{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:L6GMEDA32E4XWEYYPAAJY736IV","short_pith_number":"pith:L6GMEDA3","canonical_record":{"source":{"id":"1803.06170","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-16T11:27:19Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"472da2f4232288e07291e88860cab3973da29bc8c7f3bb25c7316e9abf133e24","abstract_canon_sha256":"5e33cb2daf17382d69a77386507ff1db5225f78ac6caced93bef3a4817afae44"},"schema_version":"1.0"},"canonical_sha256":"5f8cc20c1bd1397b131878009c7f7e45750bd2315879e43831954c5933c05f03","source":{"kind":"arxiv","id":"1803.06170","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.06170","created_at":"2026-05-18T00:20:50Z"},{"alias_kind":"arxiv_version","alias_value":"1803.06170v1","created_at":"2026-05-18T00:20:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.06170","created_at":"2026-05-18T00:20:50Z"},{"alias_kind":"pith_short_12","alias_value":"L6GMEDA32E4X","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"L6GMEDA32E4XWEYY","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"L6GMEDA3","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:L6GMEDA32E4XWEYYPAAJY736IV","target":"record","payload":{"canonical_record":{"source":{"id":"1803.06170","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-16T11:27:19Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"472da2f4232288e07291e88860cab3973da29bc8c7f3bb25c7316e9abf133e24","abstract_canon_sha256":"5e33cb2daf17382d69a77386507ff1db5225f78ac6caced93bef3a4817afae44"},"schema_version":"1.0"},"canonical_sha256":"5f8cc20c1bd1397b131878009c7f7e45750bd2315879e43831954c5933c05f03","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:50.387186Z","signature_b64":"W4YORzOjtgOWGvNcM/9/wfEJ4HGKiyyo6qqKCJPN5S7VbqPjU+Ti1N+IQeJ37OeOOvs5U6wYax3T6jSqS53eBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f8cc20c1bd1397b131878009c7f7e45750bd2315879e43831954c5933c05f03","last_reissued_at":"2026-05-18T00:20:50.386751Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:50.386751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.06170","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":"2026-05-18T00:20:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A2IGR7NrcK1bz1jprPF8KY5H5XTprtSRH/SGCam79aIWTfjLSx8C6hRb0XS98Lr1qvGS+v0AVEHeemCjg5x/DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:35:43.756981Z"},"content_sha256":"dd8dfb115f8f65e0f1d2fa8e1e19d8326745e26d8cf34b9c474c723e3c0d770d","schema_version":"1.0","event_id":"sha256:dd8dfb115f8f65e0f1d2fa8e1e19d8326745e26d8cf34b9c474c723e3c0d770d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:L6GMEDA32E4XWEYYPAAJY736IV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence and smoothness of the density for the stochastic continuity equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Christian Olivera, Ciprian A. Tudor, David A.C. Mollinedo","submitted_at":"2018-03-16T11:27:19Z","abstract_excerpt":"We consider the stochastic continuity equation driven by Brownian motion. We use the techniques of the Malliavin calculus to show that the law of the solution has a density with respect to the Lebesgue measure. We also prove that the density is Holder continuous and satisfies some Gaussian-type estimates."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06170","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":"2026-05-18T00:20:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Jzuko09ISX/E5V57G4AxnrXkakJtkgB6BGHaEeG6IYR8BgDWNbyAewRzU/DAIh0gguqBYrTX/x47HpHYRC4AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:35:43.758060Z"},"content_sha256":"d7d9793af80b673aaa09ea731ceee810c280f4102aa440dddc9ebc032ca2ee6c","schema_version":"1.0","event_id":"sha256:d7d9793af80b673aaa09ea731ceee810c280f4102aa440dddc9ebc032ca2ee6c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L6GMEDA32E4XWEYYPAAJY736IV/bundle.json","state_url":"https://pith.science/pith/L6GMEDA32E4XWEYYPAAJY736IV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L6GMEDA32E4XWEYYPAAJY736IV/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":"2026-05-28T22:35:43Z","links":{"resolver":"https://pith.science/pith/L6GMEDA32E4XWEYYPAAJY736IV","bundle":"https://pith.science/pith/L6GMEDA32E4XWEYYPAAJY736IV/bundle.json","state":"https://pith.science/pith/L6GMEDA32E4XWEYYPAAJY736IV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L6GMEDA32E4XWEYYPAAJY736IV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:L6GMEDA32E4XWEYYPAAJY736IV","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":"5e33cb2daf17382d69a77386507ff1db5225f78ac6caced93bef3a4817afae44","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-16T11:27:19Z","title_canon_sha256":"472da2f4232288e07291e88860cab3973da29bc8c7f3bb25c7316e9abf133e24"},"schema_version":"1.0","source":{"id":"1803.06170","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.06170","created_at":"2026-05-18T00:20:50Z"},{"alias_kind":"arxiv_version","alias_value":"1803.06170v1","created_at":"2026-05-18T00:20:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.06170","created_at":"2026-05-18T00:20:50Z"},{"alias_kind":"pith_short_12","alias_value":"L6GMEDA32E4X","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"L6GMEDA32E4XWEYY","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"L6GMEDA3","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:d7d9793af80b673aaa09ea731ceee810c280f4102aa440dddc9ebc032ca2ee6c","target":"graph","created_at":"2026-05-18T00:20:50Z","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":"We consider the stochastic continuity equation driven by Brownian motion. We use the techniques of the Malliavin calculus to show that the law of the solution has a density with respect to the Lebesgue measure. We also prove that the density is Holder continuous and satisfies some Gaussian-type estimates.","authors_text":"Christian Olivera, Ciprian A. Tudor, David A.C. Mollinedo","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-16T11:27:19Z","title":"Existence and smoothness of the density for the stochastic continuity equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06170","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:dd8dfb115f8f65e0f1d2fa8e1e19d8326745e26d8cf34b9c474c723e3c0d770d","target":"record","created_at":"2026-05-18T00:20:50Z","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":"5e33cb2daf17382d69a77386507ff1db5225f78ac6caced93bef3a4817afae44","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-16T11:27:19Z","title_canon_sha256":"472da2f4232288e07291e88860cab3973da29bc8c7f3bb25c7316e9abf133e24"},"schema_version":"1.0","source":{"id":"1803.06170","kind":"arxiv","version":1}},"canonical_sha256":"5f8cc20c1bd1397b131878009c7f7e45750bd2315879e43831954c5933c05f03","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f8cc20c1bd1397b131878009c7f7e45750bd2315879e43831954c5933c05f03","first_computed_at":"2026-05-18T00:20:50.386751Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:50.386751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W4YORzOjtgOWGvNcM/9/wfEJ4HGKiyyo6qqKCJPN5S7VbqPjU+Ti1N+IQeJ37OeOOvs5U6wYax3T6jSqS53eBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:50.387186Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.06170","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd8dfb115f8f65e0f1d2fa8e1e19d8326745e26d8cf34b9c474c723e3c0d770d","sha256:d7d9793af80b673aaa09ea731ceee810c280f4102aa440dddc9ebc032ca2ee6c"],"state_sha256":"dff546d3a3494b11e67c16d0dd7b2150b537c5808ca9a21a2b7f9abb2158a40f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M6hSm9fHAHliyZFf/Mui2T4RvpuxNsxwBGoI+Ry8/6jMjRuzDP6lSw6EpKDvzD57ZqaWDSFuiJ138TbsjPWjDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:35:43.762100Z","bundle_sha256":"317457525511628309bafa29b66fbf136ab02bbbfe2c59ce9821ecf8ac91b28b"}}