{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JYZMGC2NPJKVZZ5F2THUCWQFA5","short_pith_number":"pith:JYZMGC2N","canonical_record":{"source":{"id":"1503.09019","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-31T12:22:37Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"70a2ae283fe15670092c9941c7e9efe0c44faee09568c35e436d534d2fcc6e55","abstract_canon_sha256":"47895e4b32cdc868c41d3c6a4fdbdd5dae0346f9f4226d17687e1fed251b42c0"},"schema_version":"1.0"},"canonical_sha256":"4e32c30b4d7a555ce7a5d4cf415a0507660b4ae7c588ecc6832b514c5d09d3af","source":{"kind":"arxiv","id":"1503.09019","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.09019","created_at":"2026-05-18T02:19:51Z"},{"alias_kind":"arxiv_version","alias_value":"1503.09019v1","created_at":"2026-05-18T02:19:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.09019","created_at":"2026-05-18T02:19:51Z"},{"alias_kind":"pith_short_12","alias_value":"JYZMGC2NPJKV","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JYZMGC2NPJKVZZ5F","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JYZMGC2N","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JYZMGC2NPJKVZZ5F2THUCWQFA5","target":"record","payload":{"canonical_record":{"source":{"id":"1503.09019","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-31T12:22:37Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"70a2ae283fe15670092c9941c7e9efe0c44faee09568c35e436d534d2fcc6e55","abstract_canon_sha256":"47895e4b32cdc868c41d3c6a4fdbdd5dae0346f9f4226d17687e1fed251b42c0"},"schema_version":"1.0"},"canonical_sha256":"4e32c30b4d7a555ce7a5d4cf415a0507660b4ae7c588ecc6832b514c5d09d3af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:51.619290Z","signature_b64":"xE+essRRZbdo5C6iH22ISv4/YFGKW0BKpBXMSOF4T7zSfD4QeINIywa1SVBfRTweEyWuAAUIRzcSpRHsNWN3BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e32c30b4d7a555ce7a5d4cf415a0507660b4ae7c588ecc6832b514c5d09d3af","last_reissued_at":"2026-05-18T02:19:51.618631Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:51.618631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.09019","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":"2026-05-18T02:19:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d5z2O6vyxs/mUIkvEiw5HNhLGs1yf6KmQ8UCWQV7YGYRRyO6lJ5jnkhvKTFHiv003ljLsSpG9p+h9y/yfOM4DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:21:28.725355Z"},"content_sha256":"b4a6ac927168fac520da56ee69a7b303179227303951187f4292e4b8d66ed82c","schema_version":"1.0","event_id":"sha256:b4a6ac927168fac520da56ee69a7b303179227303951187f4292e4b8d66ed82c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JYZMGC2NPJKVZZ5F2THUCWQFA5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Construction of Malliavin differentiable strong solutions of SDEs under an integrability condition on the drift without the Yamada-Watanabe principle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"David R. Ba\\~nos, Frank Proske, Sindre Duedahl, Thilo Meyer-Brandis","submitted_at":"2015-03-31T12:22:37Z","abstract_excerpt":"In this paper we aim at employing a compactness criterion of Da Prato, Malliavin, Nualart for square integrable Brownian functionals to construct unique strong solutions of SDE's under an integrability condition on the drift coefficient. The obtained solutions turn out to be Malliavin differentiable and are used to derive a Bismut-Elworthy-Li formula for solutions of the Kolmogorov equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.09019","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":"2026-05-18T02:19:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MHdYKf5ly3h6YFCqjc8RyV27hC/nx3n44r3cIjF855jrNOjRfZ1SVf6gHaM7GwmByFFVZv6hPhka5QRDfPKxDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:21:28.726033Z"},"content_sha256":"711907acdb10eab36148d7b98fe8f08f62de2a2754325af57a566b5c30187392","schema_version":"1.0","event_id":"sha256:711907acdb10eab36148d7b98fe8f08f62de2a2754325af57a566b5c30187392"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JYZMGC2NPJKVZZ5F2THUCWQFA5/bundle.json","state_url":"https://