{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:DKN5JVY35F6CKMY2GLYEYQSAZM","short_pith_number":"pith:DKN5JVY3","canonical_record":{"source":{"id":"1909.09448","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-09-20T12:21:14Z","cross_cats_sorted":["cs.LG","cs.NA","physics.comp-ph","stat.ML"],"title_canon_sha256":"68da4d5ca2a1d6e08b353b40972fe28707ae51123b258ad4f8e5aaf898449ac7","abstract_canon_sha256":"830ddda20023728cbe9fef20cf78fd3ec395b489c538adb648ba123ae757c42f"},"schema_version":"1.0"},"canonical_sha256":"1a9bd4d71be97c25331a32f04c4240cb113eee854908dba07490de3f6a79ba8d","source":{"kind":"arxiv","id":"1909.09448","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.09448","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"arxiv_version","alias_value":"1909.09448v2","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.09448","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"pith_short_12","alias_value":"DKN5JVY35F6C","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"pith_short_16","alias_value":"DKN5JVY35F6CKMY2","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"pith_short_8","alias_value":"DKN5JVY3","created_at":"2026-07-05T01:15:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:DKN5JVY35F6CKMY2GLYEYQSAZM","target":"record","payload":{"canonical_record":{"source":{"id":"1909.09448","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-09-20T12:21:14Z","cross_cats_sorted":["cs.LG","cs.NA","physics.comp-ph","stat.ML"],"title_canon_sha256":"68da4d5ca2a1d6e08b353b40972fe28707ae51123b258ad4f8e5aaf898449ac7","abstract_canon_sha256":"830ddda20023728cbe9fef20cf78fd3ec395b489c538adb648ba123ae757c42f"},"schema_version":"1.0"},"canonical_sha256":"1a9bd4d71be97c25331a32f04c4240cb113eee854908dba07490de3f6a79ba8d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:15:55.429208Z","signature_b64":"pZPM3ygT6XEa3qIBZnSsqzy9bW/PMU2giRtTGwb++nAVxTH+gxsy7aUDvLJSDOqo3y9Kraz3nY4XL+1Soh4ODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a9bd4d71be97c25331a32f04c4240cb113eee854908dba07490de3f6a79ba8d","last_reissued_at":"2026-07-05T01:15:55.428799Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:15:55.428799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1909.09448","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:15:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lig5blQQ3AJi/JL6ibTFzUVnguaDODKVvfyJzKs+PlH/lR/TnSfWdKDo+fJWSs8AMa8MRi0WZkzr9SktfqHdBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T15:53:01.010286Z"},"content_sha256":"38dc257a2fdad8e14cb6d31b8c21fb14c4c0cab92a3312d9ed788303b9be085b","schema_version":"1.0","event_id":"sha256:38dc257a2fdad8e14cb6d31b8c21fb14c4c0cab92a3312d9ed788303b9be085b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:DKN5JVY35F6CKMY2GLYEYQSAZM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Multi-level procedure for enhancing accuracy of machine learning algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","physics.comp-ph","stat.ML"],"primary_cat":"math.NA","authors_text":"Kjetil O. Lye, Roberto Molinaro, Siddhartha Mishra","submitted_at":"2019-09-20T12:21:14Z","abstract_excerpt":"We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations. The algorithm relies on judiciously combining a large number of computationally cheap training data on coarse resolutions with a few expensive training samples on fine grid resolutions. Theoretical arguments for lowering the generalization error, based on reducing the variance of the underlying maps, are provided and numerical evidence, indicating significant gains over underlyi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.09448","kind":"arxiv","version":2},"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/1909.09448/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":"2026-07-05T01:15:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ptdx7BMKIf0ivC7a0BRIPTbp8cKlF6GKlpeua2JCGVQ9kbmKeIomVYwqu4AFYJNHN9mS0a+Pv5TCm+0w7SPaCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T15:53:01.010736Z"},"content_sha256":"15d3d033f41c9907a8d666c2995c4db8fcb6a0f94070a761af5890a39742fbfb","schema_version":"1.0","event_id":"sha256:15d3d033f41c9907a8d666c2995c4db8fcb6a0f94070a761af5890a39742fbfb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DKN5JVY35F6CKMY2GLYEYQSAZM/bundle.json","state_url