{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YWTGGGC372NRDG3ZPFBOYIZOLT","short_pith_number":"pith:YWTGGGC3","canonical_record":{"source":{"id":"1305.0647","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-03T09:14:41Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"2ff10f1239313cdffe53618c0493d1fe66faa6ec2b63f64101b1e7ec60769781","abstract_canon_sha256":"a5021b19f735330d163572cca8988f3abdb8b718719f34a5c57a7c8b5803d254"},"schema_version":"1.0"},"canonical_sha256":"c5a663185bfe9b119b797942ec232e5cda82d105408c92f39f56259f90f80681","source":{"kind":"arxiv","id":"1305.0647","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0647","created_at":"2026-05-18T03:24:41Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0647v2","created_at":"2026-05-18T03:24:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0647","created_at":"2026-05-18T03:24:41Z"},{"alias_kind":"pith_short_12","alias_value":"YWTGGGC372NR","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YWTGGGC372NRDG3Z","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YWTGGGC3","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YWTGGGC372NRDG3ZPFBOYIZOLT","target":"record","payload":{"canonical_record":{"source":{"id":"1305.0647","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-03T09:14:41Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"2ff10f1239313cdffe53618c0493d1fe66faa6ec2b63f64101b1e7ec60769781","abstract_canon_sha256":"a5021b19f735330d163572cca8988f3abdb8b718719f34a5c57a7c8b5803d254"},"schema_version":"1.0"},"canonical_sha256":"c5a663185bfe9b119b797942ec232e5cda82d105408c92f39f56259f90f80681","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:24:41.139533Z","signature_b64":"n8MF1r49O6f3Szp4903JS8poxL/5aR84cDE6u8auc5+JoJglDKmn9HWd+L+d5YQqqpq4DVJhQs65gsTZQRjuDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5a663185bfe9b119b797942ec232e5cda82d105408c92f39f56259f90f80681","last_reissued_at":"2026-05-18T03:24:41.138821Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:24:41.138821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.0647","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":"2026-05-18T03:24:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hEsSxPSc2LivuoeBnmtMLW5wWaN903sp4WI4E6V4ZYlwBcsxgYgJ/t4MS3D7Z7BT+QonhUuSEnPXvUjL98PVDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:25:14.677015Z"},"content_sha256":"9b7b939dd3bff46233d9481397d5b770b9c1c1ff4a78c35e86cbc319b5bf7069","schema_version":"1.0","event_id":"sha256:9b7b939dd3bff46233d9481397d5b770b9c1c1ff4a78c35e86cbc319b5bf7069"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YWTGGGC372NRDG3ZPFBOYIZOLT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Navier-Stokes equation and forward-backward stochastic differential system in the Besov spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Ana Bela Cruzeiro, Xin Chen, Zhongmin Qian","submitted_at":"2013-05-03T09:14:41Z","abstract_excerpt":"The Navier-Stokes equation on Rd (d greater or equal to 3) formulated on Besov spaces is considered. Using a stochastic forward-backward differential system, the local existence of a unique solution in B_ r, with r > 1 + d is obtained. We also show p,p p the convergence to solutions of the Euler equation when the viscosity tends to zero. Moreover, we prove the local existence of a unique solution in B_ pr,q, with p > 1, 1 greater or equal to q greater or equal to infinity, r > max(1, d); here the maximal time interval depends on p the viscosity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0647","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":"2026-05-18T03:24:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2t9dBwi6pujT6whhaRg5K1hMLfmCFtBP6ypwbErOBzAqpSERNuRqy0P6iHzFBUs2c4aWyRyNZf1IR04iGwpYCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:25:14.677788Z"},"content_sha256":"f1363fd7d7bc715b7f08c8c6b00e168ed26cff374b17c82f3f953f916ac89b64","schema_version":"1.0","event_id":"sha256:f1363fd7d7bc715b7f08c8c6b00e168ed26cff374b17c82f3f953f916ac89b64"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YWTGGGC372NRDG3ZPFBOYIZOLT/bundle.json","state_url":"https://pith.science