{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:O2MUHO5XOEN2IQVYAFU447PXXN","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":"2ce6afbd37bc5a7d0a538008d42c79436fd12be799c5aff838f972228b619cb3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-04-14T19:58:56Z","title_canon_sha256":"feb922f6334d66e56a16c8c382d8c7c9690f921c21a4d2c7f0d91a318a4f3683"},"schema_version":"1.0","source":{"id":"1204.3201","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3201","created_at":"2026-05-18T02:47:51Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3201v2","created_at":"2026-05-18T02:47:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3201","created_at":"2026-05-18T02:47:51Z"},{"alias_kind":"pith_short_12","alias_value":"O2MUHO5XOEN2","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"O2MUHO5XOEN2IQVY","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"O2MUHO5X","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:af97399e7c090e8833120f5bb7cfb65e42599f9ec0c99200bdfb41f63d3f80f2","target":"graph","created_at":"2026-05-18T02:47:51Z","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 provide a series of examples of finite groups G and mod p representations V of G whose stable endomorphisms are all given by scalars such that V has a universal deformation ring R(G,V) which is large in the sense that R(G,V)/pR(G,V) is isomorphic to a power series algebra in one variable.","authors_text":"Frauke M. Bleher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-04-14T19:58:56Z","title":"Large universal deformation rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3201","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:bc63d24e854444efb4365d6a8353f1232fc96f5c22b2c36115359035404d7d3b","target":"record","created_at":"2026-05-18T02:47:51Z","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":"2ce6afbd37bc5a7d0a538008d42c79436fd12be799c5aff838f972228b619cb3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-04-14T19:58:56Z","title_canon_sha256":"feb922f6334d66e56a16c8c382d8c7c9690f921c21a4d2c7f0d91a318a4f3683"},"schema_version":"1.0","source":{"id":"1204.3201","kind":"arxiv","version":2}},"canonical_sha256":"769943bbb7711ba442b80169ce7df7bb7e187d55697ac0e5f2cdfdcb052d956d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"769943bbb7711ba442b80169ce7df7bb7e187d55697ac0e5f2cdfdcb052d956d","first_computed_at":"2026-05-18T02:47:51.211593Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:51.211593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PfktiOHhLhgUSvwoNulQpTlqdSURClP4DbwiImYG+crm9+pY3TGNGLaVdaLB3tBB9/+MUXfutuQgucd/heI8Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:51.212255Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.3201","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc63d24e854444efb4365d6a8353f1232fc96f5c22b2c36115359035404d7d3b","sha256:af97399e7c090e8833120f5bb7cfb65e42599f9ec0c99200bdfb41f63d3f80f2"],"state_sha256":"1d07d8fdf191bdde26902484d674a5f5a8196137469a8033cbcccc84b88610da"}