{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:3NVANO537WSW73EEARGOADHR25","short_pith_number":"pith:3NVANO53","schema_version":"1.0","canonical_sha256":"db6a06bbbbfda56fec84044ce00cf1d75a8b9119e0a6bd38b2c468ee10a9c5ae","source":{"kind":"arxiv","id":"1812.10749","version":1},"attestation_state":"computed","paper":{"title":"Properties of shape-invariant tridiagonal Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Hashim A. Yamani, Zouha\\\"ir Mouayn","submitted_at":"2018-12-27T15:56:39Z","abstract_excerpt":"It has been established that a positive semi-definite Hamiltonian,$H$, that has a tridiagonal matrix representation in a basis set, allows a definition of forward (and backward) shift operators that can be used to define the matrix representation of the supersymmetric partner Hamiltonian $H^{\\left( +\\right) \\text{\\ }}$ in the same basis. \\ We show that if, additionally, the Hamiltonian has a shape invariant property, the matrix elements of the Hamiltonian are related in a such a way that the energy spectrum is known in terms of these elements. It is also possible to determine the matrix elemen"},"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":"1812.10749","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-27T15:56:39Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"2c8e04be25e13293147aa21a67e5a7a7813703e3f963ca19464e91f289b039f5","abstract_canon_sha256":"2d144bd888cc04673eaadcafea5cc336aa2f3061e88a50f764c3909792a18bfe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:20.089231Z","signature_b64":"kCbv6HwDXpSVS3qrEI4Tdt5zEs0Y7od5Qi8FmC36Xw84cNFxpaEFaid+j0nY/ve1ZEZDXryY9X+2KfxI4HmQAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db6a06bbbbfda56fec84044ce00cf1d75a8b9119e0a6bd38b2c468ee10a9c5ae","last_reissued_at":"2026-05-17T23:57:20.088685Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:20.088685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Properties of shape-invariant tridiagonal Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Hashim A. Yamani, Zouha\\\"ir Mouayn","submitted_at":"2018-12-27T15:56:39Z","abstract_excerpt":"It has been established that a positive semi-definite Hamiltonian,$H$, that has a tridiagonal matrix representation in a basis set, allows a definition of forward (and backward) shift operators that can be used to define the matrix representation of the supersymmetric partner Hamiltonian $H^{\\left( +\\right) \\text{\\ }}$ in the same basis. \\ We show that if, additionally, the Hamiltonian has a shape invariant property, the matrix elements of the Hamiltonian are related in a such a way that the energy spectrum is known in terms of these elements. It is also possible to determine the matrix elemen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10749","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":"1812.10749","created_at":"2026-05-17T23:57:20.088767+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.10749v1","created_at":"2026-05-17T23:57:20.088767+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10749","created_at":"2026-05-17T23:57:20.088767+00:00"},{"alias_kind":"pith_short_12","alias_value":"3NVANO537WSW","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"3NVANO537WSW73EE","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"3NVANO53","created_at":"2026-05-18T12:32:02.567920+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/3NVANO537WSW73EEARGOADHR25","json":"https://pith.science/pith/3NVANO537WSW73EEARGOADHR25.json","graph_json":"https://pith.science/api/pith-number/3NVANO537WSW73EEARGOADHR25/graph.json","events_json":"https://pith.science/api/pith-number/3NVANO537WSW73EEARGOADHR25/events.json","paper":"https://pith.science/paper/3NVANO53"},"agent_actions":{"view_html":"https://pith.science/pith/3NVANO537WSW73EEARGOADHR25","download_json":"https://pith.science/pith/3NVANO537WSW73EEARGOADHR25.json","view_paper":"https://pith.science/paper/3NVANO53","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.10749&json=true","fetch_graph":"https://pith.science/api/pith-number/3NVANO537WSW73EEARGOADHR25/graph.json","fetch_events":"https://pith.science/api/pith-number/3NVANO537WSW73EEARGOADHR25/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3NVANO537WSW73EEARGOADHR25/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3NVANO537WSW73EEARGOADHR25/action/storage_attestation","attest_author":"https://pith.science/pith/3NVANO537WSW73EEARGOADHR25/action/author_attestation","sign_citation":"https://pith.science/pith/3NVANO537WSW73EEARGOADHR25/action/citation_signature","submit_replication":"https://pith.science/pith/3NVANO537WSW73EEARGOADHR25/action/replication_record"}},"created_at":"2026-05-17T23:57:20.088767+00:00","updated_at":"2026-05-17T23:57:20.088767+00:00"}