":"https://pith.science/pith/DKN5JVY35F6CKMY2GLYEYQSAZM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DKN5JVY35F6CKMY2GLYEYQSAZM/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":"2026-08-01T15:53:01Z","links":{"resolver":"https://pith.science/pith/DKN5JVY35F6CKMY2GLYEYQSAZM","bundle":"https://pith.science/pith/DKN5JVY35F6CKMY2GLYEYQSAZM/bundle.json","state":"https://pith.science/pith/DKN5JVY35F6CKMY2GLYEYQSAZM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DKN5JVY35F6CKMY2GLYEYQSAZM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:DKN5JVY35F6CKMY2GLYEYQSAZM","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":"830ddda20023728cbe9fef20cf78fd3ec395b489c538adb648ba123ae757c42f","cross_cats_sorted":["cs.LG","cs.NA","physics.comp-ph","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-09-20T12:21:14Z","title_canon_sha256":"68da4d5ca2a1d6e08b353b40972fe28707ae51123b258ad4f8e5aaf898449ac7"},"schema_version":"1.0","source":{"id":"1909.09448","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.09448","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"arxiv_version","alias_value":"1909.09448v2","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.09448","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"pith_short_12","alias_value":"DKN5JVY35F6C","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"pith_short_16","alias_value":"DKN5JVY35F6CKMY2","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"pith_short_8","alias_value":"DKN5JVY3","created_at":"2026-07-05T01:15:55Z"}],"graph_snapshots":[{"event_id":"sha256:15d3d033f41c9907a8d666c2995c4db8fcb6a0f94070a761af5890a39742fbfb","target":"graph","created_at":"2026-07-05T01:15:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1909.09448/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations. The algorithm relies on judiciously combining a large number of computationally cheap training data on coarse resolutions with a few expensive training samples on fine grid resolutions. Theoretical arguments for lowering the generalization error, based on reducing the variance of the underlying maps, are provided and numerical evidence, indicating significant gains over underlyi","authors_text":"Kjetil O. Lye, Roberto Molinaro, Siddhartha Mishra","cross_cats":["cs.LG","cs.NA","physics.comp-ph","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-09-20T12:21:14Z","title":"A Multi-level procedure for enhancing accuracy of machine learning algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.09448","kind":"arxiv","version":2},"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":"sha256:38dc257a2fdad8e14cb6d31b8c21fb14c4c0cab92a3312d9ed788303b9be085b","target":"record","created_at":"2026-07-05T01:15:55Z","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":"830ddda20023728cbe9fef20cf78fd3ec395b489c538adb648ba123ae757c42f","cross_cats_sorted":["cs.LG","cs.NA","physics.comp-ph","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-09-20T12:21:14Z","title_canon_sha256":"68da4d5ca2a1d6e08b353b40972fe28707ae51123b258ad4f8e5aaf898449ac7"},"schema_version":"1.0","source":{"id":"1909.09448","kind":"arxiv","version":2}},"canonical_sha256":"1a9bd4d71be97c25331a32f04c4240cb113eee854908dba07490de3f6a79ba8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a9bd4d71be97c25331a32f04c4240cb113eee854908dba07490de3f6a79ba8d","first_computed_at":"2026-07-05T01:15:55.428799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:15:55.428799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pZPM3ygT6XEa3qIBZnSsqzy9bW/PMU2giRtTGwb++nAVxTH+gxsy7aUDvLJSDOqo3y9Kraz3nY4XL+1Soh4ODw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:15:55.429208Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.09448","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38dc257a2fdad8e14cb6d31b8c21fb14c4c0cab92a3312d9ed788303b9be085b","sha256:15d3d033f41c9907a8d666c2995c4db8fcb6a0f94070a761af5890a39742fbfb"],"state_sha256":"91fd9ff2927eca5697c4367d0faa17c4b2848134c7b21add3a7265d220ac3b79"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nhAHHCO2wyRRuKebVpkHzKuqrRYmKTMjWtVbCdLekKvCqLrFEqglD9tTmskhzYu3dzr67iw7797gjNMQfjwODg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-01T15:53:01.013839Z","bundle_sha256":"b9d377c407a23c63a7fde42aabd4b5ab552f737c82bad180e1913a91cdd6da45"}}