{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:UEJMVNJDI7SIZDZLPBP7HYSAGQ","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":"73ff9997df96d0e025fead466eaaaabbea9c5d588d590e030aaca31cedf42331","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-30T23:56:45Z","title_canon_sha256":"dded81dd0fe2a5df012166271c0a8486606e45169268418dd77b316eb09c3c06"},"schema_version":"1.0","source":{"id":"1305.0057","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0057","created_at":"2026-05-17T23:54:42Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0057v4","created_at":"2026-05-17T23:54:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0057","created_at":"2026-05-17T23:54:42Z"},{"alias_kind":"pith_short_12","alias_value":"UEJMVNJDI7SI","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UEJMVNJDI7SIZDZL","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UEJMVNJD","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:1e5bfdbaf87ef09ecc2308b0a22c11cbd6db160e6aaf4d819455ff59a9526326","target":"graph","created_at":"2026-05-17T23:54:42Z","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 R be a connected noetherian commutative ring, and let G be a simply connected reductive group over R of isotropic rank ge 2. The elementary subgroup E(R) of G(R) is the subgroup generated by the R-points U_P^+(R) and U_P^-(R) of the unipotent radicals of two opposite parabolic subgroups P^+ and P^- of G. Assume that 2 is invertible in R if G is of type B_n,C_n,F_4,G_2 and 3 is invertible in R if G is of type G_2. We prove that the congruence kernel of E(R), defined as the kernel of the natural homomorphism between the profinite completion of E(R) and the congruence completion of E(R) with ","authors_text":"A. Stavrova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-30T23:56:45Z","title":"On the congruence kernel of isotropic groups over rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0057","kind":"arxiv","version":4},"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":"sha256:9068458146cc8dd8fbc9f52410fdde706dbe70e18ec87140f98506832a9065b6","target":"record","created_at":"2026-05-17T23:54:42Z","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":"73ff9997df96d0e025fead466eaaaabbea9c5d588d590e030aaca31cedf42331","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-30T23:56:45Z","title_canon_sha256":"dded81dd0fe2a5df012166271c0a8486606e45169268418dd77b316eb09c3c06"},"schema_version":"1.0","source":{"id":"1305.0057","kind":"arxiv","version":4}},"canonical_sha256":"a112cab52347e48c8f2b785ff3e240342899117c858e251d71d7713d0f7019fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a112cab52347e48c8f2b785ff3e240342899117c858e251d71d7713d0f7019fa","first_computed_at":"2026-05-17T23:54:42.125538Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:42.125538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rPDLlzSkxa0o9Ngpbwl7i+lqjbY0ANCP+tRNoUxAzWwAPFsW7xSK6iN6ikn3t3iFd/KqyvZ3pfnuG9YpwifQDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:42.126210Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.0057","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9068458146cc8dd8fbc9f52410fdde706dbe70e18ec87140f98506832a9065b6","sha256:1e5bfdbaf87ef09ecc2308b0a22c11cbd6db160e6aaf4d819455ff59a9526326"],"state_sha256":"066d0b428722cf4eb2efb4b54ecf09046aced003b587e507a17553902ea42591"}