{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:4DL3MQO2SQ4KOQZDT4PRHCOQGG","short_pith_number":"pith:4DL3MQO2","canonical_record":{"source":{"id":"2403.06732","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-03-11T13:53:12Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"705788a726101f08ef6753c246180ca1043da4177807744f33ab2025f57b4f08","abstract_canon_sha256":"e4800e2f96de32db2b1e25fb5556799eaf940ea92c0d58512f89b735cf2f26d2"},"schema_version":"1.0"},"canonical_sha256":"e0d7b641da9438a743239f1f1389d031b37e6705eb431c4a535e90203e95bdea","source":{"kind":"arxiv","id":"2403.06732","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.06732","created_at":"2026-07-05T09:48:12Z"},{"alias_kind":"arxiv_version","alias_value":"2403.06732v2","created_at":"2026-07-05T09:48:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.06732","created_at":"2026-07-05T09:48:12Z"},{"alias_kind":"pith_short_12","alias_value":"4DL3MQO2SQ4K","created_at":"2026-07-05T09:48:12Z"},{"alias_kind":"pith_short_16","alias_value":"4DL3MQO2SQ4KOQZD","created_at":"2026-07-05T09:48:12Z"},{"alias_kind":"pith_short_8","alias_value":"4DL3MQO2","created_at":"2026-07-05T09:48:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:4DL3MQO2SQ4KOQZDT4PRHCOQGG","target":"record","payload":{"canonical_record":{"source":{"id":"2403.06732","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-03-11T13:53:12Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"705788a726101f08ef6753c246180ca1043da4177807744f33ab2025f57b4f08","abstract_canon_sha256":"e4800e2f96de32db2b1e25fb5556799eaf940ea92c0d58512f89b735cf2f26d2"},"schema_version":"1.0"},"canonical_sha256":"e0d7b641da9438a743239f1f1389d031b37e6705eb431c4a535e90203e95bdea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:48:12.720700Z","signature_b64":"vv54kRah2ObIWCiIFdP0eJMrjgh0/NrwmSyjkj+9tirWZo/rNz1xfe3OvaCbX6LnxenzvLKtpl90/dcQMQLiAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0d7b641da9438a743239f1f1389d031b37e6705eb431c4a535e90203e95bdea","last_reissued_at":"2026-07-05T09:48:12.720259Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:48:12.720259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.06732","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":"2026-07-05T09:48:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DZYRGzTdTOpPsF99waAu2lXHKJZj9Xo772uunklo9SmlBKdp7O7v20v7nACtrVW031DptSkMUxneYrIRCLXwDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T14:05:06.762195Z"},"content_sha256":"f27f2db1b6165db42542525b89832e118ff63b6051018e8ad0c40dc72d981f46","schema_version":"1.0","event_id":"sha256:f27f2db1b6165db42542525b89832e118ff63b6051018e8ad0c40dc72d981f46"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:4DL3MQO2SQ4KOQZDT4PRHCOQGG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Greedy construction of quadratic manifolds for nonlinear dimensionality reduction and nonlinear model reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Benjamin Peherstorfer, Paul Schwerdtner","submitted_at":"2024-03-11T13:53:12Z","abstract_excerpt":"Dimensionality reduction on quadratic manifolds augments linear approximations with quadratic correction terms. Previous works rely on linear approximations given by projections onto the first few leading principal components of the training data; however, linear approximations in subspaces spanned by the leading principal components alone can miss information that are necessary for the quadratic correction terms to be efficient. In this work, we propose a greedy method that constructs subspaces from leading as well as later principal components so that the corresponding linear approximations "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.06732","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/2403.06732/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":"2026-07-05T09:48:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bMcbVtxHpHVslm/HowHXGneV1fk749cF/42AjE4ilX0feLKtRPkr88miKwwNSlPoiiGtYqPBUHbQfwcX+4C7DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T14:05:06.762717Z"},"content_sha256":"24b015f5b62cee689104200df80b390b7f206ba255f0921aa655b0b91df1b38a","schema_version":"1.0","event_id":"sha256:24b015f5b62cee689104200df80b390b7f206ba255f0921aa655b0b91df1b38a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4DL3MQO2SQ4KOQZDT4PRHCOQGG/bundle.json","state_url":"https://pith