{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3MIEAAEPLV4YX2I7VPZXCYESQ2","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":"a557b341fbcd2e64e929c33cb21b6b05b761685da4dcf87c7f26f135addf9b97","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-05-19T22:11:55Z","title_canon_sha256":"53070fccbc18fca219adda6a2a1fd5f1d4e4537d289f96912ca44bfc56678e5f"},"schema_version":"1.0","source":{"id":"1805.07664","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07664","created_at":"2026-05-18T00:04:29Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07664v2","created_at":"2026-05-18T00:04:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07664","created_at":"2026-05-18T00:04:29Z"},{"alias_kind":"pith_short_12","alias_value":"3MIEAAEPLV4Y","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3MIEAAEPLV4YX2I7","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3MIEAAEP","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:5203812dc315795c75bc09025043eb6ad5fdf56a6e591237c849cb93ed8f1240","target":"graph","created_at":"2026-05-18T00:04:29Z","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 prove two approximations of the open problem of whether the adjoint group of a non-nilpotent nil ring can be finitely generated: We show that the adjoint group of a non-nilpotent Jacobson radical cannot be boundedly generated, and on the other hand construct a finitely generated, infinite dimensional nil algebra whose adjoint group is generated by elements of bounded torsion.","authors_text":"Be'eri Greenfeld","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-05-19T22:11:55Z","title":"Generating adjoint groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07664","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:c0233df2f8e23b2611b11c9d51b565ea506cb0ea1087e90b7c0cc6836a170ba7","target":"record","created_at":"2026-05-18T00:04:29Z","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":"a557b341fbcd2e64e929c33cb21b6b05b761685da4dcf87c7f26f135addf9b97","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-05-19T22:11:55Z","title_canon_sha256":"53070fccbc18fca219adda6a2a1fd5f1d4e4537d289f96912ca44bfc56678e5f"},"schema_version":"1.0","source":{"id":"1805.07664","kind":"arxiv","version":2}},"canonical_sha256":"db1040008f5d798be91fabf371609286ab34c02246df99e423f56fe738246b23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db1040008f5d798be91fabf371609286ab34c02246df99e423f56fe738246b23","first_computed_at":"2026-05-18T00:04:29.883339Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:29.883339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qFnU+Y/i+HIr9ioTzOxVStD5P9SRqTJT2bHhZHq/oZWAzFdjGjSYX3SM3A3PfGxd3He0OPYGvrFFPmgqq7bYCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:29.883776Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.07664","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0233df2f8e23b2611b11c9d51b565ea506cb0ea1087e90b7c0cc6836a170ba7","sha256:5203812dc315795c75bc09025043eb6ad5fdf56a6e591237c849cb93ed8f1240"],"state_sha256":"b91057e0d315b151018381599b187ce34b172f880994488f24bd778e224fb904"}