{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:6URQGTQR7OZP2I5TBKE76BURRE","short_pith_number":"pith:6URQGTQR","schema_version":"1.0","canonical_sha256":"f523034e11fbb2fd23b30a89ff06918918acc8e5629c4446d2cac0aff1ab4582","source":{"kind":"arxiv","id":"1607.06033","version":5},"attestation_state":"computed","paper":{"title":"Canonical bases of quantum Schubert cells and their symmetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Arkady Berenstein, Jacob Greenstein","submitted_at":"2016-07-20T17:17:50Z","abstract_excerpt":"The goal of this work is to provide an elementary construction of the canonical basis $\\mathbf B(w)$ in each quantum Schubert cell~$U_q(w)$ and to establish its invariance under modified Lusztig's symmetries. To that effect, we obtain a direct characterization of the upper global basis $\\mathbf B^{up}$ in terms of a suitable bilinear form and show that $\\mathbf B(w)$ is contained in $\\mathbf B^{up}$ and its large part is preserved by modified Lusztig's symmetries."},"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":"1607.06033","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-07-20T17:17:50Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"48ade7377c866922ba0255af3ec771b4a7c5f103c2618af39dc988cd761608c3","abstract_canon_sha256":"a003bc4e0a00e808fb33ad405c051757c56192b40f0e6fd581e789d10bd2f2bb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:47.841850Z","signature_b64":"CYILdQqu2NHCjcBquhycwUnaEJe+4L+Yxe3V3/nUNSPsIv5KhZpQDYxcBpVXaZhYqc60JL57K6HqPPVAB/VwCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f523034e11fbb2fd23b30a89ff06918918acc8e5629c4446d2cac0aff1ab4582","last_reissued_at":"2026-05-18T00:19:47.841103Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:47.841103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Canonical bases of quantum Schubert cells and their symmetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Arkady Berenstein, Jacob Greenstein","submitted_at":"2016-07-20T17:17:50Z","abstract_excerpt":"The goal of this work is to provide an elementary construction of the canonical basis $\\mathbf B(w)$ in each quantum Schubert cell~$U_q(w)$ and to establish its invariance under modified Lusztig's symmetries. To that effect, we obtain a direct characterization of the upper global basis $\\mathbf B^{up}$ in terms of a suitable bilinear form and show that $\\mathbf B(w)$ is contained in $\\mathbf B^{up}$ and its large part is preserved by modified Lusztig's symmetries."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06033","kind":"arxiv","version":5},"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":"1607.06033","created_at":"2026-05-18T00:19:47.841213+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.06033v5","created_at":"2026-05-18T00:19:47.841213+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06033","created_at":"2026-05-18T00:19:47.841213+00:00"},{"alias_kind":"pith_short_12","alias_value":"6URQGTQR7OZP","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"6URQGTQR7OZP2I5T","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"6URQGTQR","created_at":"2026-05-18T12:30:04.600751+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/6URQGTQR7OZP2I5TBKE76BURRE","json":"https://pith.science/pith/6URQGTQR7OZP2I5TBKE76BURRE.json","graph_json":"https://pith.science/api/pith-number/6URQGTQR7OZP2I5TBKE76BURRE/graph.json","events_json":"https://pith.science/api/pith-number/6URQGTQR7OZP2I5TBKE76BURRE/events.json","paper":"https://pith.science/paper/6URQGTQR"},"agent_actions":{"view_html":"https://pith.science/pith/6URQGTQR7OZP2I5TBKE76BURRE","download_json":"https://pith.science/pith/6URQGTQR7OZP2I5TBKE76BURRE.json","view_paper":"https://pith.science/paper/6URQGTQR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.06033&json=true","fetch_graph":"https://pith.science/api/pith-number/6URQGTQR7OZP2I5TBKE76BURRE/graph.json","fetch_events":"https://pith.science/api/pith-number/6URQGTQR7OZP2I5TBKE76BURRE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6URQGTQR7OZP2I5TBKE76BURRE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6URQGTQR7OZP2I5TBKE76BURRE/action/storage_attestation","attest_author":"https://pith.science/pith/6URQGTQR7OZP2I5TBKE76BURRE/action/author_attestation","sign_citation":"https://pith.science/pith/6URQGTQR7OZP2I5TBKE76BURRE/action/citation_signature","submit_replication":"https://pith.science/pith/6URQGTQR7OZP2I5TBKE76BURRE/action/replication_record"}},"created_at":"2026-05-18T00:19:47.841213+00:00","updated_at":"2026-05-18T00:19:47.841213+00:00"}