{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:XBOJMMXT3TX3CVPVZKN2K2SJ52","short_pith_number":"pith:XBOJMMXT","canonical_record":{"source":{"id":"1305.5669","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-05-24T09:52:29Z","cross_cats_sorted":[],"title_canon_sha256":"5613d711d98d4a7f25300d3a4ddf9a141f9882183ff429f6ca69daf7f2bd00d9","abstract_canon_sha256":"9cc7fce0382d9659c7fe4f27a5d51ec7f58f88f024081730bc20cf1eff128e0d"},"schema_version":"1.0"},"canonical_sha256":"b85c9632f3dcefb155f5ca9ba56a49ee92e470aa4d3e2f3ece4830d89ccdd403","source":{"kind":"arxiv","id":"1305.5669","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.5669","created_at":"2026-05-18T03:25:03Z"},{"alias_kind":"arxiv_version","alias_value":"1305.5669v1","created_at":"2026-05-18T03:25:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5669","created_at":"2026-05-18T03:25:03Z"},{"alias_kind":"pith_short_12","alias_value":"XBOJMMXT3TX3","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XBOJMMXT3TX3CVPV","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XBOJMMXT","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:XBOJMMXT3TX3CVPVZKN2K2SJ52","target":"record","payload":{"canonical_record":{"source":{"id":"1305.5669","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-05-24T09:52:29Z","cross_cats_sorted":[],"title_canon_sha256":"5613d711d98d4a7f25300d3a4ddf9a141f9882183ff429f6ca69daf7f2bd00d9","abstract_canon_sha256":"9cc7fce0382d9659c7fe4f27a5d51ec7f58f88f024081730bc20cf1eff128e0d"},"schema_version":"1.0"},"canonical_sha256":"b85c9632f3dcefb155f5ca9ba56a49ee92e470aa4d3e2f3ece4830d89ccdd403","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:03.536579Z","signature_b64":"VpQv7tCC+4uR0RWyRGEIctT+QK8b1Fm3HEN65S+liqFT9SwHckX8c3SuZF0LyV+oNr7PP6chk7yR9Aa5+1rBDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b85c9632f3dcefb155f5ca9ba56a49ee92e470aa4d3e2f3ece4830d89ccdd403","last_reissued_at":"2026-05-18T03:25:03.535908Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:03.535908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.5669","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":"2026-05-18T03:25:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FGIofemfFys8zRzDdtjQpqaSCGDiAMzuTDuK1W0McE7TC4JAAUCUgD4o4TUXlUnUDPjUf78cVpUhuiOujhVgBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T22:20:40.913474Z"},"content_sha256":"2654e3d16e72af9d3208313a0dc89a38d605e61280379f18c7039609d7feb37c","schema_version":"1.0","event_id":"sha256:2654e3d16e72af9d3208313a0dc89a38d605e61280379f18c7039609d7feb37c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:XBOJMMXT3TX3CVPVZKN2K2SJ52","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A basic class of symmetric orthogonal polynomials using the extended Sturm-Liouville theorem for symmetric functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Mohammad Masjed-Jamei","submitted_at":"2013-05-24T09:52:29Z","abstract_excerpt":"In this research, by applying the extended Sturm-Liouville theorem for symmetric functions, a basic class of symmetric orthogonal polynomials (BCSOP) with four free parameters is introduced and all its standard properties, such as a generic second order differential equation along with its explicit polynomial solution, a generic orthogonality relation, a generic three term recurrence relation and so on, are presented. Then, it is shown that four main sequences of symmetric orthogonal polynomials can essentially be extracted from the introduced class. They are respectively the generalized ultra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5669","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":"2026-05-18T03:25:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XcenhzgLUtTcB7kaH7lkVzuicjopt5x/XIWK6KNidXEN3wPedChhWZ+BlSdllmZGwqO2JHexqtOsW2gucbqOAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T22:20:40.913818Z"},"content_sha256":"b2f7dcb3b081c0c6b815b795b4997488cd7c88a9d32b009c61c39b02591bf231","schema_version":"1.0","event_id":"sha256:b2f7dcb3b081c0c6b815b795b4997488cd7c88a9d32b009c61c39b02591bf231"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XBOJMMXT3TX3CVPVZKN2K2SJ52/bundle.json","state_url":"https://pith.