{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HT7BLQCWMFVCRIU7MCZEX4MYWG","short_pith_number":"pith:HT7BLQCW","canonical_record":{"source":{"id":"1305.2509","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-11T14:34:50Z","cross_cats_sorted":["math.MP","math.QA"],"title_canon_sha256":"96da9cdbec0941cd96cff3b0f8743909f2574ecef05b2538f14e2a0a383066e4","abstract_canon_sha256":"87c2135f8e38ed4a1c2fab25c240505faf46e0615f8295af99c8559362a8eafa"},"schema_version":"1.0"},"canonical_sha256":"3cfe15c056616a28a29f60b24bf198b19827bfa3e4a6da50e25d9b34dee16727","source":{"kind":"arxiv","id":"1305.2509","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.2509","created_at":"2026-05-18T01:50:03Z"},{"alias_kind":"arxiv_version","alias_value":"1305.2509v2","created_at":"2026-05-18T01:50:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2509","created_at":"2026-05-18T01:50:03Z"},{"alias_kind":"pith_short_12","alias_value":"HT7BLQCWMFVC","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HT7BLQCWMFVCRIU7","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HT7BLQCW","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HT7BLQCWMFVCRIU7MCZEX4MYWG","target":"record","payload":{"canonical_record":{"source":{"id":"1305.2509","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-11T14:34:50Z","cross_cats_sorted":["math.MP","math.QA"],"title_canon_sha256":"96da9cdbec0941cd96cff3b0f8743909f2574ecef05b2538f14e2a0a383066e4","abstract_canon_sha256":"87c2135f8e38ed4a1c2fab25c240505faf46e0615f8295af99c8559362a8eafa"},"schema_version":"1.0"},"canonical_sha256":"3cfe15c056616a28a29f60b24bf198b19827bfa3e4a6da50e25d9b34dee16727","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:50:03.322541Z","signature_b64":"OYvRM3n0htpod2nLWZWX+9BcDmVi51+SZeBfvrk1AaHJEaX8UoQTLlru7omX8C5w3Ugz/FSn2AHrnS5VNh9VDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3cfe15c056616a28a29f60b24bf198b19827bfa3e4a6da50e25d9b34dee16727","last_reissued_at":"2026-05-18T01:50:03.321942Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:50:03.321942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.2509","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:50:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EJ+R76aJjtXhkxWbrevY3QqWYPjNL9BfShqSVpwcF+1k41fdZx1xNRVIlKsKO14ycoMrxXTvtxig+91cNKHGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:04:32.092413Z"},"content_sha256":"94fe4fb4cc0b7cebd7363c7c71dbf8a4f8e578e2c88bb6ebbb0487da4555dfc4","schema_version":"1.0","event_id":"sha256:94fe4fb4cc0b7cebd7363c7c71dbf8a4f8e578e2c88bb6ebbb0487da4555dfc4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HT7BLQCWMFVCRIU7MCZEX4MYWG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the dimensions of the oscillator algebras induced by orthogonal polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.QA"],"primary_cat":"math-ph","authors_text":"G. Honnouvo, K. Thirulogasanthar","submitted_at":"2013-05-11T14:34:50Z","abstract_excerpt":"There is a generalized oscillator algebra associated with every class of orthogonal polynomials $\\{\\Psi_n(x)\\}_{n=0}^{\\infty}$, on the real line, satisfying a three term recurrence relation $x\\Psi_n(x)=b_n\\Psi_{n+1}(x)+b_{n-1}\\Psi_{n-1}(x), \\Psi_0(x)=1, b_{-1}=0$. This note presents necessary and safficient conditions on $b_n$ for such algebras to be of finite dimension. As examples, we discuss the dimensions of oscillator algebras associated with Hermite, Legendre and Gegenbauer polynomials. In addition we shall also discuss the dimensions of some generalized deformed oscillator algebras. Som"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2509","kind":"arxiv","version":2},"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":"2026-05-18T01:50:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XS1aN6m17XdVEclmGD3caG0GenF51Y3ACI4YY7fHOMKxCuolAhf+EpJmjCOjN9SUxm+Oc04bJWbUxm+IRUHuCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:04:32.092763Z"},"content_sha256":"731ed67ed973dacef337b0c8b60f4450b24fa7ff04e0a506a480602de5f9e4cd","schema_version":"1.0","event_id":"sha256:731ed67ed973dacef337b0c8b60f4450b24fa7ff04e0a506a480602de5f9e4cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HT7BLQCWMFVCRIU7MCZEX4MYWG/bundle.json","state_url":"https://pith.science/pith/HT