{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:X33ACTHVBMNLQLMBRWL4I66M4K","short_pith_number":"pith:X33ACTHV","canonical_record":{"source":{"id":"1404.0345","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-01T18:51:27Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"42ee354c110b3fad7f84d5a64c1b8fb163a64cfab2d6c3b309a486ea2069f882","abstract_canon_sha256":"b1a6f0c29a3524bd76c1c2d12f3caf76834f2105ca5f7cbd246f0867ac38c596"},"schema_version":"1.0"},"canonical_sha256":"bef6014cf50b1ab82d818d97c47bcce2b0af38b3c050ff81a4b3113a9294c4bd","source":{"kind":"arxiv","id":"1404.0345","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.0345","created_at":"2026-05-18T02:32:46Z"},{"alias_kind":"arxiv_version","alias_value":"1404.0345v2","created_at":"2026-05-18T02:32:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0345","created_at":"2026-05-18T02:32:46Z"},{"alias_kind":"pith_short_12","alias_value":"X33ACTHVBMNL","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"X33ACTHVBMNLQLMB","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"X33ACTHV","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:X33ACTHVBMNLQLMBRWL4I66M4K","target":"record","payload":{"canonical_record":{"source":{"id":"1404.0345","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-01T18:51:27Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"42ee354c110b3fad7f84d5a64c1b8fb163a64cfab2d6c3b309a486ea2069f882","abstract_canon_sha256":"b1a6f0c29a3524bd76c1c2d12f3caf76834f2105ca5f7cbd246f0867ac38c596"},"schema_version":"1.0"},"canonical_sha256":"bef6014cf50b1ab82d818d97c47bcce2b0af38b3c050ff81a4b3113a9294c4bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:46.180327Z","signature_b64":"gFiQbDpMBAYL6z3MNJhJPyJVtJ53W2LZeb2YPizw+y4gnxDsKwaD3kHJh2i9AQB5ZQSjjBRz25WEpCgeuN9KBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bef6014cf50b1ab82d818d97c47bcce2b0af38b3c050ff81a4b3113a9294c4bd","last_reissued_at":"2026-05-18T02:32:46.179750Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:46.179750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.0345","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":"2026-05-18T02:32:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PhZYcJpG89eNtXi64iqj+vaLAkD1uDpo3iIsWicSRpZUXrpFcbqvJJHwaYzoqoXYc0eoSCEdnIjAdgjBbDoOCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T22:46:33.431331Z"},"content_sha256":"db73552f4d60ee75e3fbf55bd8039e93110a0be5bae296dd3fdaf6ca29fb97c8","schema_version":"1.0","event_id":"sha256:db73552f4d60ee75e3fbf55bd8039e93110a0be5bae296dd3fdaf6ca29fb97c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:X33ACTHVBMNLQLMBRWL4I66M4K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Classical Solutions of Linear Stochastic Integro-Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"James-Michael Leahy, Remigijus Mikulevicius","submitted_at":"2014-04-01T18:51:27Z","abstract_excerpt":"We prove the existence of classical solutions to parabolic linear stochastic integro-differential equations with adapted coefficients using Feynman-Kac transformations, conditioning, and the interlacing of space-inverses of stochastic flows associated with the equations. The equations are forward and the derivation of existence does not use the \"general theory\" of SPDEs. Uniqueness is proved in the class of classical solutions with polynomial growth."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0345","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":"2026-05-18T02:32:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pQTMVNZGPEAKdizVUEfEbnVJZniqIfFrmVfwo/c3192AX1gEIiStCPoPQ7fK5FSNK+psNDxeRaF1k/RDZm6dDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T22:46:33.432019Z"},"content_sha256":"4d4d06d4e68c7459b686b336824a7930a76f621572f84d5669b850be4ab3cb17","schema_version":"1.0","event_id":"sha256:4d4d06d4e68c7459b686b336824a7930a76f621572f84d5669b850be4ab3cb17"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X33ACTHVBMNLQLMBRWL4I66M4K/bundle.json","state_url":"https://pith.science/pith/X33ACTHVBMNLQLMBRWL4I66M4K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X33ACTHVBMNLQLMBRWL4I66M4K/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":"2026-06-09T22:46:33Z","links":{"resolver":"https://pith.science/pith/X33ACTHVBMNLQLMBRWL4I66M4K","bundle":"https://pith.science/pith/X33ACTHVBMNLQLMBRWL4I66M4K/bundle.json","state":"https://pith.science/pith/X33ACTHVBMNLQLMBRWL4I66M4K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X33ACTHVBMNLQLMBRWL4I66M4K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:X33ACTHVBMNLQLMBRWL4I66M4K","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":"b1a6f0c29a3524bd76c1c2d12f3caf76834f2105ca5f7cbd246f0867ac38c596","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-01T18:51:27Z","title_canon_sha256":"42ee354c110b3fad7f84d5a64c1b8fb163a64cfab2d6c3b309a486ea2069f882"},"schema_version":"1.0","source":{"id":"1404.0345","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.0345","created_at":"2026-05-18T02:32:46Z"},{"alias_kind":"arxiv_version","alias_value":"1404.0345v2","created_at":"2026-05-18T02:32:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0345","created_at":"2026-05-18T02:32:46Z"},{"alias_kind":"pith_short_12","alias_value":"X33ACTHVBMNL","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"X33ACTHVBMNLQLMB","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"X33ACTHV","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:4d4d06d4e68c7459b686b336824a7930a76f621572f84d5669b850be4ab3cb17","target":"graph","created_at":"2026-05-18T02:32:46Z","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 prove the existence of classical solutions to parabolic linear stochastic integro-differential equations with adapted coefficients using Feynman-Kac transformations, conditioning, and the interlacing of space-inverses of stochastic flows associated with the equations. The equations are forward and the derivation of existence does not use the \"general theory\" of SPDEs. Uniqueness is proved in the class of classical solutions with polynomial growth.","authors_text":"James-Michael Leahy, Remigijus Mikulevicius","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-01T18:51:27Z","title":"On Classical Solutions of Linear Stochastic Integro-Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0345","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:db73552f4d60ee75e3fbf55bd8039e93110a0be5bae296dd3fdaf6ca29fb97c8","target":"record","created_at":"2026-05-18T02:32:46Z","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":"b1a6f0c29a3524bd76c1c2d12f3caf76834f2105ca5f7cbd246f0867ac38c596","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-01T18:51:27Z","title_canon_sha256":"42ee354c110b3fad7f84d5a64c1b8fb163a64cfab2d6c3b309a486ea2069f882"},"schema_version":"1.0","source":{"id":"1404.0345","kind":"arxiv","version":2}},"canonical_sha256":"bef6014cf50b1ab82d818d97c47bcce2b0af38b3c050ff81a4b3113a9294c4bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bef6014cf50b1ab82d818d97c47bcce2b0af38b3c050ff81a4b3113a9294c4bd","first_computed_at":"2026-05-18T02:32:46.179750Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:46.179750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gFiQbDpMBAYL6z3MNJhJPyJVtJ53W2LZeb2YPizw+y4gnxDsKwaD3kHJh2i9AQB5ZQSjjBRz25WEpCgeuN9KBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:46.180327Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.0345","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db73552f4d60ee75e3fbf55bd8039e93110a0be5bae296dd3fdaf6ca29fb97c8","sha256:4d4d06d4e68c7459b686b336824a7930a76f621572f84d5669b850be4ab3cb17"],"state_sha256":"e00ed7b07499442aac679f3acf21e72c55229a4fb3919414b8b5c9940932d8c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3/A+Vk/54x5prrQGmo3ewOK44swBMlmUcmp6BmGSOVlR0ChFeAo88VbLjd4HDZajJPJdjo7IcXM8wf3to7neCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T22:46:33.436050Z","bundle_sha256":"adb2ebff30757501eb30ac7a9d83f626f566d05a4f133382147666c85bfc688f"}}