{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:JCJBAYS36M64V4IA5ZMICY775J","short_pith_number":"pith:JCJBAYS3","schema_version":"1.0","canonical_sha256":"489210625bf33dcaf100ee588163ffea5183d7dbb1b5df572ef0261235182df9","source":{"kind":"arxiv","id":"1603.02992","version":2},"attestation_state":"computed","paper":{"title":"One-Dimensional Quasi-Exactly Solvable Schr\\\"odinger Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","nlin.SI"],"primary_cat":"quant-ph","authors_text":"Alexander V Turbiner","submitted_at":"2016-03-09T18:38:12Z","abstract_excerpt":"Quasi-Exactly Solvable Schr\\\"odinger Equations occupy an intermediate place between exactly-solvable (e.g. the harmonic oscillator and Coulomb problems etc) and non-solvable ones. Their major property is an explicit knowledge of several eigenstates while the remaining ones are unknown. Many of these problems are of the anharmonic oscillator type with a special type of anharmonicity. The Hamiltonians of quasi-exactly-solvable problems are characterized by the existence of a hidden algebraic structure but do not have any hidden symmetry properties. In particular, all known one-dimensional (quasi"},"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":"1603.02992","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-03-09T18:38:12Z","cross_cats_sorted":["hep-th","math-ph","math.MP","nlin.SI"],"title_canon_sha256":"0e240a50421549ef5394ab7915653bb21bc46d1608f5e60e1ca505949877decc","abstract_canon_sha256":"d63103ffc78bc95cbb71792229e885b99f7ad062248112461adb13f2f6fdedea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:46.364384Z","signature_b64":"UHtadgb8aPxGXetSo55xzcIGXN/tMC9bfIXI60wGYTtaDNQulDn+laMdIgeYTJCKY2ntMwvS1N+WeKlXIvJlCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"489210625bf33dcaf100ee588163ffea5183d7dbb1b5df572ef0261235182df9","last_reissued_at":"2026-05-18T00:56:46.363886Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:46.363886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"One-Dimensional Quasi-Exactly Solvable Schr\\\"odinger Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","nlin.SI"],"primary_cat":"quant-ph","authors_text":"Alexander V Turbiner","submitted_at":"2016-03-09T18:38:12Z","abstract_excerpt":"Quasi-Exactly Solvable Schr\\\"odinger Equations occupy an intermediate place between exactly-solvable (e.g. the harmonic oscillator and Coulomb problems etc) and non-solvable ones. Their major property is an explicit knowledge of several eigenstates while the remaining ones are unknown. Many of these problems are of the anharmonic oscillator type with a special type of anharmonicity. The Hamiltonians of quasi-exactly-solvable problems are characterized by the existence of a hidden algebraic structure but do not have any hidden symmetry properties. In particular, all known one-dimensional (quasi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02992","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1603.02992","created_at":"2026-05-18T00:56:46.363965+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.02992v2","created_at":"2026-05-18T00:56:46.363965+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.02992","created_at":"2026-05-18T00:56:46.363965+00:00"},{"alias_kind":"pith_short_12","alias_value":"JCJBAYS36M64","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"JCJBAYS36M64V4IA","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"JCJBAYS3","created_at":"2026-05-18T12:30:25.849896+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/JCJBAYS36M64V4IA5ZMICY775J","json":"https://pith.science/pith/JCJBAYS36M64V4IA5ZMICY775J.json","graph_json":"https://pith.science/api/pith-number/JCJBAYS36M64V4IA5ZMICY775J/graph.json","events_json":"https://pith.science/api/pith-number/JCJBAYS36M64V4IA5ZMICY775J/events.json","paper":"https://pith.science/paper/JCJBAYS3"},"agent_actions":{"view_html":"https://pith.science/pith/JCJBAYS36M64V4IA5ZMICY775J","download_json":"https://pith.science/pith/JCJBAYS36M64V4IA5ZMICY775J.json","view_paper":"https://pith.science/paper/JCJBAYS3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.02992&json=true","fetch_graph":"https://pith.science/api/pith-number/JCJBAYS36M64V4IA5ZMICY775J/graph.json","fetch_events":"https://pith.science/api/pith-number/JCJBAYS36M64V4IA5ZMICY775J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JCJBAYS36M64V4IA5ZMICY775J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JCJBAYS36M64V4IA5ZMICY775J/action/storage_attestation","attest_author":"https://pith.science/pith/JCJBAYS36M64V4IA5ZMICY775J/action/author_attestation","sign_citation":"https://pith.science/pith/JCJBAYS36M64V4IA5ZMICY775J/action/citation_signature","submit_replication":"https://pith.science/pith/JCJBAYS36M64V4IA5ZMICY775J/action/replication_record"}},"created_at":"2026-05-18T00:56:46.363965+00:00","updated_at":"2026-05-18T00:56:46.363965+00:00"}