{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:NIXU5HWPST6RRBUGK3PQAK3F47","short_pith_number":"pith:NIXU5HWP","schema_version":"1.0","canonical_sha256":"6a2f4e9ecf94fd18868656df002b65e7c98c4b1c53b91cd81ff9731ad1a046c4","source":{"kind":"arxiv","id":"1612.05514","version":4},"attestation_state":"computed","paper":{"title":"Durfee rectangles and pseudo-Wronskian equivalences for Hermite polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"David Gomez-Ullate, Robert Milson, Yves Grandati","submitted_at":"2016-12-16T15:47:55Z","abstract_excerpt":"We study an equivalence class of iterated rational Darboux transformations applied on the harmonic oscillator, showing that many choices of state adding and state deleting transformations lead to the same transformed potential. As a by-product, we derive new identities between determinants whose entries are Hermite polynomials. These identities have a combinatorial interpretation in terms of Maya diagrams, partitions and Durfee rectangles, and serve to characterize the equivalence class of rational Darboux transformations. Since the determinants have different orders, we analyze the problem of"},"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":"1612.05514","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-16T15:47:55Z","cross_cats_sorted":[],"title_canon_sha256":"99dd599795c6515a688714b5511797d635ce27705ec85762f7b3d3c1ff866f50","abstract_canon_sha256":"66bb35fc25670389d31f2d19adb57983514abae037f99311918df87a380204f8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:26.461951Z","signature_b64":"d2v5SCf8R7ecLtXwpDUFLV8kd9jiOukSdZnm8NQ0HA2dM4FuhaUyvajXAFkdRkyuChJpxkSuPqLIE8Kf8bq3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a2f4e9ecf94fd18868656df002b65e7c98c4b1c53b91cd81ff9731ad1a046c4","last_reissued_at":"2026-05-18T00:47:26.461236Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:26.461236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Durfee rectangles and pseudo-Wronskian equivalences for Hermite polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"David Gomez-Ullate, Robert Milson, Yves Grandati","submitted_at":"2016-12-16T15:47:55Z","abstract_excerpt":"We study an equivalence class of iterated rational Darboux transformations applied on the harmonic oscillator, showing that many choices of state adding and state deleting transformations lead to the same transformed potential. As a by-product, we derive new identities between determinants whose entries are Hermite polynomials. These identities have a combinatorial interpretation in terms of Maya diagrams, partitions and Durfee rectangles, and serve to characterize the equivalence class of rational Darboux transformations. Since the determinants have different orders, we analyze the problem of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05514","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":"1612.05514","created_at":"2026-05-18T00:47:26.461371+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.05514v4","created_at":"2026-05-18T00:47:26.461371+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05514","created_at":"2026-05-18T00:47:26.461371+00:00"},{"alias_kind":"pith_short_12","alias_value":"NIXU5HWPST6R","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"NIXU5HWPST6RRBUG","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"NIXU5HWP","created_at":"2026-05-18T12:30:32.724797+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/NIXU5HWPST6RRBUGK3PQAK3F47","json":"https://pith.science/pith/NIXU5HWPST6RRBUGK3PQAK3F47.json","graph_json":"https://pith.science/api/pith-number/NIXU5HWPST6RRBUGK3PQAK3F47/graph.json","events_json":"https://pith.science/api/pith-number/NIXU5HWPST6RRBUGK3PQAK3F47/events.json","paper":"https://pith.science/paper/NIXU5HWP"},"agent_actions":{"view_html":"https://pith.science/pith/NIXU5HWPST6RRBUGK3PQAK3F47","download_json":"https://pith.science/pith/NIXU5HWPST6RRBUGK3PQAK3F47.json","view_paper":"https://pith.science/paper/NIXU5HWP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.05514&json=true","fetch_graph":"https://pith.science/api/pith-number/NIXU5HWPST6RRBUGK3PQAK3F47/graph.json","fetch_events":"https://pith.science/api/pith-number/NIXU5HWPST6RRBUGK3PQAK3F47/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NIXU5HWPST6RRBUGK3PQAK3F47/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NIXU5HWPST6RRBUGK3PQAK3F47/action/storage_attestation","attest_author":"https://pith.science/pith/NIXU5HWPST6RRBUGK3PQAK3F47/action/author_attestation","sign_citation":"https://pith.science/pith/NIXU5HWPST6RRBUGK3PQAK3F47/action/citation_signature","submit_replication":"https://pith.science/pith/NIXU5HWPST6RRBUGK3PQAK3F47/action/replication_record"}},"created_at":"2026-05-18T00:47:26.461371+00:00","updated_at":"2026-05-18T00:47:26.461371+00:00"}