{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GM4DPQ6MM666OU2TQ74LHS345K","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":"770da187f858cfabd0de8c074a30afe6ec60345bce28b883d16c66d0bee9d689","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-03T22:29:47Z","title_canon_sha256":"a4be9ed938bf754358e981424c265e841b447471edcf1f8304010629d14a251f"},"schema_version":"1.0","source":{"id":"1509.01293","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01293","created_at":"2026-05-18T00:35:49Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01293v2","created_at":"2026-05-18T00:35:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01293","created_at":"2026-05-18T00:35:49Z"},{"alias_kind":"pith_short_12","alias_value":"GM4DPQ6MM666","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GM4DPQ6MM666OU2T","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GM4DPQ6M","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:e6ea54487cc4c9ef43ef9d64214896a38198a67f8caeca4fb3754d012ddd097a","target":"graph","created_at":"2026-05-18T00:35:49Z","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-like algebra associated with every class of orthogonal polynomials $\\{\\Psi_n(x)\\}_{n=0}^{\\infty}$, on the real line, satisfying a four term non-symmetric recurrence relation $x\\Psi_n(x)=b_n\\Psi_{n+1}(x)+a_n\\Psi_n(x)+b_{n-1}\\Psi_{n-1}(x),~\\Psi_0(x)=1,~b_{-1}=0$. This note presents necessary and sufficient conditions on $a_n$ and $b_n$ for such algebras to be of finite dimension. As examples, we discuss the dimensions of oscillator-like algebras associated with Laguerre and Jacobi polynomials.","authors_text":"G. Honnouvo, K. Thirulogasanthar","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-03T22:29:47Z","title":"On the dimensions of oscillator-like algebras induced by orthogonal polynomials: non-symmetric case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01293","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":"sha256:6a78781126b401165e391964096ea7aa893fca824898a3f93f3c0d75b602e2a6","target":"record","created_at":"2026-05-18T00:35:49Z","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":"770da187f858cfabd0de8c074a30afe6ec60345bce28b883d16c66d0bee9d689","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-03T22:29:47Z","title_canon_sha256":"a4be9ed938bf754358e981424c265e841b447471edcf1f8304010629d14a251f"},"schema_version":"1.0","source":{"id":"1509.01293","kind":"arxiv","version":2}},"canonical_sha256":"333837c3cc67bde7535387f8b3cb7ceaa849b26020dbae69e1600bde1a60abe9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"333837c3cc67bde7535387f8b3cb7ceaa849b26020dbae69e1600bde1a60abe9","first_computed_at":"2026-05-18T00:35:49.106196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:49.106196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bOneZJKbc6UlK1a4jhlAG0O46C+OTLjfOkb6rYFMV8FCuoTle480JzVvjh6AidQN6u52X66GKgyJ96yq6k6GCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:49.106967Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.01293","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a78781126b401165e391964096ea7aa893fca824898a3f93f3c0d75b602e2a6","sha256:e6ea54487cc4c9ef43ef9d64214896a38198a67f8caeca4fb3754d012ddd097a"],"state_sha256":"c31866604e365cbb38949a318fd5494e3df68a6f83e886bde66822a598fa6e8c"}