{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:XTHE4LPDDFCYSWM3EX62U2LW57","short_pith_number":"pith:XTHE4LPD","schema_version":"1.0","canonical_sha256":"bcce4e2de3194589599b25fdaa6976efdd6d6c515e866b2d89a8efc67f9948b9","source":{"kind":"arxiv","id":"2512.23476","version":2},"attestation_state":"computed","paper":{"title":"Sensitivity Analysis on the Sphere and a Spherical ANOVA Decomposition","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A function on the sphere decomposes into a sum of terms each depending on a coordinate subset and a parity vector.","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Laura Weidensager","submitted_at":"2025-12-29T13:59:36Z","abstract_excerpt":"We establish sensitivity analysis on the sphere. We present formulas that allow us to decompose a function $f\\colon \\mathbb S^d\\rightarrow \\mathbb R$ into a sum of terms $f_{\\boldsymbol u,\\boldsymbol \\xi}$. The index $\\boldsymbol u$ is a subset of $\\{1,2,\\ldots,d+1\\}$, where each term $f_{\\boldsymbol u,\\boldsymbol \\xi}$ depends only on the variables with indices in $\\boldsymbol u$. In contrast to the classical analysis of variance (ANOVA) decomposition, we additionally use the decomposition of a function into functions with different parity, which adds the additional parameter $\\boldsymbol \\xi"},"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":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2512.23476","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-12-29T13:59:36Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"dde61ceec236665529df38ade39125d36d7d4f36b2c74d6cd8acd55e55f82f7d","abstract_canon_sha256":"45a0de1cab9456946bbedc781278695e00cd1e9d7493f582bf4e274cf41f9e77"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:16.776884Z","signature_b64":"+y2UimaXVwxUsyQzMGOi2TmIrbfdQNiUAJm4kwYo1BTbPQYmKLpw7txCsCnKpip0lMmcv7SRFje1YLHkAQOmDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcce4e2de3194589599b25fdaa6976efdd6d6c515e866b2d89a8efc67f9948b9","last_reissued_at":"2026-05-17T23:39:16.776268Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:16.776268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sensitivity Analysis on the Sphere and a Spherical ANOVA Decomposition","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A function on the sphere decomposes into a sum of terms each depending on a coordinate subset and a parity vector.","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Laura Weidensager","submitted_at":"2025-12-29T13:59:36Z","abstract_excerpt":"We establish sensitivity analysis on the sphere. We present formulas that allow us to decompose a function $f\\colon \\mathbb S^d\\rightarrow \\mathbb R$ into a sum of terms $f_{\\boldsymbol u,\\boldsymbol \\xi}$. The index $\\boldsymbol u$ is a subset of $\\{1,2,\\ldots,d+1\\}$, where each term $f_{\\boldsymbol u,\\boldsymbol \\xi}$ depends only on the variables with indices in $\\boldsymbol u$. In contrast to the classical analysis of variance (ANOVA) decomposition, we additionally use the decomposition of a function into functions with different parity, which adds the additional parameter $\\boldsymbol \\xi"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We present formulas that allow us to decompose a function f : S^d → R into a sum of terms f_{u,ξ}. The index u is a subset of {1,2,…,d+1}, where each term f_{u,ξ} depends only on the variables with indices in u.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The natural geometry on the sphere naturally leads to the dependencies between the input variables, and suitable orthogonal basis functions exist that permit the decomposition and approximation.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A parity-augmented ANOVA decomposition is established for functions on the sphere using orthogonal bases to capture geometry-induced variable dependencies.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A function on the sphere decomposes into a sum of terms each depending on a coordinate subset and a parity vector.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"43bf55e48963c9f5135caa7453382b4ca68d022590202f352dceb96d43294e87"},"source":{"id":"2512.23476","kind":"arxiv","version":2},"verdict":{"id":"58e058cc-fd5f-4475-bdb9-6fc4460718c0","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T19:17:21.819647Z","strongest_claim":"We present formulas that allow us to decompose a function f : S^d → R into a sum of terms f_{u,ξ}. The index u is a subset of {1,2,…,d+1}, where each term f_{u,ξ} depends only on the variables with indices in u.","one_line_summary":"A parity-augmented ANOVA decomposition is established for functions on the sphere using orthogonal bases to capture geometry-induced variable dependencies.