{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YTMHOWLPGTQKBCD34YW4PDW27B","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":"f8478d31acdca8f107cb9126959fc670b79ed55fcb83bd807b50c2dbda22777d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-02-17T17:16:46Z","title_canon_sha256":"5da0063217afbd5b785c15f4246ebfe7f00a28038f8b0c610be0450c90f2d4c6"},"schema_version":"1.0","source":{"id":"1102.3639","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3639","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3639v1","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3639","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"pith_short_12","alias_value":"YTMHOWLPGTQK","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YTMHOWLPGTQKBCD3","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YTMHOWLP","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:91b743d9c3dd755e8eebfeb72d8fc1677805f1d9e3a54e6537e9cdb1cf6212c1","target":"graph","created_at":"2026-05-18T04:28:28Z","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":"Let $\\zeta$ be a complex $\\ell$th root of unity for an odd integer $\\ell>1$. For any complex simple Lie algebra $\\mathfrak g$, let $u_\\zeta=u_\\zeta({\\mathfrak g})$ be the associated \"small\" quantum enveloping algebra. In general, little is known about the representation theory of quantum groups (resp., algebraic groups) when $l$ (resp., $p$) is smaller than the Coxeter number $h$ of the underlying root system. For example, Lusztig's conjecture concerning the characters of the rational irreducible $G$-modules stipulates that $p \\geq h$. The main result in this paper provides a surprisingly unif","authors_text":"Brian J. Parshall, Christopher P. Bendel, Cornelius Pillen, Daniel K. Nakano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-02-17T17:16:46Z","title":"Cohomology for quantum groups via the geometry of the nullcone"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3639","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":"sha256:7067acfac31784472af46553642d42b8b131ba169aa2e83a3279189d296ea7d1","target":"record","created_at":"2026-05-18T04:28:28Z","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":"f8478d31acdca8f107cb9126959fc670b79ed55fcb83bd807b50c2dbda22777d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-02-17T17:16:46Z","title_canon_sha256":"5da0063217afbd5b785c15f4246ebfe7f00a28038f8b0c610be0450c90f2d4c6"},"schema_version":"1.0","source":{"id":"1102.3639","kind":"arxiv","version":1}},"canonical_sha256":"c4d877596f34e0a0887be62dc78edaf843ed4fec83155c31718ec0f0c8b17fd5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4d877596f34e0a0887be62dc78edaf843ed4fec83155c31718ec0f0c8b17fd5","first_computed_at":"2026-05-18T04:28:28.710480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:28.710480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dsoOU5KU8kxtaKjbEV8L+vr99g1hzjID16T9S/t+lUwq+UbRiUjW7kgIH0MFwgjFgu/meIjD1qOXD0Ic6KYPCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:28.710903Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.3639","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7067acfac31784472af46553642d42b8b131ba169aa2e83a3279189d296ea7d1","sha256:91b743d9c3dd755e8eebfeb72d8fc1677805f1d9e3a54e6537e9cdb1cf6212c1"],"state_sha256":"272d0fcc5bf8c26fb4d1c4ffa1c786bab0ddb0e2fc5b789737f12e97d4d1699e"}