/pith/YWTGGGC372NRDG3ZPFBOYIZOLT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YWTGGGC372NRDG3ZPFBOYIZOLT/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":"2026-05-31T12:25:14Z","links":{"resolver":"https://pith.science/pith/YWTGGGC372NRDG3ZPFBOYIZOLT","bundle":"https://pith.science/pith/YWTGGGC372NRDG3ZPFBOYIZOLT/bundle.json","state":"https://pith.science/pith/YWTGGGC372NRDG3ZPFBOYIZOLT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YWTGGGC372NRDG3ZPFBOYIZOLT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YWTGGGC372NRDG3ZPFBOYIZOLT","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":"a5021b19f735330d163572cca8988f3abdb8b718719f34a5c57a7c8b5803d254","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-03T09:14:41Z","title_canon_sha256":"2ff10f1239313cdffe53618c0493d1fe66faa6ec2b63f64101b1e7ec60769781"},"schema_version":"1.0","source":{"id":"1305.0647","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0647","created_at":"2026-05-18T03:24:41Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0647v2","created_at":"2026-05-18T03:24:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0647","created_at":"2026-05-18T03:24:41Z"},{"alias_kind":"pith_short_12","alias_value":"YWTGGGC372NR","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YWTGGGC372NRDG3Z","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YWTGGGC3","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:f1363fd7d7bc715b7f08c8c6b00e168ed26cff374b17c82f3f953f916ac89b64","target":"graph","created_at":"2026-05-18T03:24:41Z","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":"The Navier-Stokes equation on Rd (d greater or equal to 3) formulated on Besov spaces is considered. Using a stochastic forward-backward differential system, the local existence of a unique solution in B_ r, with r > 1 + d is obtained. We also show p,p p the convergence to solutions of the Euler equation when the viscosity tends to zero. Moreover, we prove the local existence of a unique solution in B_ pr,q, with p > 1, 1 greater or equal to q greater or equal to infinity, r > max(1, d); here the maximal time interval depends on p the viscosity.","authors_text":"Ana Bela Cruzeiro, Xin Chen, Zhongmin Qian","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-03T09:14:41Z","title":"Navier-Stokes equation and forward-backward stochastic differential system in the Besov spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0647","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":"sha256:9b7b939dd3bff46233d9481397d5b770b9c1c1ff4a78c35e86cbc319b5bf7069","target":"record","created_at":"2026-05-18T03:24:41Z","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":"a5021b19f735330d163572cca8988f3abdb8b718719f34a5c57a7c8b5803d254","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-03T09:14:41Z","title_canon_sha256":"2ff10f1239313cdffe53618c0493d1fe66faa6ec2b63f64101b1e7ec60769781"},"schema_version":"1.0","source":{"id":"1305.0647","kind":"arxiv","version":2}},"canonical_sha256":"c5a663185bfe9b119b797942ec232e5cda82d105408c92f39f56259f90f80681","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5a663185bfe9b119b797942ec232e5cda82d105408c92f39f56259f90f80681","first_computed_at":"2026-05-18T03:24:41.138821Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:24:41.138821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n8MF1r49O6f3Szp4903JS8poxL/5aR84cDE6u8auc5+JoJglDKmn9HWd+L+d5YQqqpq4DVJhQs65gsTZQRjuDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:24:41.139533Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.0647","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b7b939dd3bff46233d9481397d5b770b9c1c1ff4a78c35e86cbc319b5bf7069","sha256:f1363fd7d7bc715b7f08c8c6b00e168ed26cff374b17c82f3f953f916ac89b64"],"state_sha256":"e040c7b1ee6741689a1eb6a902c40143de1bf4d7a766c413ad702f1dee817308"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"APAA3U7dqpWeXymVsf5rxoaZdFC2W/65HorE8kU+u/RKlgFb1OxI/V30qfd65q5qQoBg41zYl5mzh3teF0nkAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T12:25:14.681942Z","bundle_sha256":"14fbd62a4db14556a6d23dd433252621b98b522efab596e2d5e8f7bb957a97e4"}}