{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:AVAYPVYGIABVEDDSGR7PFT4VDU","short_pith_number":"pith:AVAYPVYG","schema_version":"1.0","canonical_sha256":"054187d7064003520c72347ef2cf951d32288938d06c7cea010e9700be211e6b","source":{"kind":"arxiv","id":"math/0407448","version":1},"attestation_state":"computed","paper":{"title":"Polynomial Interpolation on the Unit Sphere II","license":"","headline":"","cross_cats":["cs.NA","math.CA"],"primary_cat":"math.NA","authors_text":"Noemi Lain Fernandez, Wolfgang zu Castell, Yuan Xu","submitted_at":"2004-07-27T00:13:26Z","abstract_excerpt":"The problem of interpolation at $(n+1)^2$ points on the unit sphere $\\mathbb{S}^2$ by spherical polynomials of degree at most $n$ is proved to have a unique solution for several sets of points. The points are located on a number of circles on the sphere with even number of points on each circle. The proof is based on a method of factorization of polynomials."},"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":"math/0407448","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NA","submitted_at":"2004-07-27T00:13:26Z","cross_cats_sorted":["cs.NA","math.CA"],"title_canon_sha256":"6a50e548967f433b0d1499403dbb1e4a422b1528fd24bb7d4ca365ec943646b8","abstract_canon_sha256":"9cf153af2029714b01acda38bd904940bbd6ba36b1dc53441906a7d0a289ce77"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T22:06:15.482534Z","signature_b64":"FoaAvINtTCtkZV1WsPf8x5QFmC+6XpMYos3cdjL2KijF5aIVBWNL58q9XTvB2cramml+oQuL2EouwsIzl9hjAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"054187d7064003520c72347ef2cf951d32288938d06c7cea010e9700be211e6b","last_reissued_at":"2026-06-03T22:06:15.482098Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T22:06:15.482098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polynomial Interpolation on the Unit Sphere II","license":"","headline":"","cross_cats":["cs.NA","math.CA"],"primary_cat":"math.NA","authors_text":"Noemi Lain Fernandez, Wolfgang zu Castell, Yuan Xu","submitted_at":"2004-07-27T00:13:26Z","abstract_excerpt":"The problem of interpolation at $(n+1)^2$ points on the unit sphere $\\mathbb{S}^2$ by spherical polynomials of degree at most $n$ is proved to have a unique solution for several sets of points. The points are located on a number of circles on the sphere with even number of points on each circle. The proof is based on a method of factorization of polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0407448","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/math/0407448/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":"math/0407448","created_at":"2026-06-03T22:06:15.482168+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0407448v1","created_at":"2026-06-03T22:06:15.482168+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0407448","created_at":"2026-06-03T22:06:15.482168+00:00"},{"alias_kind":"pith_short_12","alias_value":"AVAYPVYGIABV","created_at":"2026-06-03T22:06:15.482168+00:00"},{"alias_kind":"pith_short_16","alias_value":"AVAYPVYGIABVEDDS","created_at":"2026-06-03T22:06:15.482168+00:00"},{"alias_kind":"pith_short_8","alias_value":"AVAYPVYG","created_at":"2026-06-03T22:06:15.482168+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/AVAYPVYGIABVEDDSGR7PFT4VDU","json":"https://pith.science/pith/AVAYPVYGIABVEDDSGR7PFT4VDU.json","graph_json":"https://pith.science/api/pith-number/AVAYPVYGIABVEDDSGR7PFT4VDU/graph.json","events_json":"https://pith.science/api/pith-number/AVAYPVYGIABVEDDSGR7PFT4VDU/events.json","paper":"https://pith.science/paper/AVAYPVYG"},"agent_actions":{"view_html":"https://pith.science/pith/AVAYPVYGIABVEDDSGR7PFT4VDU","download_json":"https://pith.science/pith/AVAYPVYGIABVEDDSGR7PFT4VDU.json","view_paper":"https://pith.science/paper/AVAYPVYG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0407448&json=true","fetch_graph":"https://pith.science/api/pith-number/AVAYPVYGIABVEDDSGR7PFT4VDU/graph.json","fetch_events":"https://pith.science/api/pith-number/AVAYPVYGIABVEDDSGR7PFT4VDU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AVAYPVYGIABVEDDSGR7PFT4VDU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AVAYPVYGIABVEDDSGR7PFT4VDU/action/storage_attestation","attest_author":"https://pith.science/pith/AVAYPVYGIABVEDDSGR7PFT4VDU/action/author_attestation","sign_citation":"https://pith.science/pith/AVAYPVYGIABVEDDSGR7PFT4VDU/action/citation_signature","submit_replication":"https://pith.science/pith/AVAYPVYGIABVEDDSGR7PFT4VDU/action/replication_record"}},"created_at":"2026-06-03T22:06:15.482168+00:00","updated_at":"2026-06-03T22:06:15.482168+00:00"}