{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:SSDICOI2JTD3WZGEOGDI75RC6B","short_pith_number":"pith:SSDICOI2","schema_version":"1.0","canonical_sha256":"948681391a4cc7bb64c471868ff622f06353d6cc6b75731716f5e7b05afc9339","source":{"kind":"arxiv","id":"2410.10685","version":2},"attestation_state":"computed","paper":{"title":"On Chalykh's approach to eigenfunctions of DIM-induced integrable Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA"],"primary_cat":"hep-th","authors_text":"A. Mironov, A. Morozov, A. Popolitov","submitted_at":"2024-10-14T16:25:07Z","abstract_excerpt":"Quite some years ago, Oleg Chalykh has built a nice theory from the observation that the Macdonald polynomial reduces at $t=q^{-m}$ to a sum over permutations of simpler polynomials called Baker-Akhiezer functions, which can be unambiguously constructed from a system of linear difference equations. Moreover, he also proposed a generalization of these polynomials to the twisted Baker-Akhiezer functions. Recently, in a private communication Oleg suggested that these twisted Baker-Akhiezer functions could provide eigenfunctions of the commuting Hamiltonians associated with the $(-1,a)$ rays of th"},"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":"2410.10685","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-10-14T16:25:07Z","cross_cats_sorted":["math-ph","math.MP","math.QA"],"title_canon_sha256":"2d3df4886cd7a8b71b1105031c21a35a29fb6a7b2ffd1687e7259f937ce0098d","abstract_canon_sha256":"101786f0870731d121b306ee0bd1c0a4a331e5c3ad79c9a3bfa4a8a0b3eedc1e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:29:24.692785Z","signature_b64":"10c21fI/3vp/POUabE6r5vs1R+CeZVXXhQYMN7igNQ6q2pItGNfnHqsy2AAbPIsd1XAfGIjv5QALsvp24O8UDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"948681391a4cc7bb64c471868ff622f06353d6cc6b75731716f5e7b05afc9339","last_reissued_at":"2026-07-05T10:29:24.691982Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:29:24.691982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Chalykh's approach to eigenfunctions of DIM-induced integrable Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA"],"primary_cat":"hep-th","authors_text":"A. Mironov, A. Morozov, A. Popolitov","submitted_at":"2024-10-14T16:25:07Z","abstract_excerpt":"Quite some years ago, Oleg Chalykh has built a nice theory from the observation that the Macdonald polynomial reduces at $t=q^{-m}$ to a sum over permutations of simpler polynomials called Baker-Akhiezer functions, which can be unambiguously constructed from a system of linear difference equations. Moreover, he also proposed a generalization of these polynomials to the twisted Baker-Akhiezer functions. Recently, in a private communication Oleg suggested that these twisted Baker-Akhiezer functions could provide eigenfunctions of the commuting Hamiltonians associated with the $(-1,a)$ rays of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.10685","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.10685/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2410.10685","created_at":"2026-07-05T10:29:24.692085+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.10685v2","created_at":"2026-07-05T10:29:24.692085+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.10685","created_at":"2026-07-05T10:29:24.692085+00:00"},{"alias_kind":"pith_short_12","alias_value":"SSDICOI2JTD3","created_at":"2026-07-05T10:29:24.692085+00:00"},{"alias_kind":"pith_short_16","alias_value":"SSDICOI2JTD3WZGE","created_at":"2026-07-05T10:29:24.692085+00:00"},{"alias_kind":"pith_short_8","alias_value":"SSDICOI2","created_at":"2026-07-05T10:29:24.692085+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.06738","citing_title":"Integrable systems inspired by DAHA and DIM algebra: type $C^\\vee C$ versus type $A$","ref_index":26,"is_internal_anchor":true},{"citing_arxiv_id":"2601.10500","citing_title":"Twisted Cherednik spectrum as a $q,t$-deformation","ref_index":24,"is_internal_anchor":false},{"citing_arxiv_id":"2601.19878","citing_title":"Symmetric polynomials: DIM integrable systems versus twisted Cherednik systems","ref_index":27,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SSDICOI2JTD3WZGEOGDI75RC6B","json":"https://pith.science/pith/SSDICOI2JTD3WZGEOGDI75RC6B.json","graph_json":"https://pith.science/api/pith-number/SSDICOI2JTD3WZGEOGDI75RC6B/graph.json","events_json":"https://pith.science/api/pith-number/SSDICOI2JTD3WZGEOGDI75RC6B/events.json","paper":"https://pith.science/paper/SSDICOI2"},"agent_actions":{"view_html":"https://pith.science/pith/SSDICOI2JTD3WZGEOGDI75RC6B","download_json":"https://pith.science/pith/SSDICOI2JTD3WZGEOGDI75RC6B.json","view_paper":"https://pith.science/paper/SSDICOI2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.10685&json=true","fetch_graph":"https://pith.science/api/pith-number/SSDICOI2JTD3WZGEOGDI75RC6B/graph.json","fetch_events":"https://pith.science/api/pith-number/SSDICOI2JTD3WZGEOGDI75RC6B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SSDICOI2JTD3WZGEOGDI75RC6B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SSDICOI2JTD3WZGEOGDI75RC6B/action/storage_attestation","attest_author":"https://pith.science/pith/SSDICOI2JTD3WZGEOGDI75RC6B/action/author_attestation","sign_citation":"https://pith.science/pith/SSDICOI2JTD3WZGEOGDI75RC6B/action/citation_signature","submit_replication":"https://pith.science/pith/SSDICOI2JTD3WZGEOGDI75RC6B/action/replication_record"}},"created_at":"2026-07-05T10:29:24.692085+00:00","updated_at":"2026-07-05T10:29:24.692085+00:00"}