747","kind":"arxiv","version":2},"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":"2026-05-18T02:57:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qoaFtw8kdVFa0q31CqaqTDyW9KwjWB9LNtCP0S9vClXkBK5vaFCgyofXr0HRNcukraCops5UmekgusoUgHBqAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T02:48:37.003072Z"},"content_sha256":"ebb99ac2d0b35ba04d4cd232d1a09bd9084bb326e25c45e202ba0a1ec0b996d8","schema_version":"1.0","event_id":"sha256:ebb99ac2d0b35ba04d4cd232d1a09bd9084bb326e25c45e202ba0a1ec0b996d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3MBHWADKK4PYNVF63MD3KPQGQV/bundle.json","state_url":"https://pith.science/pith/3MBHWADKK4PYNVF63MD3KPQGQV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3MBHWADKK4PYNVF63MD3KPQGQV/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":"2026-07-02T02:48:37Z","links":{"resolver":"https://pith.science/pith/3MBHWADKK4PYNVF63MD3KPQGQV","bundle":"https://pith.science/pith/3MBHWADKK4PYNVF63MD3KPQGQV/bundle.json","state":"https://pith.science/pith/3MBHWADKK4PYNVF63MD3KPQGQV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3MBHWADKK4PYNVF63MD3KPQGQV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3MBHWADKK4PYNVF63MD3KPQGQV","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":"cf8c1e03a1b1dfce09c302d93040c40174c0d4af8630721b9a664fe37e66d8df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-29T10:03:58Z","title_canon_sha256":"df7290f5f83730a95001f1c2a693f7128d0b3543de36e2293bd6bd4f5d608e2b"},"schema_version":"1.0","source":{"id":"1305.6747","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6747","created_at":"2026-05-18T02:57:43Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6747v2","created_at":"2026-05-18T02:57:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6747","created_at":"2026-05-18T02:57:43Z"},{"alias_kind":"pith_short_12","alias_value":"3MBHWADKK4PY","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3MBHWADKK4PYNVF6","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3MBHWADK","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:ebb99ac2d0b35ba04d4cd232d1a09bd9084bb326e25c45e202ba0a1ec0b996d8","target":"graph","created_at":"2026-05-18T02:57:43Z","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":"Typically, a stochastic model relates stochastic \"inputs\" and, perhaps, controls to stochastic \"outputs\". A general version of the Yamada-Watanabe and Engelbert theorems relating existence and uniqueness of weak and strong solutions of stochastic equations is given in this context. A notion of {\\em compatibility} between inputs and outputs is critical in relating the general result to its classical forebears. The relationship between the compatibility condition and the usual formulation of stochastic differential equations driven by semimartingales is discussed.","authors_text":"Thomas G. Kurtz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-29T10:03:58Z","title":"Weak and strong solutions of general stochastic models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6747","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:b72d7b9892ca71860a87c99b2120d091e0e5df766d611f8512b38b45795685d6","target":"record","created_at":"2026-05-18T02:57:43Z","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":"cf8c1e03a1b1dfce09c302d93040c40174c0d4af8630721b9a664fe37e66d8df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-29T10:03:58Z","title_canon_sha256":"df7290f5f83730a95001f1c2a693f7128d0b3543de36e2293bd6bd4f5d608e2b"},"schema_version":"1.0","source":{"id":"1305.6747","kind":"arxiv","version":2}},"canonical_sha256":"db027b006a571f86d4bedb07b53e0685798e840b598d2856d9db77d87a3bf07f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db027b006a571f86d4bedb07b53e0685798e840b598d2856d9db77d87a3bf07f","first_computed_at":"2026-05-18T02:57:43.598098Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:43.598098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1KkYqZP169UQ4vlFcFOu/Hyjo03QYxfVV+gFgVr5EjtL9PgNYUDsqglgUMobyVC9vbqYs6rGaJIqbcSO78T4BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:43.598715Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.6747","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b72d7b9892ca71860a87c99b2120d091e0e5df766d611f8512b38b45795685d6","sha256:ebb99ac2d0b35ba04d4cd232d1a09bd9084bb326e25c45e202ba0a1ec0b996d8"],"state_sha256":"198728bc91f83fdf65a655e63e4fa1d218985b84e2e48869e79987d13149fe97"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/4jc+v/BL5nycVReefMFFNwRd4qtRZdqu6vagh96j68UHf4KuqfB3nczIT7T7kSd+EgpGWv+1OJkaQjRDr4KCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T02:48:37.008000Z","bundle_sha256":"5a7e2e97755c4772ca033544fe737277d3c2a33fc3dbf5627f296550326e661f"}}