{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:RQIQG3SG3VTFWEQUXT53XXUWZD","short_pith_number":"pith:RQIQG3SG","canonical_record":{"source":{"id":"1406.1155","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-06-04T19:22:44Z","cross_cats_sorted":[],"title_canon_sha256":"630bb14e80b3cec520afabc80238d8d0630f832a25402e1f31870e0ada931039","abstract_canon_sha256":"7da41e2899bc1ce23e92b4d9fec73193733dfaf243e5ba8874b88a6764a9f7b7"},"schema_version":"1.0"},"canonical_sha256":"8c11036e46dd665b1214bcfbbbde96c8f2f592132a973d17942ec003917964f7","source":{"kind":"arxiv","id":"1406.1155","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:RQIQG3SG3VTFWEQUXT53XXUWZD","target":"record","payload":{"canonical_record":{"source":{"id":"1406.1155","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-06-04T19:22:44Z","cross_cats_sorted":[],"title_canon_sha256":"630bb14e80b3cec520afabc80238d8d0630f832a25402e1f31870e0ada931039","abstract_canon_sha256":"7da41e2899bc1ce23e92b4d9fec73193733dfaf243e5ba8874b88a6764a9f7b7"},"schema_version":"1.0"},"canonical_sha256":"8c11036e46dd665b1214bcfbbbde96c8f2f592132a973d17942ec003917964f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:01.394859Z","signature_b64":"jtD9Fji+SmxNjQ3j/tF2SysqDN7r+sXpEyjnXw8pA8vO2aURGo5XTf/d7ww5kR03PQzStxr8T4BRZdL4wVb0CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c11036e46dd665b1214bcfbbbde96c8f2f592132a973d17942ec003917964f7","last_reissued_at":"2026-05-18T01:04:01.394246Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:01.394246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.1155","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kWDSf6Qbnpl2HAoPTodOZdV3vSilSmXJfRu4kZaikUStaH6CMxJLp3c8AEamRRlHfDcBwAucjHHTPaPVccTsCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T10:58:28.925620Z"},"content_sha256":"55a8ecb79dea8a136c562530fda79b6111361a63ed23411f13e7e0370a6c3ae7","schema_version":"1.0","event_id":"sha256:55a8ecb79dea8a136c562530fda79b6111361a63ed23411f13e7e0370a6c3ae7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:RQIQG3SG3VTFWEQUXT53XXUWZD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Singular blocks of restricted sl3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Matthew Towers","submitted_at":"2014-06-04T19:22:44Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1155","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H+IBCUnoMMY47cUkpxzo3t2boDkDPgxN4yX9AM+aSQZa15neZB0VvsPaRr368cYyYRM4U0PUOHKY/+gtLx8/DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T10:58:28.925967Z"},"content_sha256":"494c7d0683be8391c0ed8a4360e39ccff40c003617628db5f9a331b1232f1418","schema_version":"1.0","event_id":"sha256:494c7d0683be8391c0ed8a4360e39ccff40c003617628db5f9a331b1232f1418"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RQIQG3SG3VTFWEQUXT53XXUWZD/bundle.json","state_url":"https://pith.science/pith/RQIQG3SG3VTFWEQUXT53XXUWZD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RQIQG3SG3VTFWEQUXT53XXUWZD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-02T10:58:28Z","links":{"resolver":"https://pith.science/pith/RQIQG3SG3VTFWEQUXT53XXUWZD","bundle":"https://pith.science/pith/RQIQG3SG3VTFWEQUXT53XXUWZD/bundle.json","state":"https://pith.science/pith/RQIQG3SG3VTFWEQUXT53XXUWZD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RQIQG3SG3VTFWEQUXT53XXUWZD/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xsAzViXGtw5ZCOFg75xxJmUleJ+k7aafisnOB3VAGlr4gWORQWTzSrpSXmR3oFTg6mBnRoouvYLWv+GWnaIjCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T10:58:28.927922Z","bundle_sha256":"7da8e18582bd9bcebbf84bf6de00f18820d0bcdad1e12a9eea2e36f2d22e3906"}}