{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:PJU2KJEILZIN2B2Y3J7MHG7Q2R","short_pith_number":"pith:PJU2KJEI","canonical_record":{"source":{"id":"1409.3927","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-13T09:25:14Z","cross_cats_sorted":[],"title_canon_sha256":"f514d10cb4da0e380f883462b7a57545d2295a2b11fd672da94886304f62b5a4","abstract_canon_sha256":"e46c71f1035ee552a57a09f7f9ba7c7d87133f4723619fc9c06706b7eb7a8375"},"schema_version":"1.0"},"canonical_sha256":"7a69a524885e50dd0758da7ec39bf0d4639b89a15bb38395fff7a0524595d9ef","source":{"kind":"arxiv","id":"1409.3927","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.3927","created_at":"2026-05-18T00:32:31Z"},{"alias_kind":"arxiv_version","alias_value":"1409.3927v2","created_at":"2026-05-18T00:32:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3927","created_at":"2026-05-18T00:32:31Z"},{"alias_kind":"pith_short_12","alias_value":"PJU2KJEILZIN","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PJU2KJEILZIN2B2Y","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PJU2KJEI","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:PJU2KJEILZIN2B2Y3J7MHG7Q2R","target":"record","payload":{"canonical_record":{"source":{"id":"1409.3927","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-13T09:25:14Z","cross_cats_sorted":[],"title_canon_sha256":"f514d10cb4da0e380f883462b7a57545d2295a2b11fd672da94886304f62b5a4","abstract_canon_sha256":"e46c71f1035ee552a57a09f7f9ba7c7d87133f4723619fc9c06706b7eb7a8375"},"schema_version":"1.0"},"canonical_sha256":"7a69a524885e50dd0758da7ec39bf0d4639b89a15bb38395fff7a0524595d9ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:31.674517Z","signature_b64":"CwXreDDz9JzAlNFILdZFTO6Kt4XudC0F1DLvHZtkUNjyDKTnIZLZXcIVL3c2KAKcfvgmYzHQM9TyCSvov6rqDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a69a524885e50dd0758da7ec39bf0d4639b89a15bb38395fff7a0524595d9ef","last_reissued_at":"2026-05-18T00:32:31.673885Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:31.673885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.3927","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":"2026-05-18T00:32:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mHA/wvyY1yCsKehPicPa/geSfd22NayK0D3/IOefOopdFvHInaoxnHLj78gnsBnHkFzBaWdT/ThDqsmWqqdxBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T04:59:33.377604Z"},"content_sha256":"ccd310c4570b08e759db0fe44bd50100b2625d7a1e446f2cdf51433b523f9f0d","schema_version":"1.0","event_id":"sha256:ccd310c4570b08e759db0fe44bd50100b2625d7a1e446f2cdf51433b523f9f0d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:PJU2KJEILZIN2B2Y3J7MHG7Q2R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Smoothness of density for stochastic differential equations with Markovian switching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Nualart, Xiaobin Sun, Yaozhong Hu, Yingchao Xie","submitted_at":"2014-09-13T09:25:14Z","abstract_excerpt":"This paper is concerned with a class of stochastic differential equations with Markovian switching. The Malliavin calculus is used to study the smoothness of the density of the solution under a H\\\"{o}rmander type condition. Furthermore, we obtain a Bismut type formula which is used to establish the strong Feller property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3927","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":"2026-05-18T00:32:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NjHfphU/L5GFx17uGktJUkINfBeEtJwTwcbSiz4LEZapfR96n/XpR1bAu9XBvMS8sJtyPThU6J6T5X1oWrmqDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T04:59:33.378259Z"},"content_sha256":"134b41c6663d9a8072e5d7a24bd1df4856553094417bbaa2689f271bd9ea04db","schema_version":"1.0","event_id":"sha256:134b41c6663d9a8072e5d7a24bd1df4856553094417bbaa2689f271bd9ea04db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PJU2KJEILZIN2B2Y3J7MHG7Q2R/bundle.json","state_url":"https://pith.science