{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HPH4RAWENWRUSC7PZZASICJWAT","short_pith_number":"pith:HPH4RAWE","canonical_record":{"source":{"id":"1503.04787","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-03-16T19:45:41Z","cross_cats_sorted":[],"title_canon_sha256":"6276b7df5173cce952ced3c1924f6474f86091a6ad59fc0da1a69d47d0b81189","abstract_canon_sha256":"cf1a82fd7a39049da1e81a2e8ef0b21dead28903541fe846e79d502097fd6ff5"},"schema_version":"1.0"},"canonical_sha256":"3bcfc882c46da3490befce4124093604f7a07539e349bd875a6108a3fabf58ea","source":{"kind":"arxiv","id":"1503.04787","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HPH4RAWENWRUSC7PZZASICJWAT","target":"record","payload":{"canonical_record":{"source":{"id":"1503.04787","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-03-16T19:45:41Z","cross_cats_sorted":[],"title_canon_sha256":"6276b7df5173cce952ced3c1924f6474f86091a6ad59fc0da1a69d47d0b81189","abstract_canon_sha256":"cf1a82fd7a39049da1e81a2e8ef0b21dead28903541fe846e79d502097fd6ff5"},"schema_version":"1.0"},"canonical_sha256":"3bcfc882c46da3490befce4124093604f7a07539e349bd875a6108a3fabf58ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:24.029295Z","signature_b64":"8y/5yMr00ryBRPpLGVfhkm3HNfh+I/DlGWE5K+sE06eGEzjMBrmO0TW9WpZ9F0pJ68Kel3IS/CD9OLdrTbz7CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3bcfc882c46da3490befce4124093604f7a07539e349bd875a6108a3fabf58ea","last_reissued_at":"2026-05-18T02:23:24.028718Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:24.028718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.04787","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":"2026-05-18T02:23:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JcthcKN+JQkX4gvhMgPnIPUiQMYdnDw5h1iApRWHM3oHLXx3WNLNewRsQFh6qzs+RCCQEjY8BT8xkB8SsKF9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:43:51.484110Z"},"content_sha256":"fcb9115889f8413a54352c7c965b7c3e92ef91d9d4fbc8704c63e715588a7cd0","schema_version":"1.0","event_id":"sha256:fcb9115889f8413a54352c7c965b7c3e92ef91d9d4fbc8704c63e715588a7cd0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HPH4RAWENWRUSC7PZZASICJWAT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pre-sequences of matrix orthogonal polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Juan Tirao","submitted_at":"2015-03-16T19:45:41Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04787","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":"2026-05-18T02:23:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S5L31kcw3WL6Jhl8ax2LtmKRj8TeT+4youBLhodRi68cbp0kVH2FDUrk7gEIntAMG56URm+Xj8jR64VJeS+3DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:43:51.484620Z"},"content_sha256":"a0365c93370bc875e0ef6a49a5486107988e54b72f9d8a17c4e968fe29d1d959","schema_version":"1.0","event_id":"sha256:a0365c93370bc875e0ef6a49a5486107988e54b72f9d8a17c4e968fe29d1d959"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HPH4RAWENWRUSC7PZZASICJWAT/bundle.json","state_url":"https://pith.science/pith/HPH4RAWENWRUSC7PZZASICJWAT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HPH4RAWENWRUSC7PZZASICJWAT/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":"2026-06-25T20:43:51Z","links":{"resolver":"https://pith.science/pith/HPH4RAWENWRUSC7PZZASICJWAT","bundle":"https://pith.science/pith/HPH4RAWENWRUSC7PZZASICJWAT/bundle.json","state":"https://pith.science/pith/HPH4RAWENWRUSC7PZZASICJWAT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HPH4RAWENWRUSC7PZZASICJWAT/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fOsohhzUWvrHB1BfijBII1+f+22YHezY2GjkLnkXRxRJUAgVt7/boArKSMQO2i4DfwLKcVqz7QX9gXk+RS/ECA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T20:43:51.487143Z","bundle_sha256":"b8f663b9adf318c63c6b8488d1ef7656014adbc00a4df01fd60cd3f175a3c73a"}}