{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:BVKLYGQUQCPFSN2P6N2W23JQAK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2d87293d24e0c55419af87dff181fa0e40c7e86ec3a1aa171d267fc31a7bd8cd","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-07-29T06:17:47Z","title_canon_sha256":"b8d7334782f3251334b1566bab6fe8b518cb8ee2c5c48d1cb1b0787c92a4e000"},"schema_version":"1.0","source":{"id":"1007.5116","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.5116","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"arxiv_version","alias_value":"1007.5116v1","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.5116","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"pith_short_12","alias_value":"BVKLYGQUQCPF","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BVKLYGQUQCPFSN2P","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BVKLYGQU","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:e288d0a39a9e57f2362fa57bd9f75d892a4bfa48d5c87c3bef0d28d72da1c490","target":"graph","created_at":"2026-05-18T04:36:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Factorization of quantum mechanical Hamiltonians has been a useful technique for some time. This procedure has been given an elegant description by supersymmetric quantum mechanics, and the subject has become well-developed. We demonstrate that the existence of raising and lowering operators for the harmonic oscillator (and many other potentials) can be extended to their supersymmetric partners. The use of double supersymmetry (or a factorization chain) is used to obtain non-singular isospectral potentials, and the explicit expressions for the ladder operators, wave functions and probability d","authors_text":"Micheal S. Berger, Nail S. Ussembayev","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-07-29T06:17:47Z","title":"Second-order Supersymmetric Operators and Excited States"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.5116","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d956ff62b63c7c9133508de16cd865063322289438e6031c000d99817af9a679","target":"record","created_at":"2026-05-18T04:36:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2d87293d24e0c55419af87dff181fa0e40c7e86ec3a1aa171d267fc31a7bd8cd","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-07-29T06:17:47Z","title_canon_sha256":"b8d7334782f3251334b1566bab6fe8b518cb8ee2c5c48d1cb1b0787c92a4e000"},"schema_version":"1.0","source":{"id":"1007.5116","kind":"arxiv","version":1}},"canonical_sha256":"0d54bc1a14809e59374ff3756d6d300282d680e873a5dbc0bb0de940be67aeb6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d54bc1a14809e59374ff3756d6d300282d680e873a5dbc0bb0de940be67aeb6","first_computed_at":"2026-05-18T04:36:51.137153Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:51.137153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r3zYbIgjGWeNqz5XK47pEwmyI/k6JRWN7dC1JJZzzUrlQsgldxeMe91Kic0L2FMSrdbEsb9PqEETc6CXorfwCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:51.137780Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.5116","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d956ff62b63c7c9133508de16cd865063322289438e6031c000d99817af9a679","sha256:e288d0a39a9e57f2362fa57bd9f75d892a4bfa48d5c87c3bef0d28d72da1c490"],"state_sha256":"9ef0b88f11b5feb88ca4e4149c4db82b3b35c721b5505c5428423d680d789831"}