{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:MGVECSGGVYX2L2YNPAW5BI7KCD","short_pith_number":"pith:MGVECSGG","canonical_record":{"source":{"id":"1107.0096","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-01T02:56:21Z","cross_cats_sorted":[],"title_canon_sha256":"5d0ea9b4d4cc102ac5755e2ce6f519194901f3b962a254d92c1fd493965eadaa","abstract_canon_sha256":"d9776d4da0f70293ad0369ccbb2ebfbf0e2b7f8ae774edbcaf8c44283cbeb197"},"schema_version":"1.0"},"canonical_sha256":"61aa4148c6ae2fa5eb0d782dd0a3ea10f61a87dc64c729b9c34b2292a5868234","source":{"kind":"arxiv","id":"1107.0096","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0096","created_at":"2026-05-18T04:00:26Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0096v3","created_at":"2026-05-18T04:00:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0096","created_at":"2026-05-18T04:00:26Z"},{"alias_kind":"pith_short_12","alias_value":"MGVECSGGVYX2","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MGVECSGGVYX2L2YN","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MGVECSGG","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:MGVECSGGVYX2L2YNPAW5BI7KCD","target":"record","payload":{"canonical_record":{"source":{"id":"1107.0096","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-01T02:56:21Z","cross_cats_sorted":[],"title_canon_sha256":"5d0ea9b4d4cc102ac5755e2ce6f519194901f3b962a254d92c1fd493965eadaa","abstract_canon_sha256":"d9776d4da0f70293ad0369ccbb2ebfbf0e2b7f8ae774edbcaf8c44283cbeb197"},"schema_version":"1.0"},"canonical_sha256":"61aa4148c6ae2fa5eb0d782dd0a3ea10f61a87dc64c729b9c34b2292a5868234","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:26.698876Z","signature_b64":"4c7WyG05EbMF8Ztu644kFICZq3d6io9Xf1X0EdqbTXm+Md1bLByyTK/xK7VVL6+ULHJHYYlIll2QlVOi315PCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61aa4148c6ae2fa5eb0d782dd0a3ea10f61a87dc64c729b9c34b2292a5868234","last_reissued_at":"2026-05-18T04:00:26.698195Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:26.698195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.0096","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:00:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VltcVpUWfvAfLRWkcBNKARNSDO5JUM1lKG4oqAUQmZ3qaKGneAH7u0aLx9LKLBugd3LsgVMUF66vEPRzQQi3CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T12:14:34.567670Z"},"content_sha256":"18ecc16a604c4536bace0a12488c377104e70e4e3993f802cfea96a003d28698","schema_version":"1.0","event_id":"sha256:18ecc16a604c4536bace0a12488c377104e70e4e3993f802cfea96a003d28698"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:MGVECSGGVYX2L2YNPAW5BI7KCD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Derivative Formula and Applications for Degenerate Diffusion Semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Feng-Yu Wang, Xi-Cheng Zhang","submitted_at":"2011-07-01T02:56:21Z","abstract_excerpt":"By using the Malliavin calculus and solving a control problem, Bismut type derivative formulae are established for a class of degenerate diffusion semigroups with non-linear drifts. As applications, explicit gradient estimates and Harnack inequalities are derived."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0096","kind":"arxiv","version":3},"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":"2026-05-18T04:00:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pzUYbQKNlYASq7Arj/DI6u1lOPwX0aUaUxJFTmjaxaIHMP9UqvW6xgm4YmFZ/DpKhEX6cWg7a8kh+Ry7OxPWAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T12:14:34.568343Z"},"content_sha256":"d5104172be4e2dc89d054e2130d006bbb0ddcdd8513e432b7b9281aa4a57b1ce","schema_version":"1.0","event_id":"sha256:d5104172be4e2dc89d054e2130d006bbb0ddcdd8513e432b7b9281aa4a57b1ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MGVECSGGVYX2L2YNPAW5BI7KCD/bundle.json","state_url":"https://pith.science/pith