{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:67EI4W5RJOSIOJEITW34PTLCMD","short_pith_number":"pith:67EI4W5R","schema_version":"1.0","canonical_sha256":"f7c88e5bb14ba48724889db7c7cd6260d13908000691aac5276be81dd38b34a4","source":{"kind":"arxiv","id":"1502.06714","version":1},"attestation_state":"computed","paper":{"title":"Monoidal categorification of cluster algebras II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Masaki Kashiwara, MyungHo Kim, Se-Jin Oh, Seok-Jin Kang","submitted_at":"2015-02-24T08:52:17Z","abstract_excerpt":"We prove that the quantum unipotent coordinate algebra $A_q(\\mathfrak{n}(w))\\ $ associated with a symmetric Kac-Moody algebra and its Weyl group element $w$ has a monoidal categorification as a quantum cluster algebra. As an application of our earlier work, we achieve it by showing the existence of a quantum monoidal seed of $A_q(\\mathfrak{n}(w))$ which admits the first-step mutations in all the directions. As a consequence, we solve the conjecture that any cluster monomial is a member of the upper global basis up to a power of $q^{1/2}$."},"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":"1502.06714","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-24T08:52:17Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"7ec7cfa8af0d0eef76f687e0ee78734c3f2067784f3e45448897ffa6651533cf","abstract_canon_sha256":"f4580458c44fe2bfe22b7dd99d08c912a73fbfb733356a02393e02e6182b3fcd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:29.351676Z","signature_b64":"0a5DH7o8zl+SYWn+cXE2kyIclDQ375evE5sCfJBvq0Ldtp6Oew3e3BliocJIYTyZ16VGaJd8jM7HTJeDkTLFDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7c88e5bb14ba48724889db7c7cd6260d13908000691aac5276be81dd38b34a4","last_reissued_at":"2026-05-18T02:26:29.351221Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:29.351221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Monoidal categorification of cluster algebras II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Masaki Kashiwara, MyungHo Kim, Se-Jin Oh, Seok-Jin Kang","submitted_at":"2015-02-24T08:52:17Z","abstract_excerpt":"We prove that the quantum unipotent coordinate algebra $A_q(\\mathfrak{n}(w))\\ $ associated with a symmetric Kac-Moody algebra and its Weyl group element $w$ has a monoidal categorification as a quantum cluster algebra. As an application of our earlier work, we achieve it by showing the existence of a quantum monoidal seed of $A_q(\\mathfrak{n}(w))$ which admits the first-step mutations in all the directions. As a consequence, we solve the conjecture that any cluster monomial is a member of the upper global basis up to a power of $q^{1/2}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06714","kind":"arxiv","version":1},"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":"1502.06714","created_at":"2026-05-18T02:26:29.351284+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.06714v1","created_at":"2026-05-18T02:26:29.351284+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06714","created_at":"2026-05-18T02:26:29.351284+00:00"},{"alias_kind":"pith_short_12","alias_value":"67EI4W5RJOSI","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"67EI4W5RJOSIOJEI","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"67EI4W5R","created_at":"2026-05-18T12:29:07.941421+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/67EI4W5RJOSIOJEITW34PTLCMD","json":"https://pith.science/pith/67EI4W5RJOSIOJEITW34PTLCMD.json","graph_json":"https://pith.science/api/pith-number/67EI4W5RJOSIOJEITW34PTLCMD/graph.json","events_json":"https://pith.science/api/pith-number/67EI4W5RJOSIOJEITW34PTLCMD/events.json","paper":"https://pith.science/paper/67EI4W5R"},"agent_actions":{"view_html":"https://pith.science/pith/67EI4W5RJOSIOJEITW34PTLCMD","download_json":"https://pith.science/pith/67EI4W5RJOSIOJEITW34PTLCMD.json","view_paper":"https://pith.science/paper/67EI4W5R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.06714&json=true","fetch_graph":"https://pith.science/api/pith-number/67EI4W5RJOSIOJEITW34PTLCMD/graph.json","fetch_events":"https://pith.science/api/pith-number/67EI4W5RJOSIOJEITW34PTLCMD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/67EI4W5RJOSIOJEITW34PTLCMD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/67EI4W5RJOSIOJEITW34PTLCMD/action/storage_attestation","attest_author":"https://pith.science/pith/67EI4W5RJOSIOJEITW34PTLCMD/action/author_attestation","sign_citation":"https://pith.science/pith/67EI4W5RJOSIOJEITW34PTLCMD/action/citation_signature","submit_replication":"https://pith.science/pith/67EI4W5RJOSIOJEITW34PTLCMD/action/replication_record"}},"created_at":"2026-05-18T02:26:29.351284+00:00","updated_at":"2026-05-18T02:26:29.351284+00:00"}