{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HHV6TP7KWV36KWN5YSR6QFHNUE","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":"f56a3e44be1fae58f1a40e88e6cb5c738e992d3b4653d9a751374adb3411c9db","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-08-23T06:33:08Z","title_canon_sha256":"b0448ed493d607ba58e45c54e5380032997ff33f0c69dbd358576c9b47f2141a"},"schema_version":"1.0","source":{"id":"1108.4503","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.4503","created_at":"2026-05-18T02:00:49Z"},{"alias_kind":"arxiv_version","alias_value":"1108.4503v2","created_at":"2026-05-18T02:00:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4503","created_at":"2026-05-18T02:00:49Z"},{"alias_kind":"pith_short_12","alias_value":"HHV6TP7KWV36","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HHV6TP7KWV36KWN5","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HHV6TP7K","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:95ff623c792001f881e64aa93a10a719894cd4533bd7bb4767d1b7846d30b301","target":"graph","created_at":"2026-05-18T02:00:49Z","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":"In some recent articles we developed a new systematic approach to generate solvable rational extensions of primary translationally shape invariant potentials. In this generalized SUSY QM partnership, the DBT are built on the excited states Riccati-Schr\\\"odinger (RS) functions regularized via specific discrete symmetries of the considered potential. In the present paper, we prove that this scheme can be extended in a multistep formulation. Applying this scheme to the isotonic oscillator, we obtain new towers of regular rational extensions of this potential which are strictly isospectral to it. ","authors_text":"Yves Grandati (FCN)","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-08-23T06:33:08Z","title":"Multistep DBT and regular rational extensions of the isotonic oscillator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4503","kind":"arxiv","version":2},"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":"sha256:1fc11dd333bcf235c527240e877ed269b868d9a1a15aaa1f8d54c00929bbb73c","target":"record","created_at":"2026-05-18T02:00:49Z","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":"f56a3e44be1fae58f1a40e88e6cb5c738e992d3b4653d9a751374adb3411c9db","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-08-23T06:33:08Z","title_canon_sha256":"b0448ed493d607ba58e45c54e5380032997ff33f0c69dbd358576c9b47f2141a"},"schema_version":"1.0","source":{"id":"1108.4503","kind":"arxiv","version":2}},"canonical_sha256":"39ebe9bfeab577e559bdc4a3e814eda10285f88e151de4234581fb95f24ffa58","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39ebe9bfeab577e559bdc4a3e814eda10285f88e151de4234581fb95f24ffa58","first_computed_at":"2026-05-18T02:00:49.438728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:49.438728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iXXm3d70HNk8wlF1FrZ3L9926W4MhYTlJ/D4mYe9Ytn2I9UpOdchC5gCIucRYQMM4G6Q4UxB6Pa1BDXETinHAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:49.439715Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.4503","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1fc11dd333bcf235c527240e877ed269b868d9a1a15aaa1f8d54c00929bbb73c","sha256:95ff623c792001f881e64aa93a10a719894cd4533bd7bb4767d1b7846d30b301"],"state_sha256":"4934870ca7bcb26eba756d56fcfedacc042242c4d5b3b52c5480edf9b36868fc"}