{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:GIDKYOGSFMQ5T6RZZGCBUWRE5A","short_pith_number":"pith:GIDKYOGS","schema_version":"1.0","canonical_sha256":"3206ac38d22b21d9fa39c9841a5a24e815b9912c08eba6536283caf4bfd489e0","source":{"kind":"arxiv","id":"1605.07200","version":1},"attestation_state":"computed","paper":{"title":"A new generalisation of Macdonald polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MP","math.QA","math.RT"],"primary_cat":"math-ph","authors_text":"Alexandr Garbali, Jan de Gier, Michael Wheeler","submitted_at":"2016-05-23T20:08:43Z","abstract_excerpt":"We introduce a new family of symmetric multivariate polynomials, whose coefficients are meromorphic functions of two parameters $(q,t)$ and polynomial in a further two parameters $(u,v)$. We evaluate these polynomials explicitly as a matrix product. At $u=v=0$ they reduce to Macdonald polynomials, while at $q=0$, $u=v=s$ they recover a family of inhomogeneous symmetric functions originally introduced by Borodin."},"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":"1605.07200","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-05-23T20:08:43Z","cross_cats_sorted":["math.CO","math.MP","math.QA","math.RT"],"title_canon_sha256":"8bac3216794df227ada9446aba5feffc789472297c75d5b26c42bf98b355a3e3","abstract_canon_sha256":"20466cf2fc7f2580e295e68e7cc47cb2bfa454dca15b6d6b286fa5b32c039f3f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:20.932132Z","signature_b64":"Gb5uIll4YoJmFWEbDVoM/zN8NSlKXbAvuZnW2hFBiz2yBGkozZnd12CG3sFd0Ml/1d7bpuWiz3YquPWRJponAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3206ac38d22b21d9fa39c9841a5a24e815b9912c08eba6536283caf4bfd489e0","last_reissued_at":"2026-05-18T00:47:20.931480Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:20.931480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A new generalisation of Macdonald polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MP","math.QA","math.RT"],"primary_cat":"math-ph","authors_text":"Alexandr Garbali, Jan de Gier, Michael Wheeler","submitted_at":"2016-05-23T20:08:43Z","abstract_excerpt":"We introduce a new family of symmetric multivariate polynomials, whose coefficients are meromorphic functions of two parameters $(q,t)$ and polynomial in a further two parameters $(u,v)$. We evaluate these polynomials explicitly as a matrix product. At $u=v=0$ they reduce to Macdonald polynomials, while at $q=0$, $u=v=s$ they recover a family of inhomogeneous symmetric functions originally introduced by Borodin."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07200","kind":"arxiv","version":1},"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":"1605.07200","created_at":"2026-05-18T00:47:20.931596+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.07200v1","created_at":"2026-05-18T00:47:20.931596+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.07200","created_at":"2026-05-18T00:47:20.931596+00:00"},{"alias_kind":"pith_short_12","alias_value":"GIDKYOGSFMQ5","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"GIDKYOGSFMQ5T6RZ","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"GIDKYOGS","created_at":"2026-05-18T12:30:19.053100+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.13432","citing_title":"Inhomogeneous $q$-Whittaker polynomials II: ring theorem and positive specializations","ref_index":9,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GIDKYOGSFMQ5T6RZZGCBUWRE5A","json":"https://pith.science/pith/GIDKYOGSFMQ5T6RZZGCBUWRE5A.json","graph_json":"https://pith.science/api/pith-number/GIDKYOGSFMQ5T6RZZGCBUWRE5A/graph.json","events_json":"https://pith.science/api/pith-number/GIDKYOGSFMQ5T6RZZGCBUWRE5A/events.json","paper":"https://pith.science/paper/GIDKYOGS"},"agent_actions":{"view_html":"https://pith.science/pith/GIDKYOGSFMQ5T6RZZGCBUWRE5A","download_json":"https://pith.science/pith/GIDKYOGSFMQ5T6RZZGCBUWRE5A.json","view_paper":"https://pith.science/paper/GIDKYOGS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.07200&json=true","fetch_graph":"https://pith.science/api/pith-number/GIDKYOGSFMQ5T6RZZGCBUWRE5A/graph.json","fetch_events":"https://pith.science/api/pith-number/GIDKYOGSFMQ5T6RZZGCBUWRE5A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GIDKYOGSFMQ5T6RZZGCBUWRE5A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GIDKYOGSFMQ5T6RZZGCBUWRE5A/action/storage_attestation","attest_author":"https://pith.science/pith/GIDKYOGSFMQ5T6RZZGCBUWRE5A/action/author_attestation","sign_citation":"https://pith.science/pith/GIDKYOGSFMQ5T6RZZGCBUWRE5A/action/citation_signature","submit_replication":"https://pith.science/pith/GIDKYOGSFMQ5T6RZZGCBUWRE5A/action/replication_record"}},"created_at":"2026-05-18T00:47:20.931596+00:00","updated_at":"2026-05-18T00:47:20.931596+00:00"}