{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QM2V33FSIMZALI5CSDIYE3XDQ7","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":"afd597a0003cd2ead52dd1bc21ce45ea564dba4b71d35c9d67aebd87cd12430c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-11-30T11:02:47Z","title_canon_sha256":"eeddbd425b52a72784f32b61af4a337f3bcdf0c3e20ce2fc79a4c5531a43a13c"},"schema_version":"1.0","source":{"id":"1611.10089","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.10089","created_at":"2026-05-18T00:44:15Z"},{"alias_kind":"arxiv_version","alias_value":"1611.10089v2","created_at":"2026-05-18T00:44:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.10089","created_at":"2026-05-18T00:44:15Z"},{"alias_kind":"pith_short_12","alias_value":"QM2V33FSIMZA","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QM2V33FSIMZALI5C","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QM2V33FS","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:c99bacfa6c0e0377cd8df7fb444cfe18e5cd629d5b60269c86d487702b09d4ea","target":"graph","created_at":"2026-05-18T00:44:15Z","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 give a simple crystal theoretic interpretation of the Lascoux's expansion of a non-symmetric Cauchy kernel $\\prod_{i+ j\\leq n+1}(1-x_iy_j)^{-1}$, which is given in terms of Demazure characters and atoms. We give a bijective proof of the non-symmetric Cauchy identity using the crystal of Lakshmibai-Seshadri paths, and extend it to the case of continuous crystals.","authors_text":"Jae-Hoon Kwon, Seung-Il Choi","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-11-30T11:02:47Z","title":"Lakshmibai-Seshadri paths and non-symmetric Cauchy identity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.10089","kind":"arxiv","version":2},"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":"sha256:31d0756ad430f1240af51576292a4b927c370e79dfa7ca2ead5b27d75f5966fe","target":"record","created_at":"2026-05-18T00:44:15Z","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":"afd597a0003cd2ead52dd1bc21ce45ea564dba4b71d35c9d67aebd87cd12430c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-11-30T11:02:47Z","title_canon_sha256":"eeddbd425b52a72784f32b61af4a337f3bcdf0c3e20ce2fc79a4c5531a43a13c"},"schema_version":"1.0","source":{"id":"1611.10089","kind":"arxiv","version":2}},"canonical_sha256":"83355decb2433205a3a290d1826ee387cdf5f7ea7d4fc24d2b2725091cdb5a94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83355decb2433205a3a290d1826ee387cdf5f7ea7d4fc24d2b2725091cdb5a94","first_computed_at":"2026-05-18T00:44:15.761814Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:15.761814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qvcTXZnh4+IOp5dihbmzcG5gnnFBSSihq3un7nXmy0Eu+1B56HdUZchk4EaNibPQZfGoEEXWHoHTYcCqRWMSCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:15.762249Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.10089","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31d0756ad430f1240af51576292a4b927c370e79dfa7ca2ead5b27d75f5966fe","sha256:c99bacfa6c0e0377cd8df7fb444cfe18e5cd629d5b60269c86d487702b09d4ea"],"state_sha256":"937426e1d76ebda90f8df808c60e0da7f6cc5a541e589f1a505d86e263e481b7"}