{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:NEFTEY5Q4CRHSLZZJI4NGULT3S","short_pith_number":"pith:NEFTEY5Q","schema_version":"1.0","canonical_sha256":"690b3263b0e0a2792f394a38d35173dcbc8a48c7f1dfe6e5b03c44d66677e2b6","source":{"kind":"arxiv","id":"1012.0290","version":4},"attestation_state":"computed","paper":{"title":"Supersymmetric Quantum Mechanics and Painlev\\'e IV Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"David Bermudez, David J. Fern\\'andez C","submitted_at":"2010-12-01T20:31:57Z","abstract_excerpt":"As it has been proven, the determination of general one-dimensional Schr\\\"odinger Hamiltonians having third-order differential ladder operators requires to solve the Painlev\\'e IV equation. In this work, it will be shown that some specific subsets of the higher-order supersymmetric partners of the harmonic oscillator possess third-order differential ladder operators. This allows us to introduce a simple technique for generating solutions of the Painlev\\'e IV equation. Finally, we classify these solutions into three relevant hierarchies."},"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":"1012.0290","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-01T20:31:57Z","cross_cats_sorted":["hep-th","math.MP","quant-ph"],"title_canon_sha256":"fb19f6158f25c403ba2f7f2d136d96eb677c6324cae839d66ebbef208a8eb948","abstract_canon_sha256":"884af0b92d737c8e094a32d7cb048a2c338e95d56588c8770224db42ef53d46f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:33.352334Z","signature_b64":"p4xtLRXimuea0KwI9jhaHBA3fSoPiaEiE1uovB/fEyI6GEcaD/KhisEdZbwP+BNCjqiZm2on4GZ0hz0KeH2PBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"690b3263b0e0a2792f394a38d35173dcbc8a48c7f1dfe6e5b03c44d66677e2b6","last_reissued_at":"2026-05-18T04:06:33.351602Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:33.351602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Supersymmetric Quantum Mechanics and Painlev\\'e IV Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"David Bermudez, David J. Fern\\'andez C","submitted_at":"2010-12-01T20:31:57Z","abstract_excerpt":"As it has been proven, the determination of general one-dimensional Schr\\\"odinger Hamiltonians having third-order differential ladder operators requires to solve the Painlev\\'e IV equation. In this work, it will be shown that some specific subsets of the higher-order supersymmetric partners of the harmonic oscillator possess third-order differential ladder operators. This allows us to introduce a simple technique for generating solutions of the Painlev\\'e IV equation. Finally, we classify these solutions into three relevant hierarchies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0290","kind":"arxiv","version":4},"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":"1012.0290","created_at":"2026-05-18T04:06:33.351719+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.0290v4","created_at":"2026-05-18T04:06:33.351719+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0290","created_at":"2026-05-18T04:06:33.351719+00:00"},{"alias_kind":"pith_short_12","alias_value":"NEFTEY5Q4CRH","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_16","alias_value":"NEFTEY5Q4CRHSLZZ","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_8","alias_value":"NEFTEY5Q","created_at":"2026-05-18T12:26:10.704358+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/NEFTEY5Q4CRHSLZZJI4NGULT3S","json":"https://pith.science/pith/NEFTEY5Q4CRHSLZZJI4NGULT3S.json","graph_json":"https://pith.science/api/pith-number/NEFTEY5Q4CRHSLZZJI4NGULT3S/graph.json","events_json":"https://pith.science/api/pith-number/NEFTEY5Q4CRHSLZZJI4NGULT3S/events.json","paper":"https://pith.science/paper/NEFTEY5Q"},"agent_actions":{"view_html":"https://pith.science/pith/NEFTEY5Q4CRHSLZZJI4NGULT3S","download_json":"https://pith.science/pith/NEFTEY5Q4CRHSLZZJI4NGULT3S.json","view_paper":"https://pith.science/paper/NEFTEY5Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.0290&json=true","fetch_graph":"https://pith.science/api/pith-number/NEFTEY5Q4CRHSLZZJI4NGULT3S/graph.json","fetch_events":"https://pith.science/api/pith-number/NEFTEY5Q4CRHSLZZJI4NGULT3S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NEFTEY5Q4CRHSLZZJI4NGULT3S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NEFTEY5Q4CRHSLZZJI4NGULT3S/action/storage_attestation","attest_author":"https://pith.science/pith/NEFTEY5Q4CRHSLZZJI4NGULT3S/action/author_attestation","sign_citation":"https://pith.science/pith/NEFTEY5Q4CRHSLZZJI4NGULT3S/action/citation_signature","submit_replication":"https://pith.science/pith/NEFTEY5Q4CRHSLZZJI4NGULT3S/action/replication_record"}},"created_at":"2026-05-18T04:06:33.351719+00:00","updated_at":"2026-05-18T04:06:33.351719+00:00"}