{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:JNO3XQD6BAJFWOE65WA3NEEGKN","short_pith_number":"pith:JNO3XQD6","canonical_record":{"source":{"id":"1809.09170","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-24T19:11:32Z","cross_cats_sorted":["cs.LG","cs.NA","math.DS","stat.ML"],"title_canon_sha256":"d2e6cfaae1dd3f490c99fe10b0dcaaec68916fcb2cfc53d4ddae82e33447eefe","abstract_canon_sha256":"4f3a84f52dfd9f362efad9d7d113310688645567bf5c0b7402c71c28cefc7a09"},"schema_version":"1.0"},"canonical_sha256":"4b5dbbc07e08125b389eed81b69086534670005b503f5f1123b0d28664dab4d1","source":{"kind":"arxiv","id":"1809.09170","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.09170","created_at":"2026-06-04T20:13:22Z"},{"alias_kind":"arxiv_version","alias_value":"1809.09170v1","created_at":"2026-06-04T20:13:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09170","created_at":"2026-06-04T20:13:22Z"},{"alias_kind":"pith_short_12","alias_value":"JNO3XQD6BAJF","created_at":"2026-06-04T20:13:22Z"},{"alias_kind":"pith_short_16","alias_value":"JNO3XQD6BAJFWOE6","created_at":"2026-06-04T20:13:22Z"},{"alias_kind":"pith_short_8","alias_value":"JNO3XQD6","created_at":"2026-06-04T20:13:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:JNO3XQD6BAJFWOE65WA3NEEGKN","target":"record","payload":{"canonical_record":{"source":{"id":"1809.09170","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-24T19:11:32Z","cross_cats_sorted":["cs.LG","cs.NA","math.DS","stat.ML"],"title_canon_sha256":"d2e6cfaae1dd3f490c99fe10b0dcaaec68916fcb2cfc53d4ddae82e33447eefe","abstract_canon_sha256":"4f3a84f52dfd9f362efad9d7d113310688645567bf5c0b7402c71c28cefc7a09"},"schema_version":"1.0"},"canonical_sha256":"4b5dbbc07e08125b389eed81b69086534670005b503f5f1123b0d28664dab4d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T20:13:22.752105Z","signature_b64":"HkD5N75JqRy/cdMb+JZE3pdh5WS5pOKF5+M9/dBYwi+cw3AYQFm33wJugGp2npj7o8V+CaUkI5P7wI7iSx0gAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b5dbbc07e08125b389eed81b69086534670005b503f5f1123b0d28664dab4d1","last_reissued_at":"2026-06-04T20:13:22.751630Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T20:13:22.751630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.09170","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":"2026-06-04T20:13:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A6X2sY6DmrfOUojsW2dFniuxnYQlZWtxrX/z/8H9EC+nF87cy+Izd+OL2/kjr9SYAyZJAl4uB6HtoR4PfzitCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T20:59:24.749794Z"},"content_sha256":"9ce540859d7858ec8cb872d5551cde0590ba39235768df7b021dee49c54ed6c7","schema_version":"1.0","event_id":"sha256:9ce540859d7858ec8cb872d5551cde0590ba39235768df7b021dee49c54ed6c7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:JNO3XQD6BAJFWOE65WA3NEEGKN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical Aspects for Approximating Governing Equations Using Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.DS","stat.ML"],"primary_cat":"math.NA","authors_text":"Dongbin Xiu, Kailiang Wu","submitted_at":"2018-09-24T19:11:32Z","abstract_excerpt":"We present effective numerical algorithms for locally recovering unknown governing differential equations from measurement data. We employ a set of standard basis functions, e.g., polynomials, to approximate the governing equation with high accuracy. Upon recasting the problem into a function approximation problem, we discuss several important aspects for accurate approximation. Most notably, we discuss the importance of using a large number of short bursts of trajectory data, rather than using data from a single long trajectory. Several options for the numerical algorithms to perform accurate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09170","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/1809.09170/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":"2026-06-04T20:13:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bZILp6xFVAjslJdyOdybJw8CnFImtGsciaKmKKFUNNxwBTYUAITybmJZsbx6yxsC3jPhYMgvXL4BfDLcoOHsCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T20:59:24.750161Z"},"content_sha256":"b7ea4f59e50d646fb55fd053ce4a6be38bb3dca5aec6cb3a6de4ed8ef3b1e3bb","schema_version":"1.0","event_id":"sha256:b7ea4f59e50d646fb55fd053ce4a6be38bb3dca5aec6cb3a6de4ed8ef3b1e3bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JNO3XQD6BAJFWOE65WA3NEEGKN/bundle.json","state_url":"https://pith.science/pith