{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:OUW6NNEBSGEFGVW2TUO7QTABOM","short_pith_number":"pith:OUW6NNEB","schema_version":"1.0","canonical_sha256":"752de6b48191885356da9d1df84c017337aeb8c21ce9945a467072daca38d1db","source":{"kind":"arxiv","id":"0903.2604","version":1},"attestation_state":"computed","paper":{"title":"Unified theory of exactly and quasi-exactly solvable `Discrete' quantum mechanics: I. Formalism","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":"2009-03-15T04:34:41Z","abstract_excerpt":"We present a simple recipe to construct exactly and quasi-exactly solvable Hamiltonians in one-dimensional `discrete' quantum mechanics, in which the Schr\\\"{o}dinger equation is a difference equation. It reproduces all the known ones whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. The recipe also predicts several new ones. An essential role is played by the sinusoidal coordinate, which generates the closure relation and the Askey-Wilson algebra together with the Hamiltonian. The relationship between the closure r"},"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":"0903.2604","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-03-15T04:34:41Z","cross_cats_sorted":["hep-th","math.CA","math.MP","nlin.SI","quant-ph"],"title_canon_sha256":"ca612ed066d7bd6d17288e11592710de6ffa03a3c1abb06d87e6e475ce29a9ae","abstract_canon_sha256":"02fcf8653278adbcac35991c702fca0222a7e4e449ffb35bfdbc7761857c5d34"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:14:28.218138Z","signature_b64":"9xTw9p03SVFaeCzhAbLtzVWkKl+v9WHA3jmbSqkaZlT0NuRZLd4PZG1h+l8lSmRQ4PXc7wbA7uFFoQy4S5ZQCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"752de6b48191885356da9d1df84c017337aeb8c21ce9945a467072daca38d1db","last_reissued_at":"2026-05-18T02:14:28.217680Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:14:28.217680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Unified theory of exactly and quasi-exactly solvable `Discrete' quantum mechanics: I. Formalism","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":"2009-03-15T04:34:41Z","abstract_excerpt":"We present a simple recipe to construct exactly and quasi-exactly solvable Hamiltonians in one-dimensional `discrete' quantum mechanics, in which the Schr\\\"{o}dinger equation is a difference equation. It reproduces all the known ones whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. The recipe also predicts several new ones. An essential role is played by the sinusoidal coordinate, which generates the closure relation and the Askey-Wilson algebra together with the Hamiltonian. The relationship between the closure r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.2604","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":"0903.2604","created_at":"2026-05-18T02:14:28.217740+00:00"},{"alias_kind":"arxiv_version","alias_value":"0903.2604v1","created_at":"2026-05-18T02:14:28.217740+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.2604","created_at":"2026-05-18T02:14:28.217740+00:00"},{"alias_kind":"pith_short_12","alias_value":"OUW6NNEBSGEF","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"OUW6NNEBSGEFGVW2","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"OUW6NNEB","created_at":"2026-05-18T12:26:01.383474+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/OUW6NNEBSGEFGVW2TUO7QTABOM","json":"https://pith.science/pith/OUW6NNEBSGEFGVW2TUO7QTABOM.json","graph_json":"https://pith.science/api/pith-number/OUW6NNEBSGEFGVW2TUO7QTABOM/graph.json","events_json":"https://pith.science/api/pith-number/OUW6NNEBSGEFGVW2TUO7QTABOM/events.json","paper":"https://pith.science/paper/OUW6NNEB"},"agent_actions":{"view_html":"https://pith.science/pith/OUW6NNEBSGEFGVW2TUO7QTABOM","download_json":"https://pith.science/pith/OUW6NNEBSGEFGVW2TUO7QTABOM.json","view_paper":"https://pith.science/paper/OUW6NNEB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0903.2604&json=true","fetch_graph":"https://pith.science/api/pith-number/OUW6NNEBSGEFGVW2TUO7QTABOM/graph.json","fetch_events":"https://pith.science/api/pith-number/OUW6NNEBSGEFGVW2TUO7QTABOM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OUW6NNEBSGEFGVW2TUO7QTABOM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OUW6NNEBSGEFGVW2TUO7QTABOM/action/storage_attestation","attest_author":"https://pith.science/pith/OUW6NNEBSGEFGVW2TUO7QTABOM/action/author_attestation","sign_citation":"https://pith.science/pith/OUW6NNEBSGEFGVW2TUO7QTABOM/action/citation_signature","submit_replication":"https://pith.science/pith/OUW6NNEBSGEFGVW2TUO7QTABOM/action/replication_record"}},"created_at":"2026-05-18T02:14:28.217740+00:00","updated_at":"2026-05-18T02:14:28.217740+00:00"}