{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:FOJR4VDM6HJT7HZUWUMP56LK6A","short_pith_number":"pith:FOJR4VDM","schema_version":"1.0","canonical_sha256":"2b931e546cf1d33f9f34b518fef96af03eb8bcb2bba4f52ccc519bda4e6936c7","source":{"kind":"arxiv","id":"0909.1810","version":2},"attestation_state":"computed","paper":{"title":"Crystals from categorified quantum groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Aaron D. Lauda, Monica Vazirani","submitted_at":"2009-09-10T18:25:05Z","abstract_excerpt":"We study the crystal structure on categories of graded modules over algebras which categorify the negative half of the quantum Kac-Moody algebra associated to a symmetrizable Cartan data. We identify this crystal with Kashiwara's crystal for the corresponding negative half of the quantum Kac-Moody algebra. As a consequence, we show the simple graded modules for certain cyclotomic quotients carry the structure of highest weight crystals, and hence compute the rank of the corresponding Grothendieck group."},"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":"0909.1810","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-09-10T18:25:05Z","cross_cats_sorted":[],"title_canon_sha256":"33d5dba079e37b3e455354142b818a2fe688653bc8b619b7d3676395ae4486e2","abstract_canon_sha256":"799edfd2fbea6f269b09bca0948550111f7ddd328c8c3a27b1a6609b69e82a87"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:32.343029Z","signature_b64":"GSjOlEom33pcFI8oMCQI/W7FljTI8oRKbpXcIjYeqV2ns7dgNpetR4us3go35Y8D1bqbrXFXfOih3pXI7Nb4Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b931e546cf1d33f9f34b518fef96af03eb8bcb2bba4f52ccc519bda4e6936c7","last_reissued_at":"2026-05-18T04:16:32.342462Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:32.342462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Crystals from categorified quantum groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Aaron D. Lauda, Monica Vazirani","submitted_at":"2009-09-10T18:25:05Z","abstract_excerpt":"We study the crystal structure on categories of graded modules over algebras which categorify the negative half of the quantum Kac-Moody algebra associated to a symmetrizable Cartan data. We identify this crystal with Kashiwara's crystal for the corresponding negative half of the quantum Kac-Moody algebra. As a consequence, we show the simple graded modules for certain cyclotomic quotients carry the structure of highest weight crystals, and hence compute the rank of the corresponding Grothendieck group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.1810","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":"0909.1810","created_at":"2026-05-18T04:16:32.342537+00:00"},{"alias_kind":"arxiv_version","alias_value":"0909.1810v2","created_at":"2026-05-18T04:16:32.342537+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.1810","created_at":"2026-05-18T04:16:32.342537+00:00"},{"alias_kind":"pith_short_12","alias_value":"FOJR4VDM6HJT","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_16","alias_value":"FOJR4VDM6HJT7HZU","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_8","alias_value":"FOJR4VDM","created_at":"2026-05-18T12:25:59.703012+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/FOJR4VDM6HJT7HZUWUMP56LK6A","json":"https://pith.science/pith/FOJR4VDM6HJT7HZUWUMP56LK6A.json","graph_json":"https://pith.science/api/pith-number/FOJR4VDM6HJT7HZUWUMP56LK6A/graph.json","events_json":"https://pith.science/api/pith-number/FOJR4VDM6HJT7HZUWUMP56LK6A/events.json","paper":"https://pith.science/paper/FOJR4VDM"},"agent_actions":{"view_html":"https://pith.science/pith/FOJR4VDM6HJT7HZUWUMP56LK6A","download_json":"https://pith.science/pith/FOJR4VDM6HJT7HZUWUMP56LK6A.json","view_paper":"https://pith.science/paper/FOJR4VDM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0909.1810&json=true","fetch_graph":"https://pith.science/api/pith-number/FOJR4VDM6HJT7HZUWUMP56LK6A/graph.json","fetch_events":"https://pith.science/api/pith-number/FOJR4VDM6HJT7HZUWUMP56LK6A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FOJR4VDM6HJT7HZUWUMP56LK6A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FOJR4VDM6HJT7HZUWUMP56LK6A/action/storage_attestation","attest_author":"https://pith.science/pith/FOJR4VDM6HJT7HZUWUMP56LK6A/action/author_attestation","sign_citation":"https://pith.science/pith/FOJR4VDM6HJT7HZUWUMP56LK6A/action/citation_signature","submit_replication":"https://pith.science/pith/FOJR4VDM6HJT7HZUWUMP56LK6A/action/replication_record"}},"created_at":"2026-05-18T04:16:32.342537+00:00","updated_at":"2026-05-18T04:16:32.342537+00:00"}