{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:2FQIIXO52V5QWKF2DRYOO22UK2","short_pith_number":"pith:2FQIIXO5","canonical_record":{"source":{"id":"1307.6127","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2013-07-23T15:39:43Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"96eabf7d14297b1b562042845465e2a25b521696b5b8b495f08078f435fc1b57","abstract_canon_sha256":"888d72acafd9c0de7753b4db1117ba7bd7bb4b267660da7ac32d6d360736d295"},"schema_version":"1.0"},"canonical_sha256":"d160845dddd57b0b28ba1c70e76b5456b4cc28e835c883f0a13a39209e4b5cb2","source":{"kind":"arxiv","id":"1307.6127","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6127","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6127v1","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6127","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"pith_short_12","alias_value":"2FQIIXO52V5Q","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2FQIIXO52V5QWKF2","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2FQIIXO5","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:2FQIIXO52V5QWKF2DRYOO22UK2","target":"record","payload":{"canonical_record":{"source":{"id":"1307.6127","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2013-07-23T15:39:43Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"96eabf7d14297b1b562042845465e2a25b521696b5b8b495f08078f435fc1b57","abstract_canon_sha256":"888d72acafd9c0de7753b4db1117ba7bd7bb4b267660da7ac32d6d360736d295"},"schema_version":"1.0"},"canonical_sha256":"d160845dddd57b0b28ba1c70e76b5456b4cc28e835c883f0a13a39209e4b5cb2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:45.256437Z","signature_b64":"4ur42EV0v1acOxJeQdHznBpA1bQuDryjCZl5MVr3MZUboPDsWORkX++JP3URc3Nx6MKAtTr4TP/09n70rmEwDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d160845dddd57b0b28ba1c70e76b5456b4cc28e835c883f0a13a39209e4b5cb2","last_reissued_at":"2026-05-18T03:17:45.255652Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:45.255652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.6127","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":"2026-05-18T03:17:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9q1UhG/Ee5rICFKEa+BIhwlCDy40S6MmgQfVEY4igA3CxAMhNhg6UfDlh58/XEpcmur3cpzWNMD8EwKyHsG/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:12:39.394435Z"},"content_sha256":"669a498e203cba988c6ee7e4b7c59156c0e172fb8f40d1057f7f0c8bcf5baad4","schema_version":"1.0","event_id":"sha256:669a498e203cba988c6ee7e4b7c59156c0e172fb8f40d1057f7f0c8bcf5baad4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:2FQIIXO52V5QWKF2DRYOO22UK2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sequential Monte Carlo Methods for High-Dimensional Inverse Problems: A case study for the Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"stat.CO","authors_text":"Ajay Jasra, Alexandros Beskos, Nikolas Kantas","submitted_at":"2013-07-23T15:39:43Z","abstract_excerpt":"We consider the inverse problem of estimating the initial condition of a partial differential equation, which is only observed through noisy measurements at discrete time intervals. In particular, we focus on the case where Eulerian measurements are obtained from the time and space evolving vector field, whose evolution obeys the two-dimensional Navier-Stokes equations defined on a torus. This context is particularly relevant to the area of numerical weather forecasting and data assimilation. We will adopt a Bayesian formulation resulting from a particular regularization that ensures the probl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6127","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":""},"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":"2026-05-18T03:17:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cpLMblSQywsy6x1NNyrpU1X3p2f0lnBtIY1nvNyD+10/pbEBkokzpLrnHGqnqGCAG3mf5bsHDyiGTVMw5rTYBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:12:39.394780Z"},"content_sha256":"f20e7a440e57496cab43258a9dcaf39591a414febb78bfb1a89648ab34b42daa","schema_version":"1.0","event_id":"sha256:f20e7a440e57496cab43258a9dcaf39591a414febb78bfb1a89648ab34b42daa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2FQIIXO52V5QWKF2DRYOO22UK2/bundle.json","state_url":"https://pith.science/pith/2FQIIXO52V5QWKF2DRYOO22UK2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2FQIIXO52V5QWKF2DRYOO22UK2/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":"2026-05-28T13:12:39Z","links":{"resolver":"https://pith.science/pith/2FQIIXO52V5QWKF2DRYOO22UK2","bundle":"https://pith.science/pith/2FQIIXO52V5QWKF2DRYOO22UK2/bundle.json","state":"https://pith.science/pith/2FQIIXO52V5QWKF2DRYOO22UK2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2FQIIXO52V5QWKF2DRYOO22UK2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2FQIIXO52V5QWKF2DRYOO22UK2","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":"888d72acafd9c0de7753b4db1117ba7bd7bb4b267660da7ac32d6d360736d295","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2013-07-23T15:39:43Z","title_canon_sha256":"96eabf7d14297b1b562042845465e2a25b521696b5b8b495f08078f435fc1b57"},"schema_version":"1.0","source":{"id":"1307.6127","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6127","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6127v1","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6127","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"pith_short_12","alias_value":"2FQIIXO52V5Q","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2FQIIXO52V5QWKF2","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2FQIIXO5","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:f20e7a440e57496cab43258a9dcaf39591a414febb78bfb1a89648ab34b42daa","target":"graph","created_at":"2026-05-18T03:17:45Z","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 the inverse problem of estimating the initial condition of a partial differential equation, which is only observed through noisy measurements at discrete time intervals. In particular, we focus on the case where Eulerian measurements are obtained from the time and space evolving vector field, whose evolution obeys the two-dimensional Navier-Stokes equations defined on a torus. This context is particularly relevant to the area of numerical weather forecasting and data assimilation. We will adopt a Bayesian formulation resulting from a particular regularization that ensures the probl","authors_text":"Ajay Jasra, Alexandros Beskos, Nikolas Kantas","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2013-07-23T15:39:43Z","title":"Sequential Monte Carlo Methods for High-Dimensional Inverse Problems: A case study for the Navier-Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6127","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":"sha256:669a498e203cba988c6ee7e4b7c59156c0e172fb8f40d1057f7f0c8bcf5baad4","target":"record","created_at":"2026-05-18T03:17:45Z","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":"888d72acafd9c0de7753b4db1117ba7bd7bb4b267660da7ac32d6d360736d295","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2013-07-23T15:39:43Z","title_canon_sha256":"96eabf7d14297b1b562042845465e2a25b521696b5b8b495f08078f435fc1b57"},"schema_version":"1.0","source":{"id":"1307.6127","kind":"arxiv","version":1}},"canonical_sha256":"d160845dddd57b0b28ba1c70e76b5456b4cc28e835c883f0a13a39209e4b5cb2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d160845dddd57b0b28ba1c70e76b5456b4cc28e835c883f0a13a39209e4b5cb2","first_computed_at":"2026-05-18T03:17:45.255652Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:45.255652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4ur42EV0v1acOxJeQdHznBpA1bQuDryjCZl5MVr3MZUboPDsWORkX++JP3URc3Nx6MKAtTr4TP/09n70rmEwDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:45.256437Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.6127","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:669a498e203cba988c6ee7e4b7c59156c0e172fb8f40d1057f7f0c8bcf5baad4","sha256:f20e7a440e57496cab43258a9dcaf39591a414febb78bfb1a89648ab34b42daa"],"state_sha256":"3c8d8af3d3326dbf6bdf158bdb4c7d46c2e2c102fbd8b5afd024a519f34a7eac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pW1fTs/e9B6GjXNZvKxbkgvB9UKnNQVMreH5oiPV4cBC1TcxE+Pavgfs19SN01knvh/RHkJ1i32CE/zz4G9mBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:12:39.396796Z","bundle_sha256":"4067a82169faf572e1ab8cad36c9a6ba60e17907e4e8ff6e397218453226ff44"}}