{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:3TPPPCRQVPY3D2IBCTXQ3YHJNW","short_pith_number":"pith:3TPPPCRQ","schema_version":"1.0","canonical_sha256":"dcdef78a30abf1b1e90114ef0de0e96db89a0f56d4cd2a733fdeadeaee1b47d3","source":{"kind":"arxiv","id":"0911.3442","version":1},"attestation_state":"computed","paper":{"title":"Another set of infinitely many exceptional (X_{\\ell}) Laguerre polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CA","math.MP","nlin.SI","quant-ph"],"primary_cat":"math-ph","authors_text":"Ryu Sasaki, Satoru Odake","submitted_at":"2009-11-18T00:16:40Z","abstract_excerpt":"We present a new set of infinitely many shape invariant potentials and the corresponding exceptional (X_{\\ell}) Laguerre polynomials. They are to supplement the recently derived two sets of infinitely many shape invariant thus exactly solvable potentials in one dimensional quantum mechanics and the corresponding X_{\\ell} Laguerre and Jacobi polynomials (Odake and Sasaki, Phys. Lett. B679 (2009) 414-417). The new X_{\\ell} Laguerre polynomials and the potentials are obtained by a simple limiting procedure from the known X_{\\ell} Jacobi polynomials and the potentials, whereas the known X_{\\ell} L"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0911.3442","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-11-18T00:16:40Z","cross_cats_sorted":["hep-th","math.CA","math.MP","nlin.SI","quant-ph"],"title_canon_sha256":"5f0ec9698850a021d173ae50b49df96ccae7a2df792adacd081d7db8f6fc922f","abstract_canon_sha256":"327861615a5f7b22fbb3a9a7dc208747fbdad14121d83446f30f18cc8f637925"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:46.157788Z","signature_b64":"Jq6MsA2k6Odtr8tBwIYjWiWpVw8vMz67qLEMAg5SSDfxzgLgVDloU6eHqicFa/7M/i2XvzhpzjFvdfjc0YSeDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dcdef78a30abf1b1e90114ef0de0e96db89a0f56d4cd2a733fdeadeaee1b47d3","last_reissued_at":"2026-05-18T04:35:46.157262Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:46.157262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Another set of infinitely many exceptional (X_{\\ell}) Laguerre polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CA","math.MP","nlin.SI","quant-ph"],"primary_cat":"math-ph","authors_text":"Ryu Sasaki, Satoru Odake","submitted_at":"2009-11-18T00:16:40Z","abstract_excerpt":"We present a new set of infinitely many shape invariant potentials and the corresponding exceptional (X_{\\ell}) Laguerre polynomials. They are to supplement the recently derived two sets of infinitely many shape invariant thus exactly solvable potentials in one dimensional quantum mechanics and the corresponding X_{\\ell} Laguerre and Jacobi polynomials (Odake and Sasaki, Phys. Lett. B679 (2009) 414-417). The new X_{\\ell} Laguerre polynomials and the potentials are obtained by a simple limiting procedure from the known X_{\\ell} Jacobi polynomials and the potentials, whereas the known X_{\\ell} L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.3442","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0911.3442","created_at":"2026-05-18T04:35:46.157371+00:00"},{"alias_kind":"arxiv_version","alias_value":"0911.3442v1","created_at":"2026-05-18T04:35:46.157371+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.3442","created_at":"2026-05-18T04:35:46.157371+00:00"},{"alias_kind":"pith_short_12","alias_value":"3TPPPCRQVPY3","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"3TPPPCRQVPY3D2IB","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"3TPPPCRQ","created_at":"2026-05-18T12:25:58.018023+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3TPPPCRQVPY3D2IBCTXQ3YHJNW","json":"https://pith.science/pith/3TPPPCRQVPY3D2IBCTXQ3YHJNW.json","graph_json":"https://pith.science/api/pith-number/3TPPPCRQVPY3D2IBCTXQ3YHJNW/graph.json","events_json":"https://pith.science/api/pith-number/3TPPPCRQVPY3D2IBCTXQ3YHJNW/events.json","paper":"https://pith.science/paper/3TPPPCRQ"},"agent_actions":{"view_html":"https://pith.science/pith/3TPPPCRQVPY3D2IBCTXQ3YHJNW","download_json":"https://pith.science/pith/3TPPPCRQVPY3D2IBCTXQ3YHJNW.json","view_paper":"https://pith.science/paper/3TPPPCRQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0911.3442&json=true","fetch_graph":"https://pith.science/api/pith-number/3TPPPCRQVPY3D2IBCTXQ3YHJNW/graph.json","fetch_events":"https://pith.science/api/pith-number/3TPPPCRQVPY3D2IBCTXQ3YHJNW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3TPPPCRQVPY3D2IBCTXQ3YHJNW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3TPPPCRQVPY3D2IBCTXQ3YHJNW/action/storage_attestation","attest_author":"https://pith.science/pith/3TPPPCRQVPY3D2IBCTXQ3YHJNW/action/author_attestation","sign_citation":"https://pith.science/pith/3TPPPCRQVPY3D2IBCTXQ3YHJNW/action/citation_signature","submit_replication":"https://pith.science/pith/3TPPPCRQVPY3D2IBCTXQ3YHJNW/action/replication_record"}},"created_at":"2026-05-18T04:35:46.157371+00:00","updated_at":"2026-05-18T04:35:46.157371+00:00"}