{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:D2YOTTVNUESBWPH5A63YR6A47I","short_pith_number":"pith:D2YOTTVN","canonical_record":{"source":{"id":"0708.0360","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2007-08-02T15:08:57Z","cross_cats_sorted":["math.MP","math.RT"],"title_canon_sha256":"9840549badec6e6e5f7df3a58bfbfb7f55130b55e1e5554f670d4a48f6c6dbd4","abstract_canon_sha256":"2326e39106b2a15c22343f9763a74eee1e750d4249c3a9305dbff56b1f88ba1c"},"schema_version":"1.0"},"canonical_sha256":"1eb0e9ceada1241b3cfd07b788f81cfa3abb4a198e3a69e58e737087ca3dacb1","source":{"kind":"arxiv","id":"0708.0360","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.0360","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"arxiv_version","alias_value":"0708.0360v3","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.0360","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"pith_short_12","alias_value":"D2YOTTVNUESB","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"D2YOTTVNUESBWPH5","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"D2YOTTVN","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:D2YOTTVNUESBWPH5A63YR6A47I","target":"record","payload":{"canonical_record":{"source":{"id":"0708.0360","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2007-08-02T15:08:57Z","cross_cats_sorted":["math.MP","math.RT"],"title_canon_sha256":"9840549badec6e6e5f7df3a58bfbfb7f55130b55e1e5554f670d4a48f6c6dbd4","abstract_canon_sha256":"2326e39106b2a15c22343f9763a74eee1e750d4249c3a9305dbff56b1f88ba1c"},"schema_version":"1.0"},"canonical_sha256":"1eb0e9ceada1241b3cfd07b788f81cfa3abb4a198e3a69e58e737087ca3dacb1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:15.179490Z","signature_b64":"DYvKjgQcawW5i1eDtQ06fctOT8rvONHNDBaPKC6p1nBKxfeEiJ9Sc2NU8VB64riF+bDvRpx/KaRoKl57OZpyAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1eb0e9ceada1241b3cfd07b788f81cfa3abb4a198e3a69e58e737087ca3dacb1","last_reissued_at":"2026-05-18T04:09:15.179014Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:15.179014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0708.0360","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:09:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jXZaa8m5Vs3HJY4AxsXuwG8Sk4TQTDPGau4WTWBr44Hl/n8XwEvbkS2Z7B9+zc2FCdx3XxGIcmVIOlPYNtyWAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:30:58.583695Z"},"content_sha256":"77b012b8c00bd18fa8dffec99b2dabcd027593de4ab680dc26f7717b399dc3c7","schema_version":"1.0","event_id":"sha256:77b012b8c00bd18fa8dffec99b2dabcd027593de4ab680dc26f7717b399dc3c7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:D2YOTTVNUESBWPH5A63YR6A47I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The generalized matrix valued hypergeometric equation","license":"","headline":"","cross_cats":["math.MP","math.RT"],"primary_cat":"math-ph","authors_text":"P. Roman, S. Simondi","submitted_at":"2007-08-02T15:08:57Z","abstract_excerpt":"The matrix valued analog of the Euler's hypergeometric differential equation was introduced by Tirao in \\cite{T2}. This equation arises in the study of matrix valued spherical functions and in the theory of matrix valued orthogonal polynomials. The goal of this paper is to extend naturally the number of parameters of Tirao's equation in order to get a generalized matrix valued hypergeometric equation. We take advantage of the tools and strategies developed in \\cite{T2} to identify the corresponding matrix hypergeometric functions ${}_nF_m$. We prove that, if n=m+1, this functions are analytic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.0360","kind":"arxiv","version":3},"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":"2026-05-18T04:09:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G8CRJKa+J7dW5s67BSovDgAtHuaI+tQ/9Tacmfvayjq2gFygkl2YxDpaBlL8VbU9hCDk6whGEXpMrVDvcANYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:30:58.584048Z"},"content_sha256":"7afa1417ce338b997c89bae0aa91a87a918fb5fcededcd108aa808815269760c","schema_version":"1.0","event_id":"sha256:7afa1417ce338b997c89bae0aa91a87a918fb5fcededcd108aa808815269760c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D2YOTTVNUESBWPH5A63YR6A47I/bundle.json","state_url":"https://pith.science/pith/D2YOTTVNUESBWPH5A63YR6A47