{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TI7VWEAZ7E7RTI4UXDFB5DR4H2","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":"c35de47c4365a9436083e91d5097b08c3a8320b038d3023aed760ebb11ac2c81","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-12-01T10:54:58Z","title_canon_sha256":"d1b561d66cd00b5b80e56edde6ebbb67a9524cdf7774c41cf2862e3cb89fe1c5"},"schema_version":"1.0","source":{"id":"1112.0135","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.0135","created_at":"2026-05-18T04:07:16Z"},{"alias_kind":"arxiv_version","alias_value":"1112.0135v1","created_at":"2026-05-18T04:07:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0135","created_at":"2026-05-18T04:07:16Z"},{"alias_kind":"pith_short_12","alias_value":"TI7VWEAZ7E7R","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TI7VWEAZ7E7RTI4U","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TI7VWEAZ","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:54af37678dde5e1aab414a66459759174f73d15ecc46980585a6a6c00ca0ccc2","target":"graph","created_at":"2026-05-18T04:07:16Z","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 $K$ be a normal subgroup of the finite group $H$. To a block of a $K$-interior $H$-algebra we associate a group extension, and we prove that this extension is isomorphic to an extension associated to a block given by the Brauer homomorphism.\n  This may be regarded as a generalization and an alternative treatment of Dade's results \"Block extensions\" Section 12.","authors_text":"Tiberiu Coconet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-12-01T10:54:58Z","title":"$G$-algebras, group graded algebras, and Clifford extensions of blocks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0135","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":"sha256:87aeec46fcd2ff2fc72d70b9d02ff9a63892fabf9b98691473903d07207cdd86","target":"record","created_at":"2026-05-18T04:07:16Z","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":"c35de47c4365a9436083e91d5097b08c3a8320b038d3023aed760ebb11ac2c81","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-12-01T10:54:58Z","title_canon_sha256":"d1b561d66cd00b5b80e56edde6ebbb67a9524cdf7774c41cf2862e3cb89fe1c5"},"schema_version":"1.0","source":{"id":"1112.0135","kind":"arxiv","version":1}},"canonical_sha256":"9a3f5b1019f93f19a394b8ca1e8e3c3e9887378265808d8eabf7adf27c0a4779","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a3f5b1019f93f19a394b8ca1e8e3c3e9887378265808d8eabf7adf27c0a4779","first_computed_at":"2026-05-18T04:07:16.836729Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:16.836729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B45zWdNt29ZrUb7BdjBSgpEDrlY5bs+arOUhSwSVD4De3l80nLSMkT33lgg5MbZVnazZAVve5+ZgV45jOUJdCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:16.837439Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.0135","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87aeec46fcd2ff2fc72d70b9d02ff9a63892fabf9b98691473903d07207cdd86","sha256:54af37678dde5e1aab414a66459759174f73d15ecc46980585a6a6c00ca0ccc2"],"state_sha256":"2d745819ebc8d0cfdf354cf6694223aa92a2bd77c45f5123988c0a8cc894ca52"}