{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:SRI4N5MQMQNRMTKUJIZB4B23EG","short_pith_number":"pith:SRI4N5MQ","schema_version":"1.0","canonical_sha256":"9451c6f590641b164d544a321e075b219b258170a2071dedd5a54e542d12aed3","source":{"kind":"arxiv","id":"1411.3569","version":2},"attestation_state":"computed","paper":{"title":"Cluster monomials in $\\mathbb C[GL_n/N]$, a simplicial fan in the cone of semi-standard Young tableaux, and the Lusztig basis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Gleb Koshevoy","submitted_at":"2014-11-13T14:55:15Z","abstract_excerpt":"We study the cluster monomials and cluster complex in $\\mathbb C[GL_n/N]$. For we consider the {\\em tableau basis} in $\\mathbb C[GL_n/N]$. Namely, an element $\\Delta_T$ of the tableau basis labeled by a semistandard Young tableau $T$ is the product of the flag minors corresponding to columns of $T$. Our main results state: (i) cluster monomials in $\\mathbb C[GL_n/N]$ can be labeled by semistandard Young tableaux such that any cluster monomial has the form $\\Delta_T+$ lexicographically smaller terms; (ii) such labeling distinguish the cluster monomial; (iii) for any seed of the cluster algebra "},"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":"1411.3569","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-11-13T14:55:15Z","cross_cats_sorted":[],"title_canon_sha256":"4d7a574464a54c8964f7c94703ce3470fd47fd4529f3fd958cd3a62238cf0678","abstract_canon_sha256":"34e7dbc705f3f501e8fe3f3dc343599075db36bc7715a61019d612035410f128"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:55.166586Z","signature_b64":"ZlgEkSR/UF5WINh88rRk92aIsM8SkDSUuI4hst9Lww1X98rRBut1VrA5KrEkq1dBMT1pZcULdMGEeiN9LZiZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9451c6f590641b164d544a321e075b219b258170a2071dedd5a54e542d12aed3","last_reissued_at":"2026-05-18T02:32:55.165757Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:55.165757Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cluster monomials in $\\mathbb C[GL_n/N]$, a simplicial fan in the cone of semi-standard Young tableaux, and the Lusztig basis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Gleb Koshevoy","submitted_at":"2014-11-13T14:55:15Z","abstract_excerpt":"We study the cluster monomials and cluster complex in $\\mathbb C[GL_n/N]$. For we consider the {\\em tableau basis} in $\\mathbb C[GL_n/N]$. Namely, an element $\\Delta_T$ of the tableau basis labeled by a semistandard Young tableau $T$ is the product of the flag minors corresponding to columns of $T$. Our main results state: (i) cluster monomials in $\\mathbb C[GL_n/N]$ can be labeled by semistandard Young tableaux such that any cluster monomial has the form $\\Delta_T+$ lexicographically smaller terms; (ii) such labeling distinguish the cluster monomial; (iii) for any seed of the cluster algebra "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3569","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":"1411.3569","created_at":"2026-05-18T02:32:55.165874+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.3569v2","created_at":"2026-05-18T02:32:55.165874+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3569","created_at":"2026-05-18T02:32:55.165874+00:00"},{"alias_kind":"pith_short_12","alias_value":"SRI4N5MQMQNR","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"SRI4N5MQMQNRMTKU","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"SRI4N5MQ","created_at":"2026-05-18T12:28:49.207871+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/SRI4N5MQMQNRMTKUJIZB4B23EG","json":"https://pith.science/pith/SRI4N5MQMQNRMTKUJIZB4B23EG.json","graph_json":"https://pith.science/api/pith-number/SRI4N5MQMQNRMTKUJIZB4B23EG/graph.json","events_json":"https://pith.science/api/pith-number/SRI4N5MQMQNRMTKUJIZB4B23EG/events.json","paper":"https://pith.science/paper/SRI4N5MQ"},"agent_actions":{"view_html":"https://pith.science/pith/SRI4N5MQMQNRMTKUJIZB4B23EG","download_json":"https://pith.science/pith/SRI4N5MQMQNRMTKUJIZB4B23EG.json","view_paper":"https://pith.science/paper/SRI4N5MQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.3569&json=true","fetch_graph":"https://pith.science/api/pith-number/SRI4N5MQMQNRMTKUJIZB4B23EG/graph.json","fetch_events":"https://pith.science/api/pith-number/SRI4N5MQMQNRMTKUJIZB4B23EG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SRI4N5MQMQNRMTKUJIZB4B23EG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SRI4N5MQMQNRMTKUJIZB4B23EG/action/storage_attestation","attest_author":"https://pith.science/pith/SRI4N5MQMQNRMTKUJIZB4B23EG/action/author_attestation","sign_citation":"https://pith.science/pith/SRI4N5MQMQNRMTKUJIZB4B23EG/action/citation_signature","submit_replication":"https://pith.science/pith/SRI4N5MQMQNRMTKUJIZB4B23EG/action/replication_record"}},"created_at":"2026-05-18T02:32:55.165874+00:00","updated_at":"2026-05-18T02:32:55.165874+00:00"}