/JNO3XQD6BAJFWOE65WA3NEEGKN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JNO3XQD6BAJFWOE65WA3NEEGKN/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":"2026-07-04T20:59:24Z","links":{"resolver":"https://pith.science/pith/JNO3XQD6BAJFWOE65WA3NEEGKN","bundle":"https://pith.science/pith/JNO3XQD6BAJFWOE65WA3NEEGKN/bundle.json","state":"https://pith.science/pith/JNO3XQD6BAJFWOE65WA3NEEGKN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JNO3XQD6BAJFWOE65WA3NEEGKN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JNO3XQD6BAJFWOE65WA3NEEGKN","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":"4f3a84f52dfd9f362efad9d7d113310688645567bf5c0b7402c71c28cefc7a09","cross_cats_sorted":["cs.LG","cs.NA","math.DS","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-24T19:11:32Z","title_canon_sha256":"d2e6cfaae1dd3f490c99fe10b0dcaaec68916fcb2cfc53d4ddae82e33447eefe"},"schema_version":"1.0","source":{"id":"1809.09170","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.09170","created_at":"2026-06-04T20:13:22Z"},{"alias_kind":"arxiv_version","alias_value":"1809.09170v1","created_at":"2026-06-04T20:13:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09170","created_at":"2026-06-04T20:13:22Z"},{"alias_kind":"pith_short_12","alias_value":"JNO3XQD6BAJF","created_at":"2026-06-04T20:13:22Z"},{"alias_kind":"pith_short_16","alias_value":"JNO3XQD6BAJFWOE6","created_at":"2026-06-04T20:13:22Z"},{"alias_kind":"pith_short_8","alias_value":"JNO3XQD6","created_at":"2026-06-04T20:13:22Z"}],"graph_snapshots":[{"event_id":"sha256:b7ea4f59e50d646fb55fd053ce4a6be38bb3dca5aec6cb3a6de4ed8ef3b1e3bb","target":"graph","created_at":"2026-06-04T20:13:22Z","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/1809.09170/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present effective numerical algorithms for locally recovering unknown governing differential equations from measurement data. We employ a set of standard basis functions, e.g., polynomials, to approximate the governing equation with high accuracy. Upon recasting the problem into a function approximation problem, we discuss several important aspects for accurate approximation. Most notably, we discuss the importance of using a large number of short bursts of trajectory data, rather than using data from a single long trajectory. Several options for the numerical algorithms to perform accurate","authors_text":"Dongbin Xiu, Kailiang Wu","cross_cats":["cs.LG","cs.NA","math.DS","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-24T19:11:32Z","title":"Numerical Aspects for Approximating Governing Equations Using Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09170","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":"sha256:9ce540859d7858ec8cb872d5551cde0590ba39235768df7b021dee49c54ed6c7","target":"record","created_at":"2026-06-04T20:13:22Z","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":"4f3a84f52dfd9f362efad9d7d113310688645567bf5c0b7402c71c28cefc7a09","cross_cats_sorted":["cs.LG","cs.NA","math.DS","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-24T19:11:32Z","title_canon_sha256":"d2e6cfaae1dd3f490c99fe10b0dcaaec68916fcb2cfc53d4ddae82e33447eefe"},"schema_version":"1.0","source":{"id":"1809.09170","kind":"arxiv","version":1}},"canonical_sha256":"4b5dbbc07e08125b389eed81b69086534670005b503f5f1123b0d28664dab4d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b5dbbc07e08125b389eed81b69086534670005b503f5f1123b0d28664dab4d1","first_computed_at":"2026-06-04T20:13:22.751630Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T20:13:22.751630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HkD5N75JqRy/cdMb+JZE3pdh5WS5pOKF5+M9/dBYwi+cw3AYQFm33wJugGp2npj7o8V+CaUkI5P7wI7iSx0gAw==","signature_status":"signed_v1","signed_at":"2026-06-04T20:13:22.752105Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.09170","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ce540859d7858ec8cb872d5551cde0590ba39235768df7b021dee49c54ed6c7","sha256:b7ea4f59e50d646fb55fd053ce4a6be38bb3dca5aec6cb3a6de4ed8ef3b1e3bb"],"state_sha256":"3903b69b27224b4f427b9be2307d14afbb4e0812a8146f2d409a0efda7d45998"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cQm7WZjihG4BTA7kPrg8dl1JLg1oAGs/YVIbyhfDPhjlwn38ToampyXbtdiFKmd9z622JEoJanSVQE6/7IqbDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T20:59:24.752134Z","bundle_sha256":"08196add52049ec7a6ccf712ff6f9e584bc1870e38633ff00ff21ff085fe5140"}}