{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HPH4RAWENWRUSC7PZZASICJWAT","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":"cf1a82fd7a39049da1e81a2e8ef0b21dead28903541fe846e79d502097fd6ff5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-03-16T19:45:41Z","title_canon_sha256":"6276b7df5173cce952ced3c1924f6474f86091a6ad59fc0da1a69d47d0b81189"},"schema_version":"1.0","source":{"id":"1503.04787","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04787","created_at":"2026-05-18T02:23:24Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04787v1","created_at":"2026-05-18T02:23:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04787","created_at":"2026-05-18T02:23:24Z"},{"alias_kind":"pith_short_12","alias_value":"HPH4RAWENWRU","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HPH4RAWENWRUSC7P","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HPH4RAWE","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:a0365c93370bc875e0ef6a49a5486107988e54b72f9d8a17c4e968fe29d1d959","target":"graph","created_at":"2026-05-18T02:23:24Z","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"},"paper":{"abstract_excerpt":"We introduce the notion of a pre-sequence of matrix orthogonal polynomials to mean a sequence {F_n} of matrix orthogonal functions with respect to a weight function W, satisfying a three term recursion relation and such that det(F_0) is not zero almost everywhere. By now there is a uniform construction of such sequences from irreducible spherical functions of some fixed K-types associated to compact symmetric pairs (G,K) of rank one. Our main result is that {Q_n=F_nF_0^{-1}} is a sequence of matrix orthogonal polynomials with respect to the weight function F_0WF_0*, see Theorem 2.1.","authors_text":"Juan Tirao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-03-16T19:45:41Z","title":"Pre-sequences of matrix orthogonal polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04787","kind":"arxiv","version":1},"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:fcb9115889f8413a54352c7c965b7c3e92ef91d9d4fbc8704c63e715588a7cd0","target":"record","created_at":"2026-05-18T02:23:24Z","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":"cf1a82fd7a39049da1e81a2e8ef0b21dead28903541fe846e79d502097fd6ff5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-03-16T19:45:41Z","title_canon_sha256":"6276b7df5173cce952ced3c1924f6474f86091a6ad59fc0da1a69d47d0b81189"},"schema_version":"1.0","source":{"id":"1503.04787","kind":"arxiv","version":1}},"canonical_sha256":"3bcfc882c46da3490befce4124093604f7a07539e349bd875a6108a3fabf58ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3bcfc882c46da3490befce4124093604f7a07539e349bd875a6108a3fabf58ea","first_computed_at":"2026-05-18T02:23:24.028718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:24.028718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8y/5yMr00ryBRPpLGVfhkm3HNfh+I/DlGWE5K+sE06eGEzjMBrmO0TW9WpZ9F0pJ68Kel3IS/CD9OLdrTbz7CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:24.029295Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.04787","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fcb9115889f8413a54352c7c965b7c3e92ef91d9d4fbc8704c63e715588a7cd0","sha256:a0365c93370bc875e0ef6a49a5486107988e54b72f9d8a17c4e968fe29d1d959"],"state_sha256":"359241a8ab956bb60bc26b86b57bc6e07c1e4024d748f356e688c77d9f11a79b"}