{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:NC6ZFCEHQSXSN7XOHOREBVTVEM","short_pith_number":"pith:NC6ZFCEH","schema_version":"1.0","canonical_sha256":"68bd92888784af26feee3ba240d675232cd7253cca3e6ca3924e752f0993b5a5","source":{"kind":"arxiv","id":"1310.0279","version":2},"attestation_state":"computed","paper":{"title":"Specializations of nonsymmetric Macdonald-Koornwinder polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Daniel Orr, Mark Shimozono","submitted_at":"2013-10-01T13:20:14Z","abstract_excerpt":"This work records the details of the Ram-Yip formula for nonsymmetric Macdonald-Koornwinder polynomials for the double affine Hecke algebras of not-necessarily-reduced affine root systems. It is shown that the t=0 equal-parameter specialization of nonsymmetric Macdonald polynomials admits an explicit combinatorial formula in terms of quantum alcove paths, generalizing the formula of Lenart in the untwisted case. In particular our formula yields a definition of quantum Bruhat graph for all affine root systems. For mixed type the proof requires the Ram-Yip formula for the nonsymmetric Koornwinde"},"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":"1310.0279","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-10-01T13:20:14Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"e98a1fe8895de2e0774ff983c46185ef0cafbb6508aca98ffdd78b6f375ee5f7","abstract_canon_sha256":"2143aec73dcff8cbf233ab11711ee70d610df61ed5f631cae72a7480c802315e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:35.957444Z","signature_b64":"7nKPPd3UcZOKF3Zv214zd251WnCAx0fHw0H8tpl73+l8rp4oZFAeX2oTCHvpTjG3GLsO4YKKbbbND0bhvPjPBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68bd92888784af26feee3ba240d675232cd7253cca3e6ca3924e752f0993b5a5","last_reissued_at":"2026-05-18T03:08:35.956428Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:35.956428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Specializations of nonsymmetric Macdonald-Koornwinder polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Daniel Orr, Mark Shimozono","submitted_at":"2013-10-01T13:20:14Z","abstract_excerpt":"This work records the details of the Ram-Yip formula for nonsymmetric Macdonald-Koornwinder polynomials for the double affine Hecke algebras of not-necessarily-reduced affine root systems. It is shown that the t=0 equal-parameter specialization of nonsymmetric Macdonald polynomials admits an explicit combinatorial formula in terms of quantum alcove paths, generalizing the formula of Lenart in the untwisted case. In particular our formula yields a definition of quantum Bruhat graph for all affine root systems. For mixed type the proof requires the Ram-Yip formula for the nonsymmetric Koornwinde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0279","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":"1310.0279","created_at":"2026-05-18T03:08:35.956597+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.0279v2","created_at":"2026-05-18T03:08:35.956597+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0279","created_at":"2026-05-18T03:08:35.956597+00:00"},{"alias_kind":"pith_short_12","alias_value":"NC6ZFCEHQSXS","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"NC6ZFCEHQSXSN7XO","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"NC6ZFCEH","created_at":"2026-05-18T12:27:52.871228+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/NC6ZFCEHQSXSN7XOHOREBVTVEM","json":"https://pith.science/pith/NC6ZFCEHQSXSN7XOHOREBVTVEM.json","graph_json":"https://pith.science/api/pith-number/NC6ZFCEHQSXSN7XOHOREBVTVEM/graph.json","events_json":"https://pith.science/api/pith-number/NC6ZFCEHQSXSN7XOHOREBVTVEM/events.json","paper":"https://pith.science/paper/NC6ZFCEH"},"agent_actions":{"view_html":"https://pith.science/pith/NC6ZFCEHQSXSN7XOHOREBVTVEM","download_json":"https://pith.science/pith/NC6ZFCEHQSXSN7XOHOREBVTVEM.json","view_paper":"https://pith.science/paper/NC6ZFCEH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.0279&json=true","fetch_graph":"https://pith.science/api/pith-number/NC6ZFCEHQSXSN7XOHOREBVTVEM/graph.json","fetch_events":"https://pith.science/api/pith-number/NC6ZFCEHQSXSN7XOHOREBVTVEM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NC6ZFCEHQSXSN7XOHOREBVTVEM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NC6ZFCEHQSXSN7XOHOREBVTVEM/action/storage_attestation","attest_author":"https://pith.science/pith/NC6ZFCEHQSXSN7XOHOREBVTVEM/action/author_attestation","sign_citation":"https://pith.science/pith/NC6ZFCEHQSXSN7XOHOREBVTVEM/action/citation_signature","submit_replication":"https://pith.science/pith/NC6ZFCEHQSXSN7XOHOREBVTVEM/action/replication_record"}},"created_at":"2026-05-18T03:08:35.956597+00:00","updated_at":"2026-05-18T03:08:35.956597+00:00"}