{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EJNYIUIYUYXPUVRY4KUW2XGLGH","short_pith_number":"pith:EJNYIUIY","canonical_record":{"source":{"id":"1805.04158","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-05-10T20:11:52Z","cross_cats_sorted":["cs.NA","math.IT"],"title_canon_sha256":"1aee25c83ea4220e4cb78ef6f71f3a3a7307cdd54d18315635aa7203049f56e7","abstract_canon_sha256":"1ddf30f342427fb763abf5917f84541f2c63caa7aa73881a2e96d59ea16f844f"},"schema_version":"1.0"},"canonical_sha256":"225b845118a62efa5638e2a96d5ccb31d7a85af0b0b6aa6628e7cb49f70bdf90","source":{"kind":"arxiv","id":"1805.04158","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.04158","created_at":"2026-05-18T00:16:13Z"},{"alias_kind":"arxiv_version","alias_value":"1805.04158v1","created_at":"2026-05-18T00:16:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.04158","created_at":"2026-05-18T00:16:13Z"},{"alias_kind":"pith_short_12","alias_value":"EJNYIUIYUYXP","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EJNYIUIYUYXPUVRY","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EJNYIUIY","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EJNYIUIYUYXPUVRY4KUW2XGLGH","target":"record","payload":{"canonical_record":{"source":{"id":"1805.04158","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-05-10T20:11:52Z","cross_cats_sorted":["cs.NA","math.IT"],"title_canon_sha256":"1aee25c83ea4220e4cb78ef6f71f3a3a7307cdd54d18315635aa7203049f56e7","abstract_canon_sha256":"1ddf30f342427fb763abf5917f84541f2c63caa7aa73881a2e96d59ea16f844f"},"schema_version":"1.0"},"canonical_sha256":"225b845118a62efa5638e2a96d5ccb31d7a85af0b0b6aa6628e7cb49f70bdf90","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:13.459539Z","signature_b64":"0jrSYpRFUN5kjGAYWAY862nL4XrvtvV2X8bOc+bI4H0AU5T/f8II5gkS12tBFeRzUeRev+NGjA5CS2OgZ+ZiDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"225b845118a62efa5638e2a96d5ccb31d7a85af0b0b6aa6628e7cb49f70bdf90","last_reissued_at":"2026-05-18T00:16:13.458991Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:13.458991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.04158","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":"2026-05-18T00:16:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rYek73yhTqy83EITm5Q/tWgncq+kJ4oXro/y5t35QE3mQ5Q/zbj/5vze/cb9ZuED3Xu02WqzA/MixVbHQqW1Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:29:12.942120Z"},"content_sha256":"7094994cf2da453b41ae62efe19e91679a685e6d5dee8865b7a16fbe35752085","schema_version":"1.0","event_id":"sha256:7094994cf2da453b41ae62efe19e91679a685e6d5dee8865b7a16fbe35752085"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EJNYIUIYUYXPUVRY4KUW2XGLGH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extracting structured dynamical systems using sparse optimization with very few samples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.IT"],"primary_cat":"cs.IT","authors_text":"Giang Tran, Hayden Schaeffer, Linan Zhang, Rachel Ward","submitted_at":"2018-05-10T20:11:52Z","abstract_excerpt":"Learning governing equations allows for deeper understanding of the structure and dynamics of data. We present a random sampling method for learning structured dynamical systems from under-sampled and possibly noisy state-space measurements. The learning problem takes the form of a sparse least-squares fitting over a large set of candidate functions. Based on a Bernstein-like inequality for partly dependent random variables, we provide theoretical guarantees on the recovery rate of the sparse coefficients and the identification of the candidate functions for the corresponding problem. Computat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04158","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":"2026-05-18T00:16:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p+citKJa9NVaBn83rCTNxCZNZCiG6p1KAKDCPzFKunc7n3gNbQr8W3aNBMp3Kl0RJWp/8XSf2ad7gXqOs2ycCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:29:12.942640Z"},"content_sha256":"87f491ce0cfcd112c98c85febf171783dde852f7b506a6c455230bd88dfaa464","schema_version":"1.0","event_id":"sha256:87f491ce0cfcd112c98c85febf171783dde852f7b506a6c455230bd88dfaa464"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EJNYIUIYUYXPUVRY4KUW2XGLGH/bundle.json","state_url":"https://pith.science/pith/