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The natural geometry on the sphere naturally leads to the dependencies between the input variables, and suitable orthogonal basis functions exist that permit the decomposition and approximation.","pith_extraction_headline":"A function on the sphere decomposes into a sum of terms each depending on a coordinate subset and a parity vector."},"references":{"count":36,"sample":[{"doi":"","year":1964,"title":"M. Abramowitz and I. A. Stegun.Handbook of Mathematical Functions, With Formulas, Graphs, and Mathe- matical Tables. National Bureau of Standards, 1964","work_id":"0e36c975-0779-4a03-a3f0-cb4baa549a58","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2004,"title":"H.-J. Bungartz and M. Griebel. Sparse grids.Acta Numer., 13:147–269, 2004.doi:10.1017/ S0962492904000182","work_id":"c35d079f-c756-4fdf-a607-cc3f1a3b73aa","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.21314/jcf.1997.005","year":1997,"title":"R. Caflisch, W. Morokoff, and A. Owen. Valuation of mortgage-backed securities using Brownian bridges to reduce effective dimension.J. Comput. Finance, 1(1):27–46, 1997.doi:10.21314/jcf.1997.005","work_id":"d631d6b6-478d-4659-84c1-c50bf364bc44","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1137/s0895479803433295","year":2005,"title":"M. Chu, N. Del Buono, L. Lopez, and T. Politi. On the low-rank approximation of data on the unit sphere.SIAM Journal on Matrix Analysis and Applications, 27(1):46–60, Jan. 2005.doi:10.1137/s0895479803","work_id":"013c7184-367e-4404-9a51-0e94fd2be0fa","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.48550/arxiv.2101.05487","year":2021,"title":"S. da Veiga. Kernel-based ANOV A decomposition and shapley effects – application to global sensitivity analysis, 2021.arXiv:2101.05487,doi:10.48550/ARXIV.2101.05487. 24 Sensitivity Analysis on the Sph","work_id":"1d75d102-ea79-4e93-aa7f-bcf980b9a12c","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":36,"snapshot_sha256":"bf27094c84a05380e38f3a04e7856fd29d4b737dc6b740ea146f5e547abd102e","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"60613f69fcc73fb8f25f53e831ecca784b6681502f8b4dfc1e6db33a407ede03"},"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":"2512.23476","created_at":"2026-05-17T23:39:16.776373+00:00"},{"alias_kind":"arxiv_version","alias_value":"2512.23476v2","created_at":"2026-05-17T23:39:16.776373+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.23476","created_at":"2026-05-17T23:39:16.776373+00:00"},{"alias_kind":"pith_short_12","alias_value":"XTHE4LPDDFCY","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"XTHE4LPDDFCYSWM3","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"XTHE4LPD","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XTHE4LPDDFCYSWM3EX62U2LW57","json":"https://pith.science/pith/XTHE4LPDDFCYSWM3EX62U2LW57.json","graph_json":"https://pith.science/api/pith-number/XTHE4LPDDFCYSWM3EX62U2LW57/graph.json","events_json":"https://pith.science/api/pith-number/XTHE4LPDDFCYSWM3EX62U2LW57/events.json","paper":"https://pith.science/paper/XTHE4LPD"},"agent_actions":{"view_html":"https://pith.science/pith/XTHE4LPDDFCYSWM3EX62U2LW57","download_json":"https://pith.science/pith/XTHE4LPDDFCYSWM3EX62U2LW57.json","view_paper":"https://pith.science/paper/XTHE4LPD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2512.23476&json=true","fetch_graph":"https://pith.science/api/pith-number/XTHE4LPDDFCYSWM3EX62U2LW57/graph.json","fetch_events":"https://pith.science/api/pith-number/XTHE4LPDDFCYSWM3EX62U2LW57/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XTHE4LPDDFCYSWM3EX62U2LW57/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XTHE4LPDDFCYSWM3EX62U2LW57/action/storage_attestation","attest_author":"https://pith.science/pith/XTHE4LPDDFCYSWM3EX62U2LW57/action/author_attestation","sign_citation":"https://pith.science/pith/XTHE4LPDDFCYSWM3EX62U2LW57/action/citation_signature","submit_replication":"https://pith.science/pith/XTHE4LPDDFCYSWM3EX62U2LW57/action/replication_record"}},"created_at":"2026-05-17T23:39:16.776373+00:00","updated_at":"2026-05-17T23:39:16.776373+00:00"}