{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:Z3BBT5JT2QMDGIDUBLA4EFGLHR","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":"aff6f2053e2c6d09bf699ba421deb57e9c21a457ff8c3b3d4d9ed601d43faa3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-09-05T14:15:36Z","title_canon_sha256":"42fac4ebac7ffc7615cb04bdfd4d5de41b397022838d64fa87ef5ad160205c9e"},"schema_version":"1.0","source":{"id":"0909.1031","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.1031","created_at":"2026-05-18T04:40:56Z"},{"alias_kind":"arxiv_version","alias_value":"0909.1031v2","created_at":"2026-05-18T04:40:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.1031","created_at":"2026-05-18T04:40:56Z"},{"alias_kind":"pith_short_12","alias_value":"Z3BBT5JT2QMD","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"Z3BBT5JT2QMDGIDU","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"Z3BBT5JT","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:edfc9d89e6a8e299622f6c29f24e5daf49b3df0118426148a710c11a828d1234","target":"graph","created_at":"2026-05-18T04:40:56Z","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 determine the universal deformation ring R(G,V) of certain mod 2 representations V of a finite group G which belong to a 2-modular block of G whose defect groups are isomorphic to a generalized quaternion group D. We show that for these V, a question raised by the author and Chinburg concerning the relation of R(G,V) to D has an affirmative answer. We also show that R(G,V) is a complete intersection even though R(G/N,V) need not be for certain normal subgroups N of G which act trivially on V.","authors_text":"Frauke M. Bleher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-09-05T14:15:36Z","title":"Universal deformation rings and generalized quaternion defect groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.1031","kind":"arxiv","version":2},"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":"sha256:034adbc6deb31f5fd5cf6892e7ef499511a90514cf943d8206bd3d3322b3bafd","target":"record","created_at":"2026-05-18T04:40:56Z","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":"aff6f2053e2c6d09bf699ba421deb57e9c21a457ff8c3b3d4d9ed601d43faa3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-09-05T14:15:36Z","title_canon_sha256":"42fac4ebac7ffc7615cb04bdfd4d5de41b397022838d64fa87ef5ad160205c9e"},"schema_version":"1.0","source":{"id":"0909.1031","kind":"arxiv","version":2}},"canonical_sha256":"cec219f533d4183320740ac1c214cb3c6509379f8f02c88f438600f2de0fead9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cec219f533d4183320740ac1c214cb3c6509379f8f02c88f438600f2de0fead9","first_computed_at":"2026-05-18T04:40:56.162113Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:56.162113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PL3bchrU+3GF/PWTpVMOI2ebVgY9qxWSRLqX6CNbp9RsnPjP3BWw6zcezwaksXZBZnZjjUpARsJpi0b00domAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:56.162837Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.1031","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:034adbc6deb31f5fd5cf6892e7ef499511a90514cf943d8206bd3d3322b3bafd","sha256:edfc9d89e6a8e299622f6c29f24e5daf49b3df0118426148a710c11a828d1234"],"state_sha256":"99974fc095c9f5a2aa9b09f11a9f2a18a48c992a9e481216c453edafcef63ef5"}