.science/pith/4DL3MQO2SQ4KOQZDT4PRHCOQGG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4DL3MQO2SQ4KOQZDT4PRHCOQGG/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":"2026-08-08T14:05:06Z","links":{"resolver":"https://pith.science/pith/4DL3MQO2SQ4KOQZDT4PRHCOQGG","bundle":"https://pith.science/pith/4DL3MQO2SQ4KOQZDT4PRHCOQGG/bundle.json","state":"https://pith.science/pith/4DL3MQO2SQ4KOQZDT4PRHCOQGG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4DL3MQO2SQ4KOQZDT4PRHCOQGG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:4DL3MQO2SQ4KOQZDT4PRHCOQGG","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":"e4800e2f96de32db2b1e25fb5556799eaf940ea92c0d58512f89b735cf2f26d2","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-03-11T13:53:12Z","title_canon_sha256":"705788a726101f08ef6753c246180ca1043da4177807744f33ab2025f57b4f08"},"schema_version":"1.0","source":{"id":"2403.06732","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.06732","created_at":"2026-07-05T09:48:12Z"},{"alias_kind":"arxiv_version","alias_value":"2403.06732v2","created_at":"2026-07-05T09:48:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.06732","created_at":"2026-07-05T09:48:12Z"},{"alias_kind":"pith_short_12","alias_value":"4DL3MQO2SQ4K","created_at":"2026-07-05T09:48:12Z"},{"alias_kind":"pith_short_16","alias_value":"4DL3MQO2SQ4KOQZD","created_at":"2026-07-05T09:48:12Z"},{"alias_kind":"pith_short_8","alias_value":"4DL3MQO2","created_at":"2026-07-05T09:48:12Z"}],"graph_snapshots":[{"event_id":"sha256:24b015f5b62cee689104200df80b390b7f206ba255f0921aa655b0b91df1b38a","target":"graph","created_at":"2026-07-05T09:48:12Z","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/2403.06732/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Dimensionality reduction on quadratic manifolds augments linear approximations with quadratic correction terms. Previous works rely on linear approximations given by projections onto the first few leading principal components of the training data; however, linear approximations in subspaces spanned by the leading principal components alone can miss information that are necessary for the quadratic correction terms to be efficient. In this work, we propose a greedy method that constructs subspaces from leading as well as later principal components so that the corresponding linear approximations ","authors_text":"Benjamin Peherstorfer, Paul Schwerdtner","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-03-11T13:53:12Z","title":"Greedy construction of quadratic manifolds for nonlinear dimensionality reduction and nonlinear model reduction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.06732","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:f27f2db1b6165db42542525b89832e118ff63b6051018e8ad0c40dc72d981f46","target":"record","created_at":"2026-07-05T09:48:12Z","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":"e4800e2f96de32db2b1e25fb5556799eaf940ea92c0d58512f89b735cf2f26d2","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-03-11T13:53:12Z","title_canon_sha256":"705788a726101f08ef6753c246180ca1043da4177807744f33ab2025f57b4f08"},"schema_version":"1.0","source":{"id":"2403.06732","kind":"arxiv","version":2}},"canonical_sha256":"e0d7b641da9438a743239f1f1389d031b37e6705eb431c4a535e90203e95bdea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0d7b641da9438a743239f1f1389d031b37e6705eb431c4a535e90203e95bdea","first_computed_at":"2026-07-05T09:48:12.720259Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:48:12.720259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vv54kRah2ObIWCiIFdP0eJMrjgh0/NrwmSyjkj+9tirWZo/rNz1xfe3OvaCbX6LnxenzvLKtpl90/dcQMQLiAw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:48:12.720700Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.06732","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f27f2db1b6165db42542525b89832e118ff63b6051018e8ad0c40dc72d981f46","sha256:24b015f5b62cee689104200df80b390b7f206ba255f0921aa655b0b91df1b38a"],"state_sha256":"bace1871db981a689e8148880ef400234a9669317cfdaa573130f57e98fa8530"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ggiqUbwDh61w1lP0cnb/38LZItYpou+H8SnjAosEcWcMR8WZy88iHPj3Ejpjb64HudFVDRVa8/IuDvVmSXMmBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T14:05:06.767615Z","bundle_sha256":"05844ac2517400679e5c8088e8eacb3f56444627e7ad53d8fb938b630786815f"}}