{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DWCMK4WPEEYBEMW6OCCZ4JVD6X","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":"69fb77d70758cc2ea4345ae6f773b3fb4ee3e56fd7000d87dfa3c9c05d345d26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-11-02T17:10:32Z","title_canon_sha256":"c69bb22fd01aea055725b0be1237bed72cd0e9572decc344cfd9d35af833d296"},"schema_version":"1.0","source":{"id":"1211.0493","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0493","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0493v3","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0493","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"pith_short_12","alias_value":"DWCMK4WPEEYB","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DWCMK4WPEEYBEMW6","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DWCMK4WP","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:84f0d6eea79194af89da2d436a6aa869a1e4281f68d30c88860d52ebeb103f3d","target":"graph","created_at":"2026-05-18T02:29:53Z","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":"Two groups are said to have the same nilpotent genus if they have the same nilpotent quotients. We answer four questions of Baumslag concerning nilpotent completions. (i) There exists a pair of finitely generated, residually torsion-free-nilpotent groups of the same nilpotent genus such that one is finitely presented and the other is not. (ii) There exists a pair of finitely presented, residually torsion-free-nilpotent groups of the same nilpotent genus such that one has a solvable conjugacy problem and the other does not. (iii) There exists a pair of finitely generated, residually torsion-fre","authors_text":"Alan W. Reid, Martin R. Bridson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-11-02T17:10:32Z","title":"Nilpotent completions of groups, Grothendieck pairs, and four problems of Baumslag"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0493","kind":"arxiv","version":3},"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":"sha256:7e3dc837a48992f9c6774ba079d9a4170c96ee58194ba49790ef247fdada4f8d","target":"record","created_at":"2026-05-18T02:29:53Z","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":"69fb77d70758cc2ea4345ae6f773b3fb4ee3e56fd7000d87dfa3c9c05d345d26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-11-02T17:10:32Z","title_canon_sha256":"c69bb22fd01aea055725b0be1237bed72cd0e9572decc344cfd9d35af833d296"},"schema_version":"1.0","source":{"id":"1211.0493","kind":"arxiv","version":3}},"canonical_sha256":"1d84c572cf21301232de70859e26a3f5dcd1b41e7598bcca0e7ad4292bb3738d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d84c572cf21301232de70859e26a3f5dcd1b41e7598bcca0e7ad4292bb3738d","first_computed_at":"2026-05-18T02:29:53.730383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:53.730383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xFycDuRKsawn6qn03EWWGkKGk94FUFf8HG3vOOvL8q4bdu3AWVGOUMMEW8R8WxM0ahEHn11ghRe09xAceYltCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:53.731040Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0493","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e3dc837a48992f9c6774ba079d9a4170c96ee58194ba49790ef247fdada4f8d","sha256:84f0d6eea79194af89da2d436a6aa869a1e4281f68d30c88860d52ebeb103f3d"],"state_sha256":"b8c93a2b4dadc205c1fecd528afe459a93fc6e84cde357e50432ffcd0bc9b59a"}