{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:SWO5NTPK6JB6KYR2JZ54OL372G","short_pith_number":"pith:SWO5NTPK","schema_version":"1.0","canonical_sha256":"959dd6cdeaf243e5623a4e7bc72f7fd190c05440c098eb1b648e6b4524e39b71","source":{"kind":"arxiv","id":"2607.25163","version":1},"attestation_state":"computed","paper":{"title":"A Riemannian View on Active Subspaces","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.DG"],"primary_cat":"math.NA","authors_text":"Zachary Grey","submitted_at":"2026-07-28T00:22:24Z","abstract_excerpt":"Active subspaces provide an explainable, eigenvalue-ordered principle for studying how scalar-valued quantities of interest change the most, on average, over a reduced basis of Euclidean domains. Composition with parallel transport generalizes this principle from Euclidean space to quantities of interest defined over Riemannian manifolds, and the resulting intrinsic formulation is contrasted with the extrinsic, embedding-based gradient average of manifold learning. Either strategy is studied in an intrinsically local sense, restricted to mean-centered geodesic-balls, and within that scope the "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.25163","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-28T00:22:24Z","cross_cats_sorted":["cs.LG","cs.NA","math.DG"],"title_canon_sha256":"2e1c7b20ee69caf666cc2957dc07b38f00ab9a5844e79299aa93bd12f0e7c4a8","abstract_canon_sha256":"fb228f0768d7582b2d5e0b64bd547657e28fdc89783368d506207eaea541d181"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-29T00:25:06.244666Z","signature_b64":"cXb/M6TC4XG1oTRHfKqDpBO+djR8y2BK+XiO3cfYv5Ij8F3ucUQsoMVh3N/9QfgQSq5SZp7hFbha/ZvadtkQDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"959dd6cdeaf243e5623a4e7bc72f7fd190c05440c098eb1b648e6b4524e39b71","last_reissued_at":"2026-07-29T00:25:06.243851Z","signature_status":"signed_v1","first_computed_at":"2026-07-29T00:25:06.243851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Riemannian View on Active Subspaces","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.DG"],"primary_cat":"math.NA","authors_text":"Zachary Grey","submitted_at":"2026-07-28T00:22:24Z","abstract_excerpt":"Active subspaces provide an explainable, eigenvalue-ordered principle for studying how scalar-valued quantities of interest change the most, on average, over a reduced basis of Euclidean domains. Composition with parallel transport generalizes this principle from Euclidean space to quantities of interest defined over Riemannian manifolds, and the resulting intrinsic formulation is contrasted with the extrinsic, embedding-based gradient average of manifold learning. Either strategy is studied in an intrinsically local sense, restricted to mean-centered geodesic-balls, and within that scope the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.25163","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/2607.25163/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.25163","created_at":"2026-07-29T00:25:06.244260+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.25163v1","created_at":"2026-07-29T00:25:06.244260+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.25163","created_at":"2026-07-29T00:25:06.244260+00:00"},{"alias_kind":"pith_short_12","alias_value":"SWO5NTPK6JB6","created_at":"2026-07-29T00:25:06.244260+00:00"},{"alias_kind":"pith_short_16","alias_value":"SWO5NTPK6JB6KYR2","created_at":"2026-07-29T00:25:06.244260+00:00"},{"alias_kind":"pith_short_8","alias_value":"SWO5NTPK","created_at":"2026-07-29T00:25:06.244260+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SWO5NTPK6JB6KYR2JZ54OL372G","json":"https://pith.science/pith/SWO5NTPK6JB6KYR2JZ54OL372G.json","graph_json":"https://pith.science/api/pith-number/SWO5NTPK6JB6KYR2JZ54OL372G/graph.json","events_json":"https://pith.science/api/pith-number/SWO5NTPK6JB6KYR2JZ54OL372G/events.json","paper":"https://pith.science/paper/SWO5NTPK"},"agent_actions":{"view_html":"https://pith.science/pith/SWO5NTPK6JB6KYR2JZ54OL372G","download_json":"https://pith.science/pith/SWO5NTPK6JB6KYR2JZ54OL372G.json","view_paper":"https://pith.science/paper/SWO5NTPK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.25163&json=true","fetch_graph":"https://pith.science/api/pith-number/SWO5NTPK6JB6KYR2JZ54OL372G/graph.json","fetch_events":"https://pith.science/api/pith-number/SWO5NTPK6JB6KYR2JZ54OL372G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SWO5NTPK6JB6KYR2JZ54OL372G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SWO5NTPK6JB6KYR2JZ54OL372G/action/storage_attestation","attest_author":"https://pith.science/pith/SWO5NTPK6JB6KYR2JZ54OL372G/action/author_attestation","sign_citation":"https://pith.science/pith/SWO5NTPK6JB6KYR2JZ54OL372G/action/citation_signature","submit_replication":"https://pith.science/pith/SWO5NTPK6JB6KYR2JZ54OL372G/action/replication_record"}},"created_at":"2026-07-29T00:25:06.244260+00:00","updated_at":"2026-07-29T00:25:06.244260+00:00"}