{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6FAO2VCOT4X6Z6UYF573T422G2","short_pith_number":"pith:6FAO2VCO","canonical_record":{"source":{"id":"1509.01154","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-03T16:42:21Z","cross_cats_sorted":[],"title_canon_sha256":"13665349f0edfed0df4fd1dd66b443953e40e8d8f7985ff094ce16523464efa9","abstract_canon_sha256":"9954b5221c58dde146b80cf2c12b4e15dfd18764525b34598899ea410f2df2a1"},"schema_version":"1.0"},"canonical_sha256":"f140ed544e9f2fecfa982f7fb9f35a36b9966dc6b83cc19afd58e9fe4afe12df","source":{"kind":"arxiv","id":"1509.01154","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01154","created_at":"2026-05-18T00:12:35Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01154v3","created_at":"2026-05-18T00:12:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01154","created_at":"2026-05-18T00:12:35Z"},{"alias_kind":"pith_short_12","alias_value":"6FAO2VCOT4X6","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6FAO2VCOT4X6Z6UY","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6FAO2VCO","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6FAO2VCOT4X6Z6UYF573T422G2","target":"record","payload":{"canonical_record":{"source":{"id":"1509.01154","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-03T16:42:21Z","cross_cats_sorted":[],"title_canon_sha256":"13665349f0edfed0df4fd1dd66b443953e40e8d8f7985ff094ce16523464efa9","abstract_canon_sha256":"9954b5221c58dde146b80cf2c12b4e15dfd18764525b34598899ea410f2df2a1"},"schema_version":"1.0"},"canonical_sha256":"f140ed544e9f2fecfa982f7fb9f35a36b9966dc6b83cc19afd58e9fe4afe12df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:35.865395Z","signature_b64":"NIOZ7W/upyuunIJANQSRaFhJJEcIIYwFQfjhQozCeoW0gvfLL1GqigAwgqg4jJXrZ6GkZ46HR/hdaa3E5drfCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f140ed544e9f2fecfa982f7fb9f35a36b9966dc6b83cc19afd58e9fe4afe12df","last_reissued_at":"2026-05-18T00:12:35.864697Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:35.864697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.01154","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":"2026-05-18T00:12:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TOE5vTKsXOPgjV/to1sMfZnVo4QjQG0lhfnA2rz+dDUJQoINzayiiDbckYTO30gRVD+F7JjJbsHp3bxLOJ5EBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T21:08:23.288364Z"},"content_sha256":"2385e67265097d4c2234388966cc9fc0e1393694f0f7b612dbc502caff3d45d2","schema_version":"1.0","event_id":"sha256:2385e67265097d4c2234388966cc9fc0e1393694f0f7b612dbc502caff3d45d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6FAO2VCOT4X6Z6UYF573T422G2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rough linear PDE's with discontinuous coefficients - existence of solutions via regularization by fractional Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Torstein Nilssen","submitted_at":"2015-09-03T16:42:21Z","abstract_excerpt":"We consider two related linear PDE's perturbed by a fractional Brownian motion. We allow the drift to be discontinuous, in which case the corresponding deterministic equation is ill-posed. However, the noise will be shown to have a regularizing effect on the equations in the sense that we can prove existence of solutions for almost all paths of the fractional Brownian motion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01154","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":"2026-05-18T00:12:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NVrTOt7rwUzSCElOM/cF/s6w+v2xtlSmF3NNcv8lZYpclTEW9e9fcvozIy+P3HLYktZM6eVLZDtar+/bFmhFDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T21:08:23.288744Z"},"content_sha256":"9824be6d80af0224ca73aeb7948e799699e09aed9f63f1405e89009417736c17","schema_version":"1.0","event_id":"sha256:9824be6d80af0224ca73aeb7948e799699e09aed9f63f1405e89009417736c17"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6FAO2VCOT4X6Z6UYF573T422G2/bundle.json","state_url":"https://pith.science/pith/6FAO2VCOT4X6Z6UYF573T422G2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6FAO2VCOT4X6Z6UYF573T422G2/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":"2026-06-21T21:08:23Z","links":{"resolver":"https://pith.science/pith/6FAO2VCOT4X6Z6UYF573T422G2","bundle":"https://pith.science/pith/6FAO2VCOT4X6Z6UYF573T422G2/bundle.json","state":"https://pith.science/pith/6FAO2VCOT4X6Z6UYF573T422G2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6FAO2VCOT4X6Z6UYF573T422G2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6FAO2VCOT4X6Z6UYF573T422G2","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":"9954b5221c58dde146b80cf2c12b4e15dfd18764525b34598899ea410f2df2a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-03T16:42:21Z","title_canon_sha256":"13665349f0edfed0df4fd1dd66b443953e40e8d8f7985ff094ce16523464efa9"},"schema_version":"1.0","source":{"id":"1509.01154","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01154","created_at":"2026-05-18T00:12:35Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01154v3","created_at":"2026-05-18T00:12:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01154","created_at":"2026-05-18T00:12:35Z"},{"alias_kind":"pith_short_12","alias_value":"6FAO2VCOT4X6","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6FAO2VCOT4X6Z6UY","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6FAO2VCO","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:9824be6d80af0224ca73aeb7948e799699e09aed9f63f1405e89009417736c17","target":"graph","created_at":"2026-05-18T00:12:35Z","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 two related linear PDE's perturbed by a fractional Brownian motion. We allow the drift to be discontinuous, in which case the corresponding deterministic equation is ill-posed. However, the noise will be shown to have a regularizing effect on the equations in the sense that we can prove existence of solutions for almost all paths of the fractional Brownian motion.","authors_text":"Torstein Nilssen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-03T16:42:21Z","title":"Rough linear PDE's with discontinuous coefficients - existence of solutions via regularization by fractional Brownian motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01154","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":"sha256:2385e67265097d4c2234388966cc9fc0e1393694f0f7b612dbc502caff3d45d2","target":"record","created_at":"2026-05-18T00:12:35Z","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":"9954b5221c58dde146b80cf2c12b4e15dfd18764525b34598899ea410f2df2a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-03T16:42:21Z","title_canon_sha256":"13665349f0edfed0df4fd1dd66b443953e40e8d8f7985ff094ce16523464efa9"},"schema_version":"1.0","source":{"id":"1509.01154","kind":"arxiv","version":3}},"canonical_sha256":"f140ed544e9f2fecfa982f7fb9f35a36b9966dc6b83cc19afd58e9fe4afe12df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f140ed544e9f2fecfa982f7fb9f35a36b9966dc6b83cc19afd58e9fe4afe12df","first_computed_at":"2026-05-18T00:12:35.864697Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:35.864697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NIOZ7W/upyuunIJANQSRaFhJJEcIIYwFQfjhQozCeoW0gvfLL1GqigAwgqg4jJXrZ6GkZ46HR/hdaa3E5drfCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:35.865395Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.01154","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2385e67265097d4c2234388966cc9fc0e1393694f0f7b612dbc502caff3d45d2","sha256:9824be6d80af0224ca73aeb7948e799699e09aed9f63f1405e89009417736c17"],"state_sha256":"f97624c0d6eb7332c8c77fedf37b13ddb2216d64dfe9a6b345c29af2c9348379"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fakUwqgHq+C5zlajGJb2BxMJ21nLvPNRaQjsrxqWsAbM4zMtm/4/gV/qhHdVGapc7jkr+sTd3hteeKg7GoQvAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T21:08:23.291232Z","bundle_sha256":"6d00c991c6ae41025e3582013d01f5d4a9e6318578b5731c90f0b6c3fca7e934"}}