7BLQCWMFVCRIU7MCZEX4MYWG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HT7BLQCWMFVCRIU7MCZEX4MYWG/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":"2026-06-08T22:04:32Z","links":{"resolver":"https://pith.science/pith/HT7BLQCWMFVCRIU7MCZEX4MYWG","bundle":"https://pith.science/pith/HT7BLQCWMFVCRIU7MCZEX4MYWG/bundle.json","state":"https://pith.science/pith/HT7BLQCWMFVCRIU7MCZEX4MYWG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HT7BLQCWMFVCRIU7MCZEX4MYWG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HT7BLQCWMFVCRIU7MCZEX4MYWG","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":"87c2135f8e38ed4a1c2fab25c240505faf46e0615f8295af99c8559362a8eafa","cross_cats_sorted":["math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-11T14:34:50Z","title_canon_sha256":"96da9cdbec0941cd96cff3b0f8743909f2574ecef05b2538f14e2a0a383066e4"},"schema_version":"1.0","source":{"id":"1305.2509","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.2509","created_at":"2026-05-18T01:50:03Z"},{"alias_kind":"arxiv_version","alias_value":"1305.2509v2","created_at":"2026-05-18T01:50:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2509","created_at":"2026-05-18T01:50:03Z"},{"alias_kind":"pith_short_12","alias_value":"HT7BLQCWMFVC","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HT7BLQCWMFVCRIU7","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HT7BLQCW","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:731ed67ed973dacef337b0c8b60f4450b24fa7ff04e0a506a480602de5f9e4cd","target":"graph","created_at":"2026-05-18T01:50:03Z","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":"There is a generalized oscillator algebra associated with every class of orthogonal polynomials $\\{\\Psi_n(x)\\}_{n=0}^{\\infty}$, on the real line, satisfying a three term recurrence relation $x\\Psi_n(x)=b_n\\Psi_{n+1}(x)+b_{n-1}\\Psi_{n-1}(x), \\Psi_0(x)=1, b_{-1}=0$. This note presents necessary and safficient conditions on $b_n$ for such algebras to be of finite dimension. As examples, we discuss the dimensions of oscillator algebras associated with Hermite, Legendre and Gegenbauer polynomials. In addition we shall also discuss the dimensions of some generalized deformed oscillator algebras. Som","authors_text":"G. Honnouvo, K. Thirulogasanthar","cross_cats":["math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-11T14:34:50Z","title":"On the dimensions of the oscillator algebras induced by orthogonal polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2509","kind":"arxiv","version":2},"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":"sha256:94fe4fb4cc0b7cebd7363c7c71dbf8a4f8e578e2c88bb6ebbb0487da4555dfc4","target":"record","created_at":"2026-05-18T01:50:03Z","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":"87c2135f8e38ed4a1c2fab25c240505faf46e0615f8295af99c8559362a8eafa","cross_cats_sorted":["math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-11T14:34:50Z","title_canon_sha256":"96da9cdbec0941cd96cff3b0f8743909f2574ecef05b2538f14e2a0a383066e4"},"schema_version":"1.0","source":{"id":"1305.2509","kind":"arxiv","version":2}},"canonical_sha256":"3cfe15c056616a28a29f60b24bf198b19827bfa3e4a6da50e25d9b34dee16727","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cfe15c056616a28a29f60b24bf198b19827bfa3e4a6da50e25d9b34dee16727","first_computed_at":"2026-05-18T01:50:03.321942Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:50:03.321942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OYvRM3n0htpod2nLWZWX+9BcDmVi51+SZeBfvrk1AaHJEaX8UoQTLlru7omX8C5w3Ugz/FSn2AHrnS5VNh9VDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:50:03.322541Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.2509","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94fe4fb4cc0b7cebd7363c7c71dbf8a4f8e578e2c88bb6ebbb0487da4555dfc4","sha256:731ed67ed973dacef337b0c8b60f4450b24fa7ff04e0a506a480602de5f9e4cd"],"state_sha256":"c87870fd0e3892bc74bb00131716ac565df2e1fa8d496aa5b865a82ddfb3df90"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qb1Qss7Ee+fxKVoTF9/UIKmCtANcUyi82vBvLPaCxuHSYEd/iSFF8QqNTQDjWadH10QalubP+Qymp0ZjpjIZAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T22:04:32.094776Z","bundle_sha256":"fae8f65c2be3088b63b3b401631a56de34b1c7cd1b4755f2540f7a3ddb5b893b"}}