{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:S4OPMXSV7MTNAVMB6OWLJJSEA2","short_pith_number":"pith:S4OPMXSV","canonical_record":{"source":{"id":"2003.01329","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-03-03T04:40:30Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"2e7036b54994ac8ecbbadfb9322f3d6d1c364dcb49260e90786acda05be54798","abstract_canon_sha256":"afc8a2e254498b3eaf0d3d97524edc63ad0919e2747b2990b11a4e26acb0147b"},"schema_version":"1.0"},"canonical_sha256":"971cf65e55fb26d05581f3acb4a644069be5ae9353b44f40ea437198646d1775","source":{"kind":"arxiv","id":"2003.01329","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2003.01329","created_at":"2026-07-05T00:45:27Z"},{"alias_kind":"arxiv_version","alias_value":"2003.01329v1","created_at":"2026-07-05T00:45:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.01329","created_at":"2026-07-05T00:45:27Z"},{"alias_kind":"pith_short_12","alias_value":"S4OPMXSV7MTN","created_at":"2026-07-05T00:45:27Z"},{"alias_kind":"pith_short_16","alias_value":"S4OPMXSV7MTNAVMB","created_at":"2026-07-05T00:45:27Z"},{"alias_kind":"pith_short_8","alias_value":"S4OPMXSV","created_at":"2026-07-05T00:45:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:S4OPMXSV7MTNAVMB6OWLJJSEA2","target":"record","payload":{"canonical_record":{"source":{"id":"2003.01329","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-03-03T04:40:30Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"2e7036b54994ac8ecbbadfb9322f3d6d1c364dcb49260e90786acda05be54798","abstract_canon_sha256":"afc8a2e254498b3eaf0d3d97524edc63ad0919e2747b2990b11a4e26acb0147b"},"schema_version":"1.0"},"canonical_sha256":"971cf65e55fb26d05581f3acb4a644069be5ae9353b44f40ea437198646d1775","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:45:27.540137Z","signature_b64":"ZGztSWojd5q28HIAUi6M9AC8HwzBxvnQ6GKJp+KeMg5lKR/GT/PxpVezh6Kemy1ITeTv18+epGnKqh1UFfLxCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"971cf65e55fb26d05581f3acb4a644069be5ae9353b44f40ea437198646d1775","last_reissued_at":"2026-07-05T00:45:27.539595Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:45:27.539595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2003.01329","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":"2026-07-05T00:45:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7xAd/AY3jbTZ7Gcz8XngzIVhIMAtOX/RFz82hoHJcTqFOv6Z7UUyoGGf4e4YR0cxtW/mJsq9nIKnmXxLXL2lDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T03:19:26.711439Z"},"content_sha256":"e2b7620a8949bfd1db9edb7bd1c5ffc5c4ed44bec32c261af9a2c1b539bb3686","schema_version":"1.0","event_id":"sha256:e2b7620a8949bfd1db9edb7bd1c5ffc5c4ed44bec32c261af9a2c1b539bb3686"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:S4OPMXSV7MTNAVMB6OWLJJSEA2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Continuous Data Assimilation for the Three Dimensional Navier-Stokes Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.AP","authors_text":"Animikh Biswas, Randy Price","submitted_at":"2020-03-03T04:40:30Z","abstract_excerpt":"In this paper, we provide conditions, \\emph{based solely on the observed data}, for the global well-posedness, regularity and convergence of the Azouni-Olson-Titi data assimilation algorithm (AOT algorithm) for a Leray-Hopf weak solutions of the three dimensional Navier-Stokes equations (3D NSE). The aforementioned conditions on the observations, which in this case comprise either of \\emph{modal} or \\emph{volume element observations}, are automatically satisfied for solutions that are globally regular and are uniformly bounded in the $H^1$-norm. However, neither regularity nor uniqueness is ne"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.01329","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2003.01329/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:45:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HTMScetcilyt3/+QEoiBVmPduC6tSt34FjQTxJ0AUYjvbYGz5cgB1sdJ0yJ0EuzenB8qmtqfISUM/+RTEC83DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T03:19:26.711931Z"},"content_sha256":"f256f0e2ee073b77a22811ed9b5af105018f4bb3f7613f491fdb0ac81adaf75d","schema_version":"1.0","event_id":"sha256:f256f0e2ee073b77a22811ed9b5af105018f4bb3f7613f491fdb0ac81adaf75d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S4OPMXSV7MTNAVMB6OWLJJSEA2/bundle.json","state_url