/pith/PJU2KJEILZIN2B2Y3J7MHG7Q2R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PJU2KJEILZIN2B2Y3J7MHG7Q2R/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":"2026-05-25T04:59:33Z","links":{"resolver":"https://pith.science/pith/PJU2KJEILZIN2B2Y3J7MHG7Q2R","bundle":"https://pith.science/pith/PJU2KJEILZIN2B2Y3J7MHG7Q2R/bundle.json","state":"https://pith.science/pith/PJU2KJEILZIN2B2Y3J7MHG7Q2R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PJU2KJEILZIN2B2Y3J7MHG7Q2R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PJU2KJEILZIN2B2Y3J7MHG7Q2R","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":"e46c71f1035ee552a57a09f7f9ba7c7d87133f4723619fc9c06706b7eb7a8375","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-13T09:25:14Z","title_canon_sha256":"f514d10cb4da0e380f883462b7a57545d2295a2b11fd672da94886304f62b5a4"},"schema_version":"1.0","source":{"id":"1409.3927","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.3927","created_at":"2026-05-18T00:32:31Z"},{"alias_kind":"arxiv_version","alias_value":"1409.3927v2","created_at":"2026-05-18T00:32:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3927","created_at":"2026-05-18T00:32:31Z"},{"alias_kind":"pith_short_12","alias_value":"PJU2KJEILZIN","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PJU2KJEILZIN2B2Y","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PJU2KJEI","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:134b41c6663d9a8072e5d7a24bd1df4856553094417bbaa2689f271bd9ea04db","target":"graph","created_at":"2026-05-18T00:32:31Z","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":"This paper is concerned with a class of stochastic differential equations with Markovian switching. The Malliavin calculus is used to study the smoothness of the density of the solution under a H\\\"{o}rmander type condition. Furthermore, we obtain a Bismut type formula which is used to establish the strong Feller property.","authors_text":"David Nualart, Xiaobin Sun, Yaozhong Hu, Yingchao Xie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-13T09:25:14Z","title":"Smoothness of density for stochastic differential equations with Markovian switching"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3927","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:ccd310c4570b08e759db0fe44bd50100b2625d7a1e446f2cdf51433b523f9f0d","target":"record","created_at":"2026-05-18T00:32:31Z","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":"e46c71f1035ee552a57a09f7f9ba7c7d87133f4723619fc9c06706b7eb7a8375","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-13T09:25:14Z","title_canon_sha256":"f514d10cb4da0e380f883462b7a57545d2295a2b11fd672da94886304f62b5a4"},"schema_version":"1.0","source":{"id":"1409.3927","kind":"arxiv","version":2}},"canonical_sha256":"7a69a524885e50dd0758da7ec39bf0d4639b89a15bb38395fff7a0524595d9ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a69a524885e50dd0758da7ec39bf0d4639b89a15bb38395fff7a0524595d9ef","first_computed_at":"2026-05-18T00:32:31.673885Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:31.673885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CwXreDDz9JzAlNFILdZFTO6Kt4XudC0F1DLvHZtkUNjyDKTnIZLZXcIVL3c2KAKcfvgmYzHQM9TyCSvov6rqDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:31.674517Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.3927","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ccd310c4570b08e759db0fe44bd50100b2625d7a1e446f2cdf51433b523f9f0d","sha256:134b41c6663d9a8072e5d7a24bd1df4856553094417bbaa2689f271bd9ea04db"],"state_sha256":"2189d361d119d5660e65d4371a2d4112a9ba3d9d53e82a93a7aa4685ddbf7137"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aFUDdb6RxS6dw9pJQhx7uvstzzWjfnQ/jcPh9gITu/DDaBDl0uwEHmjDOioWuVV+1Om/+L6C7vi2Cy1f6DMZCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T04:59:33.381922Z","bundle_sha256":"d86794e91ca30c4970ffc79678677204d86fcf5b5a617503e32c66aa62be9f63"}}