{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:GR22GGUFKIT7FTXIN2Q3N7H24C","short_pith_number":"pith:GR22GGUF","schema_version":"1.0","canonical_sha256":"3475a31a855227f2cee86ea1b6fcfae0ac0d365d1a100118297c4b414b0bb566","source":{"kind":"arxiv","id":"1804.01766","version":2},"attestation_state":"computed","paper":{"title":"Quantum Lax pairs via Dunkl and Cherednik operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Oleg Chalykh","submitted_at":"2018-04-05T10:31:24Z","abstract_excerpt":"We establish a direct link between Dunkl operators and quantum Lax matrices $\\mathcal L$ for the Calogero--Moser systems associated to an arbitrary Weyl group $W$ (or an arbitrary finite reflection group in the rational case). This interpretation also provides a companion matrix $\\mathcal A$ so that $\\mathcal L, \\mathcal A$ form a quantum Lax pair. Moreover, such an $\\mathcal A$ can be associated to any of the higher commuting quantum Hamiltonians of the system, so we obtain a family of quantum Lax pairs. These Lax pairs can be of various sizes, matching the sizes of orbits in the reflection r"},"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":"1804.01766","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-04-05T10:31:24Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4bc2b38fbe318e14ac6dd8c91e604506cc034487b5b633fb847950172a776426","abstract_canon_sha256":"12dc7a24ee9fa2dd086b8605af0b87f6d5d398f1740f1097d1378a90502896e4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:51.311018Z","signature_b64":"+BGtvaUQD2YenKar7YJlOt15uvkPSiL49GVnxRMC0mcvEBY0Olx7sC5KIV8JwSE6gxcW1H1t3aU3ES50ZwhdAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3475a31a855227f2cee86ea1b6fcfae0ac0d365d1a100118297c4b414b0bb566","last_reissued_at":"2026-05-17T23:43:51.310328Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:51.310328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum Lax pairs via Dunkl and Cherednik operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Oleg Chalykh","submitted_at":"2018-04-05T10:31:24Z","abstract_excerpt":"We establish a direct link between Dunkl operators and quantum Lax matrices $\\mathcal L$ for the Calogero--Moser systems associated to an arbitrary Weyl group $W$ (or an arbitrary finite reflection group in the rational case). This interpretation also provides a companion matrix $\\mathcal A$ so that $\\mathcal L, \\mathcal A$ form a quantum Lax pair. Moreover, such an $\\mathcal A$ can be associated to any of the higher commuting quantum Hamiltonians of the system, so we obtain a family of quantum Lax pairs. These Lax pairs can be of various sizes, matching the sizes of orbits in the reflection r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01766","kind":"arxiv","version":2},"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":"1804.01766","created_at":"2026-05-17T23:43:51.310446+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.01766v2","created_at":"2026-05-17T23:43:51.310446+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.01766","created_at":"2026-05-17T23:43:51.310446+00:00"},{"alias_kind":"pith_short_12","alias_value":"GR22GGUFKIT7","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_16","alias_value":"GR22GGUFKIT7FTXI","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_8","alias_value":"GR22GGUF","created_at":"2026-05-18T12:32:25.280505+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/GR22GGUFKIT7FTXIN2Q3N7H24C","json":"https://pith.science/pith/GR22GGUFKIT7FTXIN2Q3N7H24C.json","graph_json":"https://pith.science/api/pith-number/GR22GGUFKIT7FTXIN2Q3N7H24C/graph.json","events_json":"https://pith.science/api/pith-number/GR22GGUFKIT7FTXIN2Q3N7H24C/events.json","paper":"https://pith.science/paper/GR22GGUF"},"agent_actions":{"view_html":"https://pith.science/pith/GR22GGUFKIT7FTXIN2Q3N7H24C","download_json":"https://pith.science/pith/GR22GGUFKIT7FTXIN2Q3N7H24C.json","view_paper":"https://pith.science/paper/GR22GGUF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.01766&json=true","fetch_graph":"https://pith.science/api/pith-number/GR22GGUFKIT7FTXIN2Q3N7H24C/graph.json","fetch_events":"https://pith.science/api/pith-number/GR22GGUFKIT7FTXIN2Q3N7H24C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GR22GGUFKIT7FTXIN2Q3N7H24C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GR22GGUFKIT7FTXIN2Q3N7H24C/action/storage_attestation","attest_author":"https://pith.science/pith/GR22GGUFKIT7FTXIN2Q3N7H24C/action/author_attestation","sign_citation":"https://pith.science/pith/GR22GGUFKIT7FTXIN2Q3N7H24C/action/citation_signature","submit_replication":"https://pith.science/pith/GR22GGUFKIT7FTXIN2Q3N7H24C/action/replication_record"}},"created_at":"2026-05-17T23:43:51.310446+00:00","updated_at":"2026-05-17T23:43:51.310446+00:00"}