{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:6DPA53WWFHYXCKKQH5MQTWELYI","short_pith_number":"pith:6DPA53WW","canonical_record":{"source":{"id":"1010.6105","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-28T23:00:47Z","cross_cats_sorted":[],"title_canon_sha256":"ae7e7a342b65b948155e09928faecabbc099a3adf1a7c9356f79f3c02fadb583","abstract_canon_sha256":"242e9278ab5120c49dd5218eaaabaace4a52171e863239b03ac412a0f4e8e1d0"},"schema_version":"1.0"},"canonical_sha256":"f0de0eeed629f17129503f5909d88bc20caa34291642d2e410578e803cc39fca","source":{"kind":"arxiv","id":"1010.6105","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.6105","created_at":"2026-05-18T02:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"1010.6105v1","created_at":"2026-05-18T02:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.6105","created_at":"2026-05-18T02:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"6DPA53WWFHYX","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6DPA53WWFHYXCKKQ","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6DPA53WW","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:6DPA53WWFHYXCKKQH5MQTWELYI","target":"record","payload":{"canonical_record":{"source":{"id":"1010.6105","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-28T23:00:47Z","cross_cats_sorted":[],"title_canon_sha256":"ae7e7a342b65b948155e09928faecabbc099a3adf1a7c9356f79f3c02fadb583","abstract_canon_sha256":"242e9278ab5120c49dd5218eaaabaace4a52171e863239b03ac412a0f4e8e1d0"},"schema_version":"1.0"},"canonical_sha256":"f0de0eeed629f17129503f5909d88bc20caa34291642d2e410578e803cc39fca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:55.093698Z","signature_b64":"gHQY+OaV0Tx4gw15WeFAOjKIWrDKBTzYOzyh8VnCxnYbKJd0GqWrNRRUhxDGMvXn/koARYQ6Cdn4YSlLYo6ABQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0de0eeed629f17129503f5909d88bc20caa34291642d2e410578e803cc39fca","last_reissued_at":"2026-05-18T02:04:55.093064Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:55.093064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.6105","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":"2026-05-18T02:04:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vjt4nR/9vkkElXy23dW/rIS5/9OfoMfJ7pMpt0gifdB/Tid1rZlpCSBxssj4hA6yLbBzajeuQZ20yqaPzUkoAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:27:29.516731Z"},"content_sha256":"66b03e6e5a3f045035441b8b006020a99822feaa2c39ede37ff74f3960ad60af","schema_version":"1.0","event_id":"sha256:66b03e6e5a3f045035441b8b006020a99822feaa2c39ede37ff74f3960ad60af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:6DPA53WWFHYXCKKQH5MQTWELYI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Discrete Data Assimilation in the Lorenz and 2D Navier--Stokes Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Edriss S. Titi, Eric Olson, Kevin Hayden","submitted_at":"2010-10-28T23:00:47Z","abstract_excerpt":"Consider a continuous dynamical system for which partial information about its current state is observed at a sequence of discrete times. Discrete data assimilation inserts these observational measurements of the reference dynamical system into an approximate solution by means of an impulsive forcing. In this way the approximating solution is coupled to the reference solution at a discrete sequence of points in time. This paper studies discrete data assimilation for the Lorenz equations and the incompressible two-dimensional Navier--Stokes equations. In both cases we obtain bounds on the time "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.6105","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":"2026-05-18T02:04:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"efKJS0SNFpKZ9xAPefK7mYTcKzvCWTDNHbDe7etLfzpYasWCOl9aH+4+b8eQvFtPgKY308JfsweK5wMi3oX7CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:27:29.517325Z"},"content_sha256":"d000806a15bcdba3d7c33a58924984eceb910940808178e27c40e58a4c96b125","schema_version":"1.0","event_id":"sha256:d000806a15bcdba3d7c33a58924984eceb910940808178e27c40e58a4c96b125"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6DPA53WWFHYXCKKQH5MQTWELYI/bundle.json","state_url":"https://pith.science