pith.science/pith/JYZMGC2NPJKVZZ5F2THUCWQFA5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JYZMGC2NPJKVZZ5F2THUCWQFA5/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":"2026-06-05T00:21:28Z","links":{"resolver":"https://pith.science/pith/JYZMGC2NPJKVZZ5F2THUCWQFA5","bundle":"https://pith.science/pith/JYZMGC2NPJKVZZ5F2THUCWQFA5/bundle.json","state":"https://pith.science/pith/JYZMGC2NPJKVZZ5F2THUCWQFA5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JYZMGC2NPJKVZZ5F2THUCWQFA5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JYZMGC2NPJKVZZ5F2THUCWQFA5","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":"47895e4b32cdc868c41d3c6a4fdbdd5dae0346f9f4226d17687e1fed251b42c0","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-31T12:22:37Z","title_canon_sha256":"70a2ae283fe15670092c9941c7e9efe0c44faee09568c35e436d534d2fcc6e55"},"schema_version":"1.0","source":{"id":"1503.09019","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.09019","created_at":"2026-05-18T02:19:51Z"},{"alias_kind":"arxiv_version","alias_value":"1503.09019v1","created_at":"2026-05-18T02:19:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.09019","created_at":"2026-05-18T02:19:51Z"},{"alias_kind":"pith_short_12","alias_value":"JYZMGC2NPJKV","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JYZMGC2NPJKVZZ5F","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JYZMGC2N","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:711907acdb10eab36148d7b98fe8f08f62de2a2754325af57a566b5c30187392","target":"graph","created_at":"2026-05-18T02:19:51Z","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 aim at employing a compactness criterion of Da Prato, Malliavin, Nualart for square integrable Brownian functionals to construct unique strong solutions of SDE's under an integrability condition on the drift coefficient. The obtained solutions turn out to be Malliavin differentiable and are used to derive a Bismut-Elworthy-Li formula for solutions of the Kolmogorov equation.","authors_text":"David R. Ba\\~nos, Frank Proske, Sindre Duedahl, Thilo Meyer-Brandis","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-31T12:22:37Z","title":"Construction of Malliavin differentiable strong solutions of SDEs under an integrability condition on the drift without the Yamada-Watanabe principle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.09019","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:b4a6ac927168fac520da56ee69a7b303179227303951187f4292e4b8d66ed82c","target":"record","created_at":"2026-05-18T02:19:51Z","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":"47895e4b32cdc868c41d3c6a4fdbdd5dae0346f9f4226d17687e1fed251b42c0","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-31T12:22:37Z","title_canon_sha256":"70a2ae283fe15670092c9941c7e9efe0c44faee09568c35e436d534d2fcc6e55"},"schema_version":"1.0","source":{"id":"1503.09019","kind":"arxiv","version":1}},"canonical_sha256":"4e32c30b4d7a555ce7a5d4cf415a0507660b4ae7c588ecc6832b514c5d09d3af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e32c30b4d7a555ce7a5d4cf415a0507660b4ae7c588ecc6832b514c5d09d3af","first_computed_at":"2026-05-18T02:19:51.618631Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:51.618631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xE+essRRZbdo5C6iH22ISv4/YFGKW0BKpBXMSOF4T7zSfD4QeINIywa1SVBfRTweEyWuAAUIRzcSpRHsNWN3BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:51.619290Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.09019","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4a6ac927168fac520da56ee69a7b303179227303951187f4292e4b8d66ed82c","sha256:711907acdb10eab36148d7b98fe8f08f62de2a2754325af57a566b5c30187392"],"state_sha256":"6ff69a00e2c3aa31d89dc19ecf95c97713838d57058eb0eebd9e568972ffea53"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s5k81KebvWSFI/DBG768Gqe8gSBdkoE4MPcx1RvfHRDrj88G9zYMFEfjrdaK8jgyl11zNXrGL8HJiA13qJoBDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T00:21:28.729799Z","bundle_sha256":"c8ad59c4b2063b1d4b3c1a97da5fc9aa20f396113c86c1468add2bf8fc3a383d"}}