{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:3WOTX2KNZC64L3NOSEM6QOF52P","short_pith_number":"pith:3WOTX2KN","schema_version":"1.0","canonical_sha256":"dd9d3be94dc8bdc5edae9119e838bdd3c31211329548cec3d954501ffc6d4b92","source":{"kind":"arxiv","id":"1312.0909","version":4},"attestation_state":"computed","paper":{"title":"Spherical Functions of Fundamental $K$-Types Associated with the $n$-Dimensional Sphere","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ignacio Nahuel Zurri\\'an, Juan Alfredo Tirao","submitted_at":"2013-12-03T19:16:47Z","abstract_excerpt":"In this paper, we describe the irreducible spherical functions of fundamental $K$-types associated with the pair $(G,K)=({\\mathrm{SO}}(n+1),{\\mathrm{SO}}(n))$ in terms of matrix hypergeometric functions. The output of this description is that the irreducible spherical functions of the same $K$-fundamental type are encoded in new examples of classical sequences of matrix-valued orthogonal polynomials, of size $2$ and $3$, with respect to a matrix-weight $W$ supported on $[0,1]$. Moreover, we show that $W$ has a second order symmetric hypergeometric operator $D$."},"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":"1312.0909","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.RT","submitted_at":"2013-12-03T19:16:47Z","cross_cats_sorted":[],"title_canon_sha256":"f3a44c517a3cb8af9d566b88002bb5e34a547f7ddb8de5de677cb436002782fe","abstract_canon_sha256":"5a79552c7d2e68137dc6a78f1be537a48b7763b334a04c420de8da23654e0391"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:17.412464Z","signature_b64":"nAFFmhSvHGOVSeNQbGOiffIUYR1GBr9jmc8Ps/QOCm6oLZaMH4SwRB1VTkAHzy+lS1ZVRO3qK6JUHoqna/jLAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd9d3be94dc8bdc5edae9119e838bdd3c31211329548cec3d954501ffc6d4b92","last_reissued_at":"2026-05-18T02:48:17.411819Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:17.411819Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spherical Functions of Fundamental $K$-Types Associated with the $n$-Dimensional Sphere","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ignacio Nahuel Zurri\\'an, Juan Alfredo Tirao","submitted_at":"2013-12-03T19:16:47Z","abstract_excerpt":"In this paper, we describe the irreducible spherical functions of fundamental $K$-types associated with the pair $(G,K)=({\\mathrm{SO}}(n+1),{\\mathrm{SO}}(n))$ in terms of matrix hypergeometric functions. The output of this description is that the irreducible spherical functions of the same $K$-fundamental type are encoded in new examples of classical sequences of matrix-valued orthogonal polynomials, of size $2$ and $3$, with respect to a matrix-weight $W$ supported on $[0,1]$. Moreover, we show that $W$ has a second order symmetric hypergeometric operator $D$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0909","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1312.0909","created_at":"2026-05-18T02:48:17.411923+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.0909v4","created_at":"2026-05-18T02:48:17.411923+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0909","created_at":"2026-05-18T02:48:17.411923+00:00"},{"alias_kind":"pith_short_12","alias_value":"3WOTX2KNZC64","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"3WOTX2KNZC64L3NO","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"3WOTX2KN","created_at":"2026-05-18T12:27:32.513160+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/3WOTX2KNZC64L3NOSEM6QOF52P","json":"https://pith.science/pith/3WOTX2KNZC64L3NOSEM6QOF52P.json","graph_json":"https://pith.science/api/pith-number/3WOTX2KNZC64L3NOSEM6QOF52P/graph.json","events_json":"https://pith.science/api/pith-number/3WOTX2KNZC64L3NOSEM6QOF52P/events.json","paper":"https://pith.science/paper/3WOTX2KN"},"agent_actions":{"view_html":"https://pith.science/pith/3WOTX2KNZC64L3NOSEM6QOF52P","download_json":"https://pith.science/pith/3WOTX2KNZC64L3NOSEM6QOF52P.json","view_paper":"https://pith.science/paper/3WOTX2KN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.0909&json=true","fetch_graph":"https://pith.science/api/pith-number/3WOTX2KNZC64L3NOSEM6QOF52P/graph.json","fetch_events":"https://pith.science/api/pith-number/3WOTX2KNZC64L3NOSEM6QOF52P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3WOTX2KNZC64L3NOSEM6QOF52P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3WOTX2KNZC64L3NOSEM6QOF52P/action/storage_attestation","attest_author":"https://pith.science/pith/3WOTX2KNZC64L3NOSEM6QOF52P/action/author_attestation","sign_citation":"https://pith.science/pith/3WOTX2KNZC64L3NOSEM6QOF52P/action/citation_signature","submit_replication":"https://pith.science/pith/3WOTX2KNZC64L3NOSEM6QOF52P/action/replication_record"}},"created_at":"2026-05-18T02:48:17.411923+00:00","updated_at":"2026-05-18T02:48:17.411923+00:00"}