science/pith/XBOJMMXT3TX3CVPVZKN2K2SJ52/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XBOJMMXT3TX3CVPVZKN2K2SJ52/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":"2026-07-01T22:20:40Z","links":{"resolver":"https://pith.science/pith/XBOJMMXT3TX3CVPVZKN2K2SJ52","bundle":"https://pith.science/pith/XBOJMMXT3TX3CVPVZKN2K2SJ52/bundle.json","state":"https://pith.science/pith/XBOJMMXT3TX3CVPVZKN2K2SJ52/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XBOJMMXT3TX3CVPVZKN2K2SJ52/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XBOJMMXT3TX3CVPVZKN2K2SJ52","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":"9cc7fce0382d9659c7fe4f27a5d51ec7f58f88f024081730bc20cf1eff128e0d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-05-24T09:52:29Z","title_canon_sha256":"5613d711d98d4a7f25300d3a4ddf9a141f9882183ff429f6ca69daf7f2bd00d9"},"schema_version":"1.0","source":{"id":"1305.5669","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.5669","created_at":"2026-05-18T03:25:03Z"},{"alias_kind":"arxiv_version","alias_value":"1305.5669v1","created_at":"2026-05-18T03:25:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5669","created_at":"2026-05-18T03:25:03Z"},{"alias_kind":"pith_short_12","alias_value":"XBOJMMXT3TX3","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XBOJMMXT3TX3CVPV","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XBOJMMXT","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:b2f7dcb3b081c0c6b815b795b4997488cd7c88a9d32b009c61c39b02591bf231","target":"graph","created_at":"2026-05-18T03:25:03Z","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 research, by applying the extended Sturm-Liouville theorem for symmetric functions, a basic class of symmetric orthogonal polynomials (BCSOP) with four free parameters is introduced and all its standard properties, such as a generic second order differential equation along with its explicit polynomial solution, a generic orthogonality relation, a generic three term recurrence relation and so on, are presented. Then, it is shown that four main sequences of symmetric orthogonal polynomials can essentially be extracted from the introduced class. They are respectively the generalized ultra","authors_text":"Mohammad Masjed-Jamei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-05-24T09:52:29Z","title":"A basic class of symmetric orthogonal polynomials using the extended Sturm-Liouville theorem for symmetric functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5669","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":"sha256:2654e3d16e72af9d3208313a0dc89a38d605e61280379f18c7039609d7feb37c","target":"record","created_at":"2026-05-18T03:25:03Z","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":"9cc7fce0382d9659c7fe4f27a5d51ec7f58f88f024081730bc20cf1eff128e0d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-05-24T09:52:29Z","title_canon_sha256":"5613d711d98d4a7f25300d3a4ddf9a141f9882183ff429f6ca69daf7f2bd00d9"},"schema_version":"1.0","source":{"id":"1305.5669","kind":"arxiv","version":1}},"canonical_sha256":"b85c9632f3dcefb155f5ca9ba56a49ee92e470aa4d3e2f3ece4830d89ccdd403","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b85c9632f3dcefb155f5ca9ba56a49ee92e470aa4d3e2f3ece4830d89ccdd403","first_computed_at":"2026-05-18T03:25:03.535908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:03.535908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VpQv7tCC+4uR0RWyRGEIctT+QK8b1Fm3HEN65S+liqFT9SwHckX8c3SuZF0LyV+oNr7PP6chk7yR9Aa5+1rBDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:03.536579Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.5669","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2654e3d16e72af9d3208313a0dc89a38d605e61280379f18c7039609d7feb37c","sha256:b2f7dcb3b081c0c6b815b795b4997488cd7c88a9d32b009c61c39b02591bf231"],"state_sha256":"0b5512b9bef8698a1c02594c81f19d96f9d4413662b35c070ddec6bd6b76e236"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hAW/EglPgrb1pQ8dXNkQFiIdbU9/SrD1q4B4+H2sw0L5Tj9fOzfBsQSITu6TJ6qY1UGlkUG9rpaDIwEvZ2bbAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T22:20:40.915694Z","bundle_sha256":"7a34bac5c43f7dac32f3a01ed971da11ae92a951ac472cb98205111ac325e336"}}