{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:YF4HI4VMSZHI4HTYEWPS5DMNW4","short_pith_number":"pith:YF4HI4VM","canonical_record":{"source":{"id":"1801.07922","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-24T11:06:33Z","cross_cats_sorted":[],"title_canon_sha256":"456801025e91902e6df6eb9a3a9e638d4a24a009ac3bf6be958ee7822e730efa","abstract_canon_sha256":"ae0ec0d66f345b19f7f19ea56bb3ed513d6763cfd6f3a935fc368345a560e036"},"schema_version":"1.0"},"canonical_sha256":"c1787472ac964e8e1e78259f2e8d8db735a34fc8c7eb27cf8a0e6e88f37b063d","source":{"kind":"arxiv","id":"1801.07922","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.07922","created_at":"2026-07-05T00:17:46Z"},{"alias_kind":"arxiv_version","alias_value":"1801.07922v3","created_at":"2026-07-05T00:17:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.07922","created_at":"2026-07-05T00:17:46Z"},{"alias_kind":"pith_short_12","alias_value":"YF4HI4VMSZHI","created_at":"2026-07-05T00:17:46Z"},{"alias_kind":"pith_short_16","alias_value":"YF4HI4VMSZHI4HTY","created_at":"2026-07-05T00:17:46Z"},{"alias_kind":"pith_short_8","alias_value":"YF4HI4VM","created_at":"2026-07-05T00:17:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:YF4HI4VMSZHI4HTYEWPS5DMNW4","target":"record","payload":{"canonical_record":{"source":{"id":"1801.07922","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-24T11:06:33Z","cross_cats_sorted":[],"title_canon_sha256":"456801025e91902e6df6eb9a3a9e638d4a24a009ac3bf6be958ee7822e730efa","abstract_canon_sha256":"ae0ec0d66f345b19f7f19ea56bb3ed513d6763cfd6f3a935fc368345a560e036"},"schema_version":"1.0"},"canonical_sha256":"c1787472ac964e8e1e78259f2e8d8db735a34fc8c7eb27cf8a0e6e88f37b063d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:17:46.450957Z","signature_b64":"tDG6xmFClShtChpES1Nq90QcFMDFwwjca1iajUunxyfn3L8f3taHs7VaNrU3IA0eEscRQr3nZwQgGkCoDDRBCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1787472ac964e8e1e78259f2e8d8db735a34fc8c7eb27cf8a0e6e88f37b063d","last_reissued_at":"2026-07-05T00:17:46.450497Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:17:46.450497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.07922","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:17:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OrTZm9oRqTUEstgPjxmj3t5vVcvunj5GjzrwhSPuUyYnlaLYupsBf7DT/LfJzTsf/PSMPdTAAMMimLWKMlJLAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T19:59:30.348717Z"},"content_sha256":"45637a6befac1075cd79a27a7bb352a4048eeb44fdb4c212850896aaef89ca80","schema_version":"1.0","event_id":"sha256:45637a6befac1075cd79a27a7bb352a4048eeb44fdb4c212850896aaef89ca80"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:YF4HI4VMSZHI4HTYEWPS5DMNW4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gradient-based dimension reduction of multivariate vector-valued functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cl\\'ementine Prieur, Olivier Zahm, Paul Constantine, Youssef Marzouk","submitted_at":"2018-01-24T11:06:33Z","abstract_excerpt":"Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary most strongly along a few dominant directions in the input parameter space. We propose a gradient-based method for detecting these directions and using them to construct ridge approximations of such functions, in the case where the functions are vector-valued (e.g., taking values in $\\mathbb{R}^n$). The methodology consists of minimizing an upper bound on the approximation error, obtained by subspace Poincar\\'e inequalities. We provide a thorough mathematical analysis in the case where the par"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07922","kind":"arxiv","version":3},"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/1801.07922/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":"2026-07-05T00:17:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G7fRS5rFs2cn6UHI8UXtPPsM20NbJXAb88PeurvCIJvMc1n4EFinBqE2z0wH+xVdbaB8xzhxIoZt6wuv2hlXDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T19:59:30.349056Z"},"content_sha256":"b8c2692e2dba91f518192ac0140db820023076e5382b0e4df77e9a96dcae87f7","schema_version":"1.0","event_id":"sha256:b8c2692e2dba91f518192ac0140db820023076e5382b0e4df77e9a96dcae87f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YF4HI4VMSZHI4HTYEWPS5DMNW4/bundle.json","state_url