{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3D5WM3HIFRCXKJKZPWOC327J3C","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":"21e1fefdcbf15686b27ab3768da829b3876b40868eb33e6346dacc4e0d9b5712","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-07-31T15:27:45Z","title_canon_sha256":"5f25b6bc5f76970d7e627708fee82975fc6c12069609b8e466a2eeb38afab390"},"schema_version":"1.0","source":{"id":"1307.8356","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.8356","created_at":"2026-05-17T23:53:15Z"},{"alias_kind":"arxiv_version","alias_value":"1307.8356v2","created_at":"2026-05-17T23:53:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.8356","created_at":"2026-05-17T23:53:15Z"},{"alias_kind":"pith_short_12","alias_value":"3D5WM3HIFRCX","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3D5WM3HIFRCXKJKZ","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3D5WM3HI","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:39b545e45bf60ecde42a8111d15d13a3938ca2dd78fdef1d72e097e40c46a5ff","target":"graph","created_at":"2026-05-17T23:53:15Z","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 show the inverse deformation problem has an affirmative answer: given a complete local noetherian ring $A$ with finite residue field $\\pmb{k}$, we show that there is a topologically finitely generated profinite group $\\Gamma$ and an absolutely irreducible continuous representation $\\bar\\rho:\\Gamma\\to GL_n(\\pmb{k})$ such that $A$ is the universal deformation ring for $\\Gamma,\\bar\\rho$.","authors_text":"Jayanta Manoharmayum, Timothy Eardley","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-07-31T15:27:45Z","title":"The inverse deformation problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.8356","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":"sha256:81d4693007b1276c201efabaad5429f9080fddc550cba577381e14dab66cfa9d","target":"record","created_at":"2026-05-17T23:53:15Z","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":"21e1fefdcbf15686b27ab3768da829b3876b40868eb33e6346dacc4e0d9b5712","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-07-31T15:27:45Z","title_canon_sha256":"5f25b6bc5f76970d7e627708fee82975fc6c12069609b8e466a2eeb38afab390"},"schema_version":"1.0","source":{"id":"1307.8356","kind":"arxiv","version":2}},"canonical_sha256":"d8fb666ce82c457525597d9c2debe9d8b1a358e66f26a18475b6e5bb5a4d8351","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8fb666ce82c457525597d9c2debe9d8b1a358e66f26a18475b6e5bb5a4d8351","first_computed_at":"2026-05-17T23:53:15.224726Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:15.224726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fRbl9xH2/XvjREDZwVjuKWIK6XG0INBCHY8jCGGD3gwPi6lzJOLnLfey5gv6xCB5I+RHYW6Q4ZcJRnSU64w5BQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:15.225335Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.8356","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81d4693007b1276c201efabaad5429f9080fddc550cba577381e14dab66cfa9d","sha256:39b545e45bf60ecde42a8111d15d13a3938ca2dd78fdef1d72e097e40c46a5ff"],"state_sha256":"de5cbf9d6d9617b93dee4cd54a7def3381d5a8c874ac620cafb838a489853d6d"}