{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:K54F3REDRYN4LB5MSDICOEBIXG","short_pith_number":"pith:K54F3RED","schema_version":"1.0","canonical_sha256":"57785dc4838e1bc587ac90d0271028b9997863b6f404bc98049b98de428da0b6","source":{"kind":"arxiv","id":"1402.2203","version":3},"attestation_state":"computed","paper":{"title":"A uniform model for Kirillov-Reshetikhin crystals II. Alcove model, path model, and P=X","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Anne Schilling, Cristian Lenart, Daisuke Sagaki, Mark Shimozono, Satoshi Naito","submitted_at":"2014-02-10T16:34:15Z","abstract_excerpt":"We establish the equality of the specialization $P_\\lambda(x;q,0)$ of the Macdonald polynomial at $t=0$ with the graded character $X_\\lambda(x;q)$ of a tensor product of \"single-column\" Kirillov-Reshetikhin (KR) modules for untwisted affine Lie algebras. This is achieved by constructing two uniform combinatorial models for the crystals associated with the mentioned tensor products: the quantum alcove model (which is naturally associated to Macdonald polynomials), and the quantum Lakshmibai-Seshadri path model. We provide an explicit affine crystal isomorphism between the two models, and realiz"},"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":"1402.2203","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-02-10T16:34:15Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"bc7d64eec0d5562225a21dde69d8b46daed78597958918b7d621545f96f08aee","abstract_canon_sha256":"51d7f3e9506840257384f12bf0ef5c5f706108fe64e47b36ba2ac75e0e4ca178"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:18.719613Z","signature_b64":"ZIsYVxckwE2TcGt24wMgeSCxrygeb8Er4Fo9pr+rENAT8wZGsjwVujg4XGDCwbEY6nIIaRcbrNtL8Qw0Sn4qBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57785dc4838e1bc587ac90d0271028b9997863b6f404bc98049b98de428da0b6","last_reissued_at":"2026-05-18T00:39:18.718885Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:18.718885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A uniform model for Kirillov-Reshetikhin crystals II. Alcove model, path model, and P=X","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Anne Schilling, Cristian Lenart, Daisuke Sagaki, Mark Shimozono, Satoshi Naito","submitted_at":"2014-02-10T16:34:15Z","abstract_excerpt":"We establish the equality of the specialization $P_\\lambda(x;q,0)$ of the Macdonald polynomial at $t=0$ with the graded character $X_\\lambda(x;q)$ of a tensor product of \"single-column\" Kirillov-Reshetikhin (KR) modules for untwisted affine Lie algebras. This is achieved by constructing two uniform combinatorial models for the crystals associated with the mentioned tensor products: the quantum alcove model (which is naturally associated to Macdonald polynomials), and the quantum Lakshmibai-Seshadri path model. We provide an explicit affine crystal isomorphism between the two models, and realiz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2203","kind":"arxiv","version":3},"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":"1402.2203","created_at":"2026-05-18T00:39:18.718989+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.2203v3","created_at":"2026-05-18T00:39:18.718989+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2203","created_at":"2026-05-18T00:39:18.718989+00:00"},{"alias_kind":"pith_short_12","alias_value":"K54F3REDRYN4","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"K54F3REDRYN4LB5M","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"K54F3RED","created_at":"2026-05-18T12:28:35.611951+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/K54F3REDRYN4LB5MSDICOEBIXG","json":"https://pith.science/pith/K54F3REDRYN4LB5MSDICOEBIXG.json","graph_json":"https://pith.science/api/pith-number/K54F3REDRYN4LB5MSDICOEBIXG/graph.json","events_json":"https://pith.science/api/pith-number/K54F3REDRYN4LB5MSDICOEBIXG/events.json","paper":"https://pith.science/paper/K54F3RED"},"agent_actions":{"view_html":"https://pith.science/pith/K54F3REDRYN4LB5MSDICOEBIXG","download_json":"https://pith.science/pith/K54F3REDRYN4LB5MSDICOEBIXG.json","view_paper":"https://pith.science/paper/K54F3RED","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.2203&json=true","fetch_graph":"https://pith.science/api/pith-number/K54F3REDRYN4LB5MSDICOEBIXG/graph.json","fetch_events":"https://pith.science/api/pith-number/K54F3REDRYN4LB5MSDICOEBIXG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K54F3REDRYN4LB5MSDICOEBIXG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K54F3REDRYN4LB5MSDICOEBIXG/action/storage_attestation","attest_author":"https://pith.science/pith/K54F3REDRYN4LB5MSDICOEBIXG/action/author_attestation","sign_citation":"https://pith.science/pith/K54F3REDRYN4LB5MSDICOEBIXG/action/citation_signature","submit_replication":"https://pith.science/pith/K54F3REDRYN4LB5MSDICOEBIXG/action/replication_record"}},"created_at":"2026-05-18T00:39:18.718989+00:00","updated_at":"2026-05-18T00:39:18.718989+00:00"}