/MGVECSGGVYX2L2YNPAW5BI7KCD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MGVECSGGVYX2L2YNPAW5BI7KCD/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":"2026-05-23T12:14:34Z","links":{"resolver":"https://pith.science/pith/MGVECSGGVYX2L2YNPAW5BI7KCD","bundle":"https://pith.science/pith/MGVECSGGVYX2L2YNPAW5BI7KCD/bundle.json","state":"https://pith.science/pith/MGVECSGGVYX2L2YNPAW5BI7KCD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MGVECSGGVYX2L2YNPAW5BI7KCD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MGVECSGGVYX2L2YNPAW5BI7KCD","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":"d9776d4da0f70293ad0369ccbb2ebfbf0e2b7f8ae774edbcaf8c44283cbeb197","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-01T02:56:21Z","title_canon_sha256":"5d0ea9b4d4cc102ac5755e2ce6f519194901f3b962a254d92c1fd493965eadaa"},"schema_version":"1.0","source":{"id":"1107.0096","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0096","created_at":"2026-05-18T04:00:26Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0096v3","created_at":"2026-05-18T04:00:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0096","created_at":"2026-05-18T04:00:26Z"},{"alias_kind":"pith_short_12","alias_value":"MGVECSGGVYX2","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MGVECSGGVYX2L2YN","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MGVECSGG","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:d5104172be4e2dc89d054e2130d006bbb0ddcdd8513e432b7b9281aa4a57b1ce","target":"graph","created_at":"2026-05-18T04:00:26Z","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":"By using the Malliavin calculus and solving a control problem, Bismut type derivative formulae are established for a class of degenerate diffusion semigroups with non-linear drifts. As applications, explicit gradient estimates and Harnack inequalities are derived.","authors_text":"Feng-Yu Wang, Xi-Cheng Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-01T02:56:21Z","title":"Derivative Formula and Applications for Degenerate Diffusion Semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0096","kind":"arxiv","version":3},"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":"sha256:18ecc16a604c4536bace0a12488c377104e70e4e3993f802cfea96a003d28698","target":"record","created_at":"2026-05-18T04:00:26Z","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":"d9776d4da0f70293ad0369ccbb2ebfbf0e2b7f8ae774edbcaf8c44283cbeb197","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-01T02:56:21Z","title_canon_sha256":"5d0ea9b4d4cc102ac5755e2ce6f519194901f3b962a254d92c1fd493965eadaa"},"schema_version":"1.0","source":{"id":"1107.0096","kind":"arxiv","version":3}},"canonical_sha256":"61aa4148c6ae2fa5eb0d782dd0a3ea10f61a87dc64c729b9c34b2292a5868234","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61aa4148c6ae2fa5eb0d782dd0a3ea10f61a87dc64c729b9c34b2292a5868234","first_computed_at":"2026-05-18T04:00:26.698195Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:26.698195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4c7WyG05EbMF8Ztu644kFICZq3d6io9Xf1X0EdqbTXm+Md1bLByyTK/xK7VVL6+ULHJHYYlIll2QlVOi315PCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:26.698876Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0096","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18ecc16a604c4536bace0a12488c377104e70e4e3993f802cfea96a003d28698","sha256:d5104172be4e2dc89d054e2130d006bbb0ddcdd8513e432b7b9281aa4a57b1ce"],"state_sha256":"1e98a8df9171ff27b25a1f47afe5d438dc99b4cf416b81bd1896f14511330c8d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dg9Gkcz4TtSHLnvur+MH6c4tNBhEbANhKWUiAGrJmu925v2Ah3PLkn3xuEaYtIRp+YOxLuVTt4aGIq+85UcIDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T12:14:34.571836Z","bundle_sha256":"1c20e038d8316f1fc072286525caa30673a396024bb43fbfb354fb8eb50159da"}}