{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RQIQG3SG3VTFWEQUXT53XXUWZD","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":"7da41e2899bc1ce23e92b4d9fec73193733dfaf243e5ba8874b88a6764a9f7b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-06-04T19:22:44Z","title_canon_sha256":"630bb14e80b3cec520afabc80238d8d0630f832a25402e1f31870e0ada931039"},"schema_version":"1.0","source":{"id":"1406.1155","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.1155","created_at":"2026-05-18T01:04:01Z"},{"alias_kind":"arxiv_version","alias_value":"1406.1155v3","created_at":"2026-05-18T01:04:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.1155","created_at":"2026-05-18T01:04:01Z"},{"alias_kind":"pith_short_12","alias_value":"RQIQG3SG3VTF","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RQIQG3SG3VTFWEQU","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RQIQG3SG","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:494c7d0683be8391c0ed8a4360e39ccff40c003617628db5f9a331b1232f1418","target":"graph","created_at":"2026-05-18T01:04:01Z","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":"We compute generators and relations for the basic algebra of a non-semisimple singular block of the restricted enveloping algebra of $\\mathfrak{sl}_3$ over an algebraically closed field of characteristic $p>3$. Working directly with the basic algebra we compute its centre and the internal degree zero part of its first Hochschild cohomology, and show its Verma modules are Koszul.","authors_text":"Matthew Towers","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-06-04T19:22:44Z","title":"Singular blocks of restricted sl3"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1155","kind":"arxiv","version":3},"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":"sha256:55a8ecb79dea8a136c562530fda79b6111361a63ed23411f13e7e0370a6c3ae7","target":"record","created_at":"2026-05-18T01:04:01Z","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":"7da41e2899bc1ce23e92b4d9fec73193733dfaf243e5ba8874b88a6764a9f7b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-06-04T19:22:44Z","title_canon_sha256":"630bb14e80b3cec520afabc80238d8d0630f832a25402e1f31870e0ada931039"},"schema_version":"1.0","source":{"id":"1406.1155","kind":"arxiv","version":3}},"canonical_sha256":"8c11036e46dd665b1214bcfbbbde96c8f2f592132a973d17942ec003917964f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c11036e46dd665b1214bcfbbbde96c8f2f592132a973d17942ec003917964f7","first_computed_at":"2026-05-18T01:04:01.394246Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:01.394246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jtD9Fji+SmxNjQ3j/tF2SysqDN7r+sXpEyjnXw8pA8vO2aURGo5XTf/d7ww5kR03PQzStxr8T4BRZdL4wVb0CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:01.394859Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.1155","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55a8ecb79dea8a136c562530fda79b6111361a63ed23411f13e7e0370a6c3ae7","sha256:494c7d0683be8391c0ed8a4360e39ccff40c003617628db5f9a331b1232f1418"],"state_sha256":"7b27ef40a0a3667ca8456ddb6e5ff78b0d6b5a2c5d4b7cfd7a40761abd1898ca"}