{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:BJFAEZFS4M6VAOMKBZ2WPTVWJP","short_pith_number":"pith:BJFAEZFS","canonical_record":{"source":{"id":"1610.01257","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-10-05T02:25:17Z","cross_cats_sorted":[],"title_canon_sha256":"bdd948630f79f70e761b1e9c9ce2588b20904b31e658935e4389a16d389b6368","abstract_canon_sha256":"6f01409d59d48596c9a4258ce830bff59daa7e0324fd33f249337146422652a1"},"schema_version":"1.0"},"canonical_sha256":"0a4a0264b2e33d50398a0e7567ceb64be9993587a88ffe08e24c02ead698eea6","source":{"kind":"arxiv","id":"1610.01257","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:BJFAEZFS4M6VAOMKBZ2WPTVWJP","target":"record","payload":{"canonical_record":{"source":{"id":"1610.01257","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-10-05T02:25:17Z","cross_cats_sorted":[],"title_canon_sha256":"bdd948630f79f70e761b1e9c9ce2588b20904b31e658935e4389a16d389b6368","abstract_canon_sha256":"6f01409d59d48596c9a4258ce830bff59daa7e0324fd33f249337146422652a1"},"schema_version":"1.0"},"canonical_sha256":"0a4a0264b2e33d50398a0e7567ceb64be9993587a88ffe08e24c02ead698eea6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:11.305574Z","signature_b64":"M1bIUTI3qqbtBM/FZPGsg+BZRrPlzfKxbSPfWnSOY5jVemE9pZGaAuq0N4uksuIHZSzgS73D6HefkJlCnsQTBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a4a0264b2e33d50398a0e7567ceb64be9993587a88ffe08e24c02ead698eea6","last_reissued_at":"2026-05-18T01:03:11.305078Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:11.305078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.01257","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xWYoCRfW6hDu99ZuJ0KQwZJ1TYXA/s3qJJX8PMUPhYCZgZXbq1NFcyL2crit0VUMISMS2Dd4fP1/NYxs3CiXDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T12:58:38.558645Z"},"content_sha256":"f78f164153cc121936755cbe2bb5ca6b7be4c987646d46f438cee43142941f0d","schema_version":"1.0","event_id":"sha256:f78f164153cc121936755cbe2bb5ca6b7be4c987646d46f438cee43142941f0d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:BJFAEZFS4M6VAOMKBZ2WPTVWJP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deformation of matrix-valued orthogonal polynomials related to Gelfand pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Maarten van Pruijssen, Pablo Rom\\'an","submitted_at":"2016-10-05T02:25:17Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01257","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NaAyhevH9x77gs0FKEMts/s1gFvD1TTbOHa3ckou9XP5fgaOlX2MfpcqusNOlsyWQQq/ABcGxM3zIKsre0B2DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T12:58:38.559172Z"},"content_sha256":"558b06df29b72cfeb43ad1655e1be4712669c23332b0d0f92f1c0d9e6d91e6c5","schema_version":"1.0","event_id":"sha256:558b06df29b72cfeb43ad1655e1be4712669c23332b0d0f92f1c0d9e6d91e6c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BJFAEZFS4M6VAOMKBZ2WPTVWJP/bundle.json","state_url":"https://pith.science/pith/BJFAEZFS4M6VAOMKBZ2WPTVWJP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BJFAEZFS4M6VAOMKBZ2WPTVWJP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-20T12:58:38Z","links":{"resolver":"https://pith.science/pith/BJFAEZFS4M6VAOMKBZ2WPTVWJP","bundle":"https://pith.science/pith/BJFAEZFS4M6VAOMKBZ2WPTVWJP/bundle.json","state":"https://pith.science/pith/BJFAEZFS4M6VAOMKBZ2WPTVWJP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BJFAEZFS4M6VAOMKBZ2WPTVWJP/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BovbHFTHy8/jx+Sd5CjyAIMfP6AmNXVVW9A/A0UpYR4Qiz1N1YBdpNjLwowtxSymuB7m11rS5w2BDwy1FuEuBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T12:58:38.562054Z","bundle_sha256":"440aa6b1dfb00f6367fd9c1399958bc57b48d0bd93b5ecd13ba6bfe2fcf6df6e"}}