/pith/6DPA53WWFHYXCKKQH5MQTWELYI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6DPA53WWFHYXCKKQH5MQTWELYI/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":"2026-06-06T15:27:29Z","links":{"resolver":"https://pith.science/pith/6DPA53WWFHYXCKKQH5MQTWELYI","bundle":"https://pith.science/pith/6DPA53WWFHYXCKKQH5MQTWELYI/bundle.json","state":"https://pith.science/pith/6DPA53WWFHYXCKKQH5MQTWELYI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6DPA53WWFHYXCKKQH5MQTWELYI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:6DPA53WWFHYXCKKQH5MQTWELYI","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":"242e9278ab5120c49dd5218eaaabaace4a52171e863239b03ac412a0f4e8e1d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-28T23:00:47Z","title_canon_sha256":"ae7e7a342b65b948155e09928faecabbc099a3adf1a7c9356f79f3c02fadb583"},"schema_version":"1.0","source":{"id":"1010.6105","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.6105","created_at":"2026-05-18T02:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"1010.6105v1","created_at":"2026-05-18T02:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.6105","created_at":"2026-05-18T02:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"6DPA53WWFHYX","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6DPA53WWFHYXCKKQ","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6DPA53WW","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:d000806a15bcdba3d7c33a58924984eceb910940808178e27c40e58a4c96b125","target":"graph","created_at":"2026-05-18T02:04:55Z","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":"Consider a continuous dynamical system for which partial information about its current state is observed at a sequence of discrete times. Discrete data assimilation inserts these observational measurements of the reference dynamical system into an approximate solution by means of an impulsive forcing. In this way the approximating solution is coupled to the reference solution at a discrete sequence of points in time. This paper studies discrete data assimilation for the Lorenz equations and the incompressible two-dimensional Navier--Stokes equations. In both cases we obtain bounds on the time ","authors_text":"Edriss S. Titi, Eric Olson, Kevin Hayden","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-28T23:00:47Z","title":"Discrete Data Assimilation in the Lorenz and 2D Navier--Stokes Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.6105","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":"sha256:66b03e6e5a3f045035441b8b006020a99822feaa2c39ede37ff74f3960ad60af","target":"record","created_at":"2026-05-18T02:04:55Z","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":"242e9278ab5120c49dd5218eaaabaace4a52171e863239b03ac412a0f4e8e1d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-28T23:00:47Z","title_canon_sha256":"ae7e7a342b65b948155e09928faecabbc099a3adf1a7c9356f79f3c02fadb583"},"schema_version":"1.0","source":{"id":"1010.6105","kind":"arxiv","version":1}},"canonical_sha256":"f0de0eeed629f17129503f5909d88bc20caa34291642d2e410578e803cc39fca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0de0eeed629f17129503f5909d88bc20caa34291642d2e410578e803cc39fca","first_computed_at":"2026-05-18T02:04:55.093064Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:55.093064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gHQY+OaV0Tx4gw15WeFAOjKIWrDKBTzYOzyh8VnCxnYbKJd0GqWrNRRUhxDGMvXn/koARYQ6Cdn4YSlLYo6ABQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:55.093698Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.6105","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66b03e6e5a3f045035441b8b006020a99822feaa2c39ede37ff74f3960ad60af","sha256:d000806a15bcdba3d7c33a58924984eceb910940808178e27c40e58a4c96b125"],"state_sha256":"f99c5f428594918656f3f8f15bcb05fcd416635d303f232686e2e03a632512e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FOlsnwbuE691JhxWEB0Q1Rl57Md1VYnPNKQa0Bhn2UUZDYESgjMBZ5LHsy+miFhwwLab66Hc9o8mdf4sLbqiAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T15:27:29.520429Z","bundle_sha256":"79320928330c6e2b2ca304d961bcb089fd9fd1fe09289cfcaf7fdbd32dcc8838"}}