":"https://pith.science/pith/YF4HI4VMSZHI4HTYEWPS5DMNW4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YF4HI4VMSZHI4HTYEWPS5DMNW4/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":"2026-08-20T19:59:30Z","links":{"resolver":"https://pith.science/pith/YF4HI4VMSZHI4HTYEWPS5DMNW4","bundle":"https://pith.science/pith/YF4HI4VMSZHI4HTYEWPS5DMNW4/bundle.json","state":"https://pith.science/pith/YF4HI4VMSZHI4HTYEWPS5DMNW4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YF4HI4VMSZHI4HTYEWPS5DMNW4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YF4HI4VMSZHI4HTYEWPS5DMNW4","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":"ae0ec0d66f345b19f7f19ea56bb3ed513d6763cfd6f3a935fc368345a560e036","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-24T11:06:33Z","title_canon_sha256":"456801025e91902e6df6eb9a3a9e638d4a24a009ac3bf6be958ee7822e730efa"},"schema_version":"1.0","source":{"id":"1801.07922","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.07922","created_at":"2026-07-05T00:17:46Z"},{"alias_kind":"arxiv_version","alias_value":"1801.07922v3","created_at":"2026-07-05T00:17:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.07922","created_at":"2026-07-05T00:17:46Z"},{"alias_kind":"pith_short_12","alias_value":"YF4HI4VMSZHI","created_at":"2026-07-05T00:17:46Z"},{"alias_kind":"pith_short_16","alias_value":"YF4HI4VMSZHI4HTY","created_at":"2026-07-05T00:17:46Z"},{"alias_kind":"pith_short_8","alias_value":"YF4HI4VM","created_at":"2026-07-05T00:17:46Z"}],"graph_snapshots":[{"event_id":"sha256:b8c2692e2dba91f518192ac0140db820023076e5382b0e4df77e9a96dcae87f7","target":"graph","created_at":"2026-07-05T00:17:46Z","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/1801.07922/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary most strongly along a few dominant directions in the input parameter space. We propose a gradient-based method for detecting these directions and using them to construct ridge approximations of such functions, in the case where the functions are vector-valued (e.g., taking values in $\\mathbb{R}^n$). The methodology consists of minimizing an upper bound on the approximation error, obtained by subspace Poincar\\'e inequalities. We provide a thorough mathematical analysis in the case where the par","authors_text":"Cl\\'ementine Prieur, Olivier Zahm, Paul Constantine, Youssef Marzouk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-24T11:06:33Z","title":"Gradient-based dimension reduction of multivariate vector-valued functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07922","kind":"arxiv","version":3},"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":"sha256:45637a6befac1075cd79a27a7bb352a4048eeb44fdb4c212850896aaef89ca80","target":"record","created_at":"2026-07-05T00:17:46Z","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":"ae0ec0d66f345b19f7f19ea56bb3ed513d6763cfd6f3a935fc368345a560e036","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-24T11:06:33Z","title_canon_sha256":"456801025e91902e6df6eb9a3a9e638d4a24a009ac3bf6be958ee7822e730efa"},"schema_version":"1.0","source":{"id":"1801.07922","kind":"arxiv","version":3}},"canonical_sha256":"c1787472ac964e8e1e78259f2e8d8db735a34fc8c7eb27cf8a0e6e88f37b063d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1787472ac964e8e1e78259f2e8d8db735a34fc8c7eb27cf8a0e6e88f37b063d","first_computed_at":"2026-07-05T00:17:46.450497Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:17:46.450497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tDG6xmFClShtChpES1Nq90QcFMDFwwjca1iajUunxyfn3L8f3taHs7VaNrU3IA0eEscRQr3nZwQgGkCoDDRBCw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:17:46.450957Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.07922","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45637a6befac1075cd79a27a7bb352a4048eeb44fdb4c212850896aaef89ca80","sha256:b8c2692e2dba91f518192ac0140db820023076e5382b0e4df77e9a96dcae87f7"],"state_sha256":"5f6c56d1e7e7788386321c671969994f5d92a52cb93e8e682478c1848cfa7353"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ndsTQhraC4lA35JA7k8RKmMWOwFE0sCE/cGe/EmaFWyYwLTGSz3ZXrNXdgaci2uJnD78YoWQiqKVfuHKJPxxBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T19:59:30.352363Z","bundle_sha256":"24d708870e1dabef6252a442b51a1439c4c0353d5604b7d570f9fba09b6966ee"}}