I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D2YOTTVNUESBWPH5A63YR6A47I/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":"2026-06-03T14:30:58Z","links":{"resolver":"https://pith.science/pith/D2YOTTVNUESBWPH5A63YR6A47I","bundle":"https://pith.science/pith/D2YOTTVNUESBWPH5A63YR6A47I/bundle.json","state":"https://pith.science/pith/D2YOTTVNUESBWPH5A63YR6A47I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D2YOTTVNUESBWPH5A63YR6A47I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:D2YOTTVNUESBWPH5A63YR6A47I","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":"2326e39106b2a15c22343f9763a74eee1e750d4249c3a9305dbff56b1f88ba1c","cross_cats_sorted":["math.MP","math.RT"],"license":"","primary_cat":"math-ph","submitted_at":"2007-08-02T15:08:57Z","title_canon_sha256":"9840549badec6e6e5f7df3a58bfbfb7f55130b55e1e5554f670d4a48f6c6dbd4"},"schema_version":"1.0","source":{"id":"0708.0360","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.0360","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"arxiv_version","alias_value":"0708.0360v3","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.0360","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"pith_short_12","alias_value":"D2YOTTVNUESB","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"D2YOTTVNUESBWPH5","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"D2YOTTVN","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:7afa1417ce338b997c89bae0aa91a87a918fb5fcededcd108aa808815269760c","target":"graph","created_at":"2026-05-18T04:09:15Z","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":"The matrix valued analog of the Euler's hypergeometric differential equation was introduced by Tirao in \\cite{T2}. This equation arises in the study of matrix valued spherical functions and in the theory of matrix valued orthogonal polynomials. The goal of this paper is to extend naturally the number of parameters of Tirao's equation in order to get a generalized matrix valued hypergeometric equation. We take advantage of the tools and strategies developed in \\cite{T2} to identify the corresponding matrix hypergeometric functions ${}_nF_m$. We prove that, if n=m+1, this functions are analytic ","authors_text":"P. Roman, S. Simondi","cross_cats":["math.MP","math.RT"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2007-08-02T15:08:57Z","title":"The generalized matrix valued hypergeometric equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.0360","kind":"arxiv","version":3},"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":"sha256:77b012b8c00bd18fa8dffec99b2dabcd027593de4ab680dc26f7717b399dc3c7","target":"record","created_at":"2026-05-18T04:09:15Z","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":"2326e39106b2a15c22343f9763a74eee1e750d4249c3a9305dbff56b1f88ba1c","cross_cats_sorted":["math.MP","math.RT"],"license":"","primary_cat":"math-ph","submitted_at":"2007-08-02T15:08:57Z","title_canon_sha256":"9840549badec6e6e5f7df3a58bfbfb7f55130b55e1e5554f670d4a48f6c6dbd4"},"schema_version":"1.0","source":{"id":"0708.0360","kind":"arxiv","version":3}},"canonical_sha256":"1eb0e9ceada1241b3cfd07b788f81cfa3abb4a198e3a69e58e737087ca3dacb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1eb0e9ceada1241b3cfd07b788f81cfa3abb4a198e3a69e58e737087ca3dacb1","first_computed_at":"2026-05-18T04:09:15.179014Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:15.179014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DYvKjgQcawW5i1eDtQ06fctOT8rvONHNDBaPKC6p1nBKxfeEiJ9Sc2NU8VB64riF+bDvRpx/KaRoKl57OZpyAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:15.179490Z","signed_message":"canonical_sha256_bytes"},"source_id":"0708.0360","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77b012b8c00bd18fa8dffec99b2dabcd027593de4ab680dc26f7717b399dc3c7","sha256:7afa1417ce338b997c89bae0aa91a87a918fb5fcededcd108aa808815269760c"],"state_sha256":"f0e42011de2eb30ed752a02d8aa87fdca09f679a2a40753ce04a15da2d7bee83"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"esGJbKrTAPTmHNla9sLDkhXlh8JjIS2Aa2Hs/SC6DlKtRXgDGgBP7rN/q5pzaS3zmW3F5DRz9+2LpXoZ2gNmCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T14:30:58.586167Z","bundle_sha256":"29dc46b392573b3595caa726aa2121999d7052ff209cbb0313cc4d9f7d31854f"}}