{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:K54F3REDRYN4LB5MSDICOEBIXG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"51d7f3e9506840257384f12bf0ef5c5f706108fe64e47b36ba2ac75e0e4ca178","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-02-10T16:34:15Z","title_canon_sha256":"bc7d64eec0d5562225a21dde69d8b46daed78597958918b7d621545f96f08aee"},"schema_version":"1.0","source":{"id":"1402.2203","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.2203","created_at":"2026-05-18T00:39:18Z"},{"alias_kind":"arxiv_version","alias_value":"1402.2203v3","created_at":"2026-05-18T00:39:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2203","created_at":"2026-05-18T00:39:18Z"},{"alias_kind":"pith_short_12","alias_value":"K54F3REDRYN4","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"K54F3REDRYN4LB5M","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"K54F3RED","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:d9889b569117fdf1f2b06185cf739fc500d7a480ca3bbe7bc640b9279f0560c0","target":"graph","created_at":"2026-05-18T00:39:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Anne Schilling, Cristian Lenart, Daisuke Sagaki, Mark Shimozono, Satoshi Naito","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-02-10T16:34:15Z","title":"A uniform model for Kirillov-Reshetikhin crystals II. Alcove model, path model, and P=X"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2203","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b77f9b82bdf5b38a2efda0c01d280530a3b5c4d223bd41d6b6a5a3dfa11d0fd5","target":"record","created_at":"2026-05-18T00:39:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"51d7f3e9506840257384f12bf0ef5c5f706108fe64e47b36ba2ac75e0e4ca178","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-02-10T16:34:15Z","title_canon_sha256":"bc7d64eec0d5562225a21dde69d8b46daed78597958918b7d621545f96f08aee"},"schema_version":"1.0","source":{"id":"1402.2203","kind":"arxiv","version":3}},"canonical_sha256":"57785dc4838e1bc587ac90d0271028b9997863b6f404bc98049b98de428da0b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57785dc4838e1bc587ac90d0271028b9997863b6f404bc98049b98de428da0b6","first_computed_at":"2026-05-18T00:39:18.718885Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:18.718885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZIsYVxckwE2TcGt24wMgeSCxrygeb8Er4Fo9pr+rENAT8wZGsjwVujg4XGDCwbEY6nIIaRcbrNtL8Qw0Sn4qBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:18.719613Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.2203","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b77f9b82bdf5b38a2efda0c01d280530a3b5c4d223bd41d6b6a5a3dfa11d0fd5","sha256:d9889b569117fdf1f2b06185cf739fc500d7a480ca3bbe7bc640b9279f0560c0"],"state_sha256":"dc4a59444268e1104607e7fe75216e704debdd1fd1eca6e485d35b8f745c3006"}