{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BJFAEZFS4M6VAOMKBZ2WPTVWJP","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":"6f01409d59d48596c9a4258ce830bff59daa7e0324fd33f249337146422652a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-10-05T02:25:17Z","title_canon_sha256":"bdd948630f79f70e761b1e9c9ce2588b20904b31e658935e4389a16d389b6368"},"schema_version":"1.0","source":{"id":"1610.01257","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.01257","created_at":"2026-05-18T01:03:11Z"},{"alias_kind":"arxiv_version","alias_value":"1610.01257v1","created_at":"2026-05-18T01:03:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01257","created_at":"2026-05-18T01:03:11Z"},{"alias_kind":"pith_short_12","alias_value":"BJFAEZFS4M6V","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BJFAEZFS4M6VAOMK","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BJFAEZFS","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:558b06df29b72cfeb43ad1655e1be4712669c23332b0d0f92f1c0d9e6d91e6c5","target":"graph","created_at":"2026-05-18T01:03:11Z","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":"In this paper we present a method to obtain deformations of families of matrix-valued orthogonal polynomials that are associated to the representation theory of compact Gelfand pairs. These polynomials have the Sturm-Liouville property in the sense that they are simultaneous eigenfunctions of a symmetric second order differential operator and we deform this operator accordingly so that the deformed families also have the Sturm-Liouville property. Our strategy is to deform the system of spherical functions that is related to the matrix-valued orthogonal polynomials and then check that the polyn","authors_text":"Maarten van Pruijssen, Pablo Rom\\'an","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-10-05T02:25:17Z","title":"Deformation of matrix-valued orthogonal polynomials related to Gelfand pairs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01257","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:f78f164153cc121936755cbe2bb5ca6b7be4c987646d46f438cee43142941f0d","target":"record","created_at":"2026-05-18T01:03:11Z","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":"6f01409d59d48596c9a4258ce830bff59daa7e0324fd33f249337146422652a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-10-05T02:25:17Z","title_canon_sha256":"bdd948630f79f70e761b1e9c9ce2588b20904b31e658935e4389a16d389b6368"},"schema_version":"1.0","source":{"id":"1610.01257","kind":"arxiv","version":1}},"canonical_sha256":"0a4a0264b2e33d50398a0e7567ceb64be9993587a88ffe08e24c02ead698eea6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a4a0264b2e33d50398a0e7567ceb64be9993587a88ffe08e24c02ead698eea6","first_computed_at":"2026-05-18T01:03:11.305078Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:11.305078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M1bIUTI3qqbtBM/FZPGsg+BZRrPlzfKxbSPfWnSOY5jVemE9pZGaAuq0N4uksuIHZSzgS73D6HefkJlCnsQTBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:11.305574Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.01257","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f78f164153cc121936755cbe2bb5ca6b7be4c987646d46f438cee43142941f0d","sha256:558b06df29b72cfeb43ad1655e1be4712669c23332b0d0f92f1c0d9e6d91e6c5"],"state_sha256":"c2a191e14d2ca3b108795241367c52850dc77338f191e7e20e8ac46a15d2e13c"}