{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:GRYAFTFB4BN7THIDS2LPAMTX7D","short_pith_number":"pith:GRYAFTFB","schema_version":"1.0","canonical_sha256":"347002cca1e05bf99d039696f03277f8d09015abe2b2ad661908da7324b7d118","source":{"kind":"arxiv","id":"1401.3802","version":2},"attestation_state":"computed","paper":{"title":"Jack-Laurent symmetric functions for special values of parameters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A.N. Sergeev, A.P. Veselov","submitted_at":"2014-01-16T00:34:53Z","abstract_excerpt":"We consider the Jack--Laurent symmetric functions for special values of parameters p_0=n+k^{-1}m, where k is not rational and m and n are natural numbers. In general, the coefficients of such functions may have poles at these values of p_0. The action of the corresponding algebra of quantum Calogero-Moser integrals D(k,p_0) on the space of Laurent symmetric functions defines the decomposition into generalised eigenspaces. We construct a basis in each generalised eigenspace as certain linear combinations of the Jack--Laurent symmetric functions, which are regular at p_0=n+k^{-1}m, and describe "},"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":"1401.3802","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-01-16T00:34:53Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"3469d7e2ef96a63b5dbb6ecfb0a8e80bd94c8709c049b18fc84bb3bd6cd7bd20","abstract_canon_sha256":"01eb8a7babe37db982436c7c6fe69c8fdd426753f11e9eef436c11723f9d81cd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:32.299441Z","signature_b64":"AQDMbUDD+1EESCPxyAStMfQiZ/DhqM2qNlMOvAN39L25fsLKwAboeH5QYOpqCeWYYlrxeknLUNyutMnVGAmVAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"347002cca1e05bf99d039696f03277f8d09015abe2b2ad661908da7324b7d118","last_reissued_at":"2026-05-18T02:30:32.298908Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:32.298908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Jack-Laurent symmetric functions for special values of parameters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A.N. Sergeev, A.P. Veselov","submitted_at":"2014-01-16T00:34:53Z","abstract_excerpt":"We consider the Jack--Laurent symmetric functions for special values of parameters p_0=n+k^{-1}m, where k is not rational and m and n are natural numbers. In general, the coefficients of such functions may have poles at these values of p_0. The action of the corresponding algebra of quantum Calogero-Moser integrals D(k,p_0) on the space of Laurent symmetric functions defines the decomposition into generalised eigenspaces. We construct a basis in each generalised eigenspace as certain linear combinations of the Jack--Laurent symmetric functions, which are regular at p_0=n+k^{-1}m, and describe "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3802","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":"1401.3802","created_at":"2026-05-18T02:30:32.298994+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.3802v2","created_at":"2026-05-18T02:30:32.298994+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.3802","created_at":"2026-05-18T02:30:32.298994+00:00"},{"alias_kind":"pith_short_12","alias_value":"GRYAFTFB4BN7","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"GRYAFTFB4BN7THID","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"GRYAFTFB","created_at":"2026-05-18T12:28:30.664211+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/GRYAFTFB4BN7THIDS2LPAMTX7D","json":"https://pith.science/pith/GRYAFTFB4BN7THIDS2LPAMTX7D.json","graph_json":"https://pith.science/api/pith-number/GRYAFTFB4BN7THIDS2LPAMTX7D/graph.json","events_json":"https://pith.science/api/pith-number/GRYAFTFB4BN7THIDS2LPAMTX7D/events.json","paper":"https://pith.science/paper/GRYAFTFB"},"agent_actions":{"view_html":"https://pith.science/pith/GRYAFTFB4BN7THIDS2LPAMTX7D","download_json":"https://pith.science/pith/GRYAFTFB4BN7THIDS2LPAMTX7D.json","view_paper":"https://pith.science/paper/GRYAFTFB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.3802&json=true","fetch_graph":"https://pith.science/api/pith-number/GRYAFTFB4BN7THIDS2LPAMTX7D/graph.json","fetch_events":"https://pith.science/api/pith-number/GRYAFTFB4BN7THIDS2LPAMTX7D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GRYAFTFB4BN7THIDS2LPAMTX7D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GRYAFTFB4BN7THIDS2LPAMTX7D/action/storage_attestation","attest_author":"https://pith.science/pith/GRYAFTFB4BN7THIDS2LPAMTX7D/action/author_attestation","sign_citation":"https://pith.science/pith/GRYAFTFB4BN7THIDS2LPAMTX7D/action/citation_signature","submit_replication":"https://pith.science/pith/GRYAFTFB4BN7THIDS2LPAMTX7D/action/replication_record"}},"created_at":"2026-05-18T02:30:32.298994+00:00","updated_at":"2026-05-18T02:30:32.298994+00:00"}