{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:C2T5GDQLFYX5YOS3IQDYQW75NW","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":"8242f5447abc2358cf299a0f1d55c9acf0605c0ea28388ba6174142d3ef10759","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-12-09T22:30:21Z","title_canon_sha256":"13e975ad803fef857420269bdee28e8cf9ab2a7d216460762cab709e767e13bf"},"schema_version":"1.0","source":{"id":"1512.03103","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.03103","created_at":"2026-05-18T01:24:37Z"},{"alias_kind":"arxiv_version","alias_value":"1512.03103v1","created_at":"2026-05-18T01:24:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03103","created_at":"2026-05-18T01:24:37Z"},{"alias_kind":"pith_short_12","alias_value":"C2T5GDQLFYX5","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"C2T5GDQLFYX5YOS3","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"C2T5GDQL","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:3db0b2d58e94f580c37b83c75c4f590d807a2196070bc4addb5ae9035487a83a","target":"graph","created_at":"2026-05-18T01:24:37Z","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":"We study first the supersymmetric quantum mechanics (SUSY QM), specially the cases of the harmonic and radial oscillators. Then, we obtain a new Wronskian formula for the confluent SUSY transformation and apply the SUSY QM to the inverted oscillator.\n  After that, we present the polynomial Heisenberg algebras (PHA). We study the general systems described by PHA: for zeroth- and first-order we obtain the harmonic and radial oscillators, respectively; for second- and third-order PHA, the potential is determined in terms of solutions to Painlev\\'e IV and V equations ($P_{IV}$ and $P_{V}$), respec","authors_text":"David Bermudez","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-12-09T22:30:21Z","title":"Polynomial Heisenberg algebras and Painlev\\'e equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03103","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":"sha256:48781038ea8ee79561b5ae04fffa3f6ae5f2054df9526b2404e57c6a490905b2","target":"record","created_at":"2026-05-18T01:24:37Z","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":"8242f5447abc2358cf299a0f1d55c9acf0605c0ea28388ba6174142d3ef10759","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-12-09T22:30:21Z","title_canon_sha256":"13e975ad803fef857420269bdee28e8cf9ab2a7d216460762cab709e767e13bf"},"schema_version":"1.0","source":{"id":"1512.03103","kind":"arxiv","version":1}},"canonical_sha256":"16a7d30e0b2e2fdc3a5b4407885bfd6d9c928befcbbc3be9df56da45b03b9bc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16a7d30e0b2e2fdc3a5b4407885bfd6d9c928befcbbc3be9df56da45b03b9bc0","first_computed_at":"2026-05-18T01:24:37.876639Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:37.876639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"avhbtkmUlD/r1M2hICm7AjnopPttWM527mZcfxWktpSB1ccIPNqjMksWwA5Hbi2mUIDjgXAbqMBwu+ntm78zCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:37.877074Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.03103","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48781038ea8ee79561b5ae04fffa3f6ae5f2054df9526b2404e57c6a490905b2","sha256:3db0b2d58e94f580c37b83c75c4f590d807a2196070bc4addb5ae9035487a83a"],"state_sha256":"1b04b1a3051da8f2462fd5bcb2d3de8729ed7d9c860e3de1e8e933010051c191"}