EJNYIUIYUYXPUVRY4KUW2XGLGH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EJNYIUIYUYXPUVRY4KUW2XGLGH/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":"2026-08-04T19:29:12Z","links":{"resolver":"https://pith.science/pith/EJNYIUIYUYXPUVRY4KUW2XGLGH","bundle":"https://pith.science/pith/EJNYIUIYUYXPUVRY4KUW2XGLGH/bundle.json","state":"https://pith.science/pith/EJNYIUIYUYXPUVRY4KUW2XGLGH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EJNYIUIYUYXPUVRY4KUW2XGLGH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EJNYIUIYUYXPUVRY4KUW2XGLGH","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":"1ddf30f342427fb763abf5917f84541f2c63caa7aa73881a2e96d59ea16f844f","cross_cats_sorted":["cs.NA","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-05-10T20:11:52Z","title_canon_sha256":"1aee25c83ea4220e4cb78ef6f71f3a3a7307cdd54d18315635aa7203049f56e7"},"schema_version":"1.0","source":{"id":"1805.04158","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.04158","created_at":"2026-05-18T00:16:13Z"},{"alias_kind":"arxiv_version","alias_value":"1805.04158v1","created_at":"2026-05-18T00:16:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.04158","created_at":"2026-05-18T00:16:13Z"},{"alias_kind":"pith_short_12","alias_value":"EJNYIUIYUYXP","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EJNYIUIYUYXPUVRY","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EJNYIUIY","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:87f491ce0cfcd112c98c85febf171783dde852f7b506a6c455230bd88dfaa464","target":"graph","created_at":"2026-05-18T00:16:13Z","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":"Learning governing equations allows for deeper understanding of the structure and dynamics of data. We present a random sampling method for learning structured dynamical systems from under-sampled and possibly noisy state-space measurements. The learning problem takes the form of a sparse least-squares fitting over a large set of candidate functions. Based on a Bernstein-like inequality for partly dependent random variables, we provide theoretical guarantees on the recovery rate of the sparse coefficients and the identification of the candidate functions for the corresponding problem. Computat","authors_text":"Giang Tran, Hayden Schaeffer, Linan Zhang, Rachel Ward","cross_cats":["cs.NA","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-05-10T20:11:52Z","title":"Extracting structured dynamical systems using sparse optimization with very few samples"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04158","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":"sha256:7094994cf2da453b41ae62efe19e91679a685e6d5dee8865b7a16fbe35752085","target":"record","created_at":"2026-05-18T00:16:13Z","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":"1ddf30f342427fb763abf5917f84541f2c63caa7aa73881a2e96d59ea16f844f","cross_cats_sorted":["cs.NA","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-05-10T20:11:52Z","title_canon_sha256":"1aee25c83ea4220e4cb78ef6f71f3a3a7307cdd54d18315635aa7203049f56e7"},"schema_version":"1.0","source":{"id":"1805.04158","kind":"arxiv","version":1}},"canonical_sha256":"225b845118a62efa5638e2a96d5ccb31d7a85af0b0b6aa6628e7cb49f70bdf90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"225b845118a62efa5638e2a96d5ccb31d7a85af0b0b6aa6628e7cb49f70bdf90","first_computed_at":"2026-05-18T00:16:13.458991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:13.458991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0jrSYpRFUN5kjGAYWAY862nL4XrvtvV2X8bOc+bI4H0AU5T/f8II5gkS12tBFeRzUeRev+NGjA5CS2OgZ+ZiDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:13.459539Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.04158","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7094994cf2da453b41ae62efe19e91679a685e6d5dee8865b7a16fbe35752085","sha256:87f491ce0cfcd112c98c85febf171783dde852f7b506a6c455230bd88dfaa464"],"state_sha256":"0cf6e3333a6e7fd786649a09bffab107afbd76ce3b96a5b6036419875c3cb861"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tryr+MirQg7wwO+Z7E1z1oi8tX3aXi5nV58zHn4b/L/AYEnstY12X3LAd9e+Z93Lk84tckYI9LCiS2/dS8muAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T19:29:12.946300Z","bundle_sha256":"b6fffa4a7382b8ecc8c36c32e134681bd72afa166f4009a6e3b56e9f96c84696"}}