{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ARBNKCTRP4BWRSFBXSUOO6QIJ3","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":"3e044ad0450d96098c271af809481df2cb2c30bce4306fd1464dae6708a6d96b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-29T19:08:15Z","title_canon_sha256":"c5622a231b81e7148347647f78581ba55feb1ba8138d4ed2d7cbc662be843c6a"},"schema_version":"1.0","source":{"id":"1407.7826","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.7826","created_at":"2026-05-18T02:46:15Z"},{"alias_kind":"arxiv_version","alias_value":"1407.7826v1","created_at":"2026-05-18T02:46:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7826","created_at":"2026-05-18T02:46:15Z"},{"alias_kind":"pith_short_12","alias_value":"ARBNKCTRP4BW","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"ARBNKCTRP4BWRSFB","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"ARBNKCTR","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:ffa7bf86a763da782a1775ac32cd1ac5101b595517238a725dd10c924603b21e","target":"graph","created_at":"2026-05-18T02:46:15Z","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":"The right key of a semistandard Young tableau is a tool used to find Demazure characters for $sl_n(\\mathbb{C})$. This thesis gives methods to obtain the right and left keys by inspection of the semistandard Young tableau. Given a partition $\\lambda$ and a Weyl group element $w$, there is a semistandard Young tableau $Y_\\lambda(w)$ of shape $\\lambda$ that corresponds to $w$. The Demazure character for $\\lambda$ and $w$ is known to be the sum of the weights of all tableaux whose right key is dominated by $Y_\\lambda(w)$. The set of all such tableaux is denoted $\\mathcal{D}_\\lambda(w)$. Exploiting","authors_text":"Matthew J. Willis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-29T19:08:15Z","title":"New Descriptions of Demazure Tableaux and Right Keys, with Applications to Convexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7826","kind":"arxiv","version":1},"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:ed33ad9815ccf247255f0c80beb9736604dbefb62ac2c90d12f17b1483fe5e2d","target":"record","created_at":"2026-05-18T02:46:15Z","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":"3e044ad0450d96098c271af809481df2cb2c30bce4306fd1464dae6708a6d96b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-29T19:08:15Z","title_canon_sha256":"c5622a231b81e7148347647f78581ba55feb1ba8138d4ed2d7cbc662be843c6a"},"schema_version":"1.0","source":{"id":"1407.7826","kind":"arxiv","version":1}},"canonical_sha256":"0442d50a717f0368c8a1bca8e77a084ed3c5a1f4599d831e82b6e6add19ad75d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0442d50a717f0368c8a1bca8e77a084ed3c5a1f4599d831e82b6e6add19ad75d","first_computed_at":"2026-05-18T02:46:15.405899Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:15.405899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l7Z1blgBcnGdprkOhRS2h1zAspY454ss7MJ8pxDECBHZgFIEYJ+GZds0VVQ3LM7PceZFu2zMlFHAit7oQtrMCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:15.406702Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.7826","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed33ad9815ccf247255f0c80beb9736604dbefb62ac2c90d12f17b1483fe5e2d","sha256:ffa7bf86a763da782a1775ac32cd1ac5101b595517238a725dd10c924603b21e"],"state_sha256":"d2d7066cf90a96acf9e5a6e1dbae5078f0368ae1315785686399964ac773e6ac"}