{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:O2MUHO5XOEN2IQVYAFU447PXXN","short_pith_number":"pith:O2MUHO5X","canonical_record":{"source":{"id":"1204.3201","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-04-14T19:58:56Z","cross_cats_sorted":[],"title_canon_sha256":"feb922f6334d66e56a16c8c382d8c7c9690f921c21a4d2c7f0d91a318a4f3683","abstract_canon_sha256":"2ce6afbd37bc5a7d0a538008d42c79436fd12be799c5aff838f972228b619cb3"},"schema_version":"1.0"},"canonical_sha256":"769943bbb7711ba442b80169ce7df7bb7e187d55697ac0e5f2cdfdcb052d956d","source":{"kind":"arxiv","id":"1204.3201","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:O2MUHO5XOEN2IQVYAFU447PXXN","target":"record","payload":{"canonical_record":{"source":{"id":"1204.3201","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-04-14T19:58:56Z","cross_cats_sorted":[],"title_canon_sha256":"feb922f6334d66e56a16c8c382d8c7c9690f921c21a4d2c7f0d91a318a4f3683","abstract_canon_sha256":"2ce6afbd37bc5a7d0a538008d42c79436fd12be799c5aff838f972228b619cb3"},"schema_version":"1.0"},"canonical_sha256":"769943bbb7711ba442b80169ce7df7bb7e187d55697ac0e5f2cdfdcb052d956d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:51.212255Z","signature_b64":"PfktiOHhLhgUSvwoNulQpTlqdSURClP4DbwiImYG+crm9+pY3TGNGLaVdaLB3tBB9/+MUXfutuQgucd/heI8Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"769943bbb7711ba442b80169ce7df7bb7e187d55697ac0e5f2cdfdcb052d956d","last_reissued_at":"2026-05-18T02:47:51.211593Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:51.211593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.3201","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:47:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tyRghPbMx7OniytXMHq0nUnfYIJvFSFY8SP269BcjRrEiQOjrCO3aR7fnO3Wac3FcC+dDakSHnnyvoo1QqFCCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T08:43:17.445028Z"},"content_sha256":"bc63d24e854444efb4365d6a8353f1232fc96f5c22b2c36115359035404d7d3b","schema_version":"1.0","event_id":"sha256:bc63d24e854444efb4365d6a8353f1232fc96f5c22b2c36115359035404d7d3b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:O2MUHO5XOEN2IQVYAFU447PXXN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large universal deformation rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Frauke M. Bleher","submitted_at":"2012-04-14T19:58:56Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3201","kind":"arxiv","version":2},"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":"2026-05-18T02:47:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RboNBDH7Awo2K+a+Autx8FUsu4oMHKFz2wq/eHnYjP++NDnykLq8LdU5DpJJVJ1/sVYcIBUoLSv0S0yfHEmhAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T08:43:17.445387Z"},"content_sha256":"af97399e7c090e8833120f5bb7cfb65e42599f9ec0c99200bdfb41f63d3f80f2","schema_version":"1.0","event_id":"sha256:af97399e7c090e8833120f5bb7cfb65e42599f9ec0c99200bdfb41f63d3f80f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O2MUHO5XOEN2IQVYAFU447PXXN/bundle.json","state_url":"https://pith.science/pith/O2MUHO5XOEN2IQVYAFU447PXXN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O2MUHO5XOEN2IQVYAFU447PXXN/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":"2026-06-12T08:43:17Z","links":{"resolver":"https://pith.science/pith/O2MUHO5XOEN2IQVYAFU447PXXN","bundle":"https://pith.science/pith/O2MUHO5XOEN2IQVYAFU447PXXN/bundle.json","state":"https://pith.science/pith/O2MUHO5XOEN2IQVYAFU447PXXN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O2MUHO5XOEN2IQVYAFU447PXXN/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9VSxb6W1i6OuOVZIFd1xxUvYbhFgPR6KEPmhMv1tgmetl/m6Vsiu3M/vqShbsyUxacwlK8otaDS9fMcoBMq6Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T08:43:17.447426Z","bundle_sha256":"f5fdf05198b37327a690ac3426f899e32528bca7da22ae8fdcdee5dd14b04be9"}}