":"https://pith.science/pith/S4OPMXSV7MTNAVMB6OWLJJSEA2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S4OPMXSV7MTNAVMB6OWLJJSEA2/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":"2026-08-23T03:19:26Z","links":{"resolver":"https://pith.science/pith/S4OPMXSV7MTNAVMB6OWLJJSEA2","bundle":"https://pith.science/pith/S4OPMXSV7MTNAVMB6OWLJJSEA2/bundle.json","state":"https://pith.science/pith/S4OPMXSV7MTNAVMB6OWLJJSEA2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S4OPMXSV7MTNAVMB6OWLJJSEA2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:S4OPMXSV7MTNAVMB6OWLJJSEA2","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":"afc8a2e254498b3eaf0d3d97524edc63ad0919e2747b2990b11a4e26acb0147b","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-03-03T04:40:30Z","title_canon_sha256":"2e7036b54994ac8ecbbadfb9322f3d6d1c364dcb49260e90786acda05be54798"},"schema_version":"1.0","source":{"id":"2003.01329","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2003.01329","created_at":"2026-07-05T00:45:27Z"},{"alias_kind":"arxiv_version","alias_value":"2003.01329v1","created_at":"2026-07-05T00:45:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.01329","created_at":"2026-07-05T00:45:27Z"},{"alias_kind":"pith_short_12","alias_value":"S4OPMXSV7MTN","created_at":"2026-07-05T00:45:27Z"},{"alias_kind":"pith_short_16","alias_value":"S4OPMXSV7MTNAVMB","created_at":"2026-07-05T00:45:27Z"},{"alias_kind":"pith_short_8","alias_value":"S4OPMXSV","created_at":"2026-07-05T00:45:27Z"}],"graph_snapshots":[{"event_id":"sha256:f256f0e2ee073b77a22811ed9b5af105018f4bb3f7613f491fdb0ac81adaf75d","target":"graph","created_at":"2026-07-05T00:45:27Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2003.01329/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we provide conditions, \\emph{based solely on the observed data}, for the global well-posedness, regularity and convergence of the Azouni-Olson-Titi data assimilation algorithm (AOT algorithm) for a Leray-Hopf weak solutions of the three dimensional Navier-Stokes equations (3D NSE). The aforementioned conditions on the observations, which in this case comprise either of \\emph{modal} or \\emph{volume element observations}, are automatically satisfied for solutions that are globally regular and are uniformly bounded in the $H^1$-norm. However, neither regularity nor uniqueness is ne","authors_text":"Animikh Biswas, Randy Price","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-03-03T04:40:30Z","title":"Continuous Data Assimilation for the Three Dimensional Navier-Stokes Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.01329","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:e2b7620a8949bfd1db9edb7bd1c5ffc5c4ed44bec32c261af9a2c1b539bb3686","target":"record","created_at":"2026-07-05T00:45:27Z","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":"afc8a2e254498b3eaf0d3d97524edc63ad0919e2747b2990b11a4e26acb0147b","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-03-03T04:40:30Z","title_canon_sha256":"2e7036b54994ac8ecbbadfb9322f3d6d1c364dcb49260e90786acda05be54798"},"schema_version":"1.0","source":{"id":"2003.01329","kind":"arxiv","version":1}},"canonical_sha256":"971cf65e55fb26d05581f3acb4a644069be5ae9353b44f40ea437198646d1775","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"971cf65e55fb26d05581f3acb4a644069be5ae9353b44f40ea437198646d1775","first_computed_at":"2026-07-05T00:45:27.539595Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:45:27.539595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZGztSWojd5q28HIAUi6M9AC8HwzBxvnQ6GKJp+KeMg5lKR/GT/PxpVezh6Kemy1ITeTv18+epGnKqh1UFfLxCg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:45:27.540137Z","signed_message":"canonical_sha256_bytes"},"source_id":"2003.01329","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2b7620a8949bfd1db9edb7bd1c5ffc5c4ed44bec32c261af9a2c1b539bb3686","sha256:f256f0e2ee073b77a22811ed9b5af105018f4bb3f7613f491fdb0ac81adaf75d"],"state_sha256":"e924ccc44b800e4b307fbaeef9b2477ddd1d2f28501f535539bb355787b7f45e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N1jcQkvB6tLp8ZzQbo0lDQXrJZjD2u/hh2gDHDFtObOU7DJyObsH8Len7EOM2m+NgAOVKzFcsHqiZU1ZK6kuDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T03:19:26.715883Z","bundle_sha256":"4f4208e59cb05ca423f56cf74608d95fd352c0d7881dce7c05aacffc55ee80da"}}