{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JOMM3GPY3HIFNYH53EDOGJPGSW","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":"ed5c34b80c7b52de8a3a0670165deb152100f8216f084631f0767a8d05399be0","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-10-11T15:31:00Z","title_canon_sha256":"dc85baaf5d9b3eef884992ec4c8fea7187b8da67ba46c70ea8a1ebc8035196d6"},"schema_version":"1.0","source":{"id":"1410.3007","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3007","created_at":"2026-05-18T02:40:17Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3007v1","created_at":"2026-05-18T02:40:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3007","created_at":"2026-05-18T02:40:17Z"},{"alias_kind":"pith_short_12","alias_value":"JOMM3GPY3HIF","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JOMM3GPY3HIFNYH5","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JOMM3GPY","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:46b357d89b479301e254345b0d5d4329a0e3476a44bd0c87a97b4b8fea5b6e10","target":"graph","created_at":"2026-05-18T02:40:17Z","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 give new upper bounds for the diameters of finite groups which do not depend on a choice of generating set. Our method exploits the commutator structure of certain profinite groups, in a fashion analogous to the Solovay-Kitaev procedure from quantum computation. We obtain polylogarithmic upper bounds for the diameters of finite quotients of: groups with an analytic structure over a pro-$p$ domain (with exponent depending on the dimension); Chevalley groups over a pro-$p$ domain (with exponent independent of the dimension) and the Nottingham group of a finite field. We also discuss some cons","authors_text":"Henry Bradford","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-10-11T15:31:00Z","title":"New Uniform Diameter Bounds in Pro-$p$ Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3007","kind":"arxiv","version":1},"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":"sha256:2a35f4cead385f5ebbecea2ecde1f21e42409a8558d8bb75380b638872d815ba","target":"record","created_at":"2026-05-18T02:40:17Z","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":"ed5c34b80c7b52de8a3a0670165deb152100f8216f084631f0767a8d05399be0","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-10-11T15:31:00Z","title_canon_sha256":"dc85baaf5d9b3eef884992ec4c8fea7187b8da67ba46c70ea8a1ebc8035196d6"},"schema_version":"1.0","source":{"id":"1410.3007","kind":"arxiv","version":1}},"canonical_sha256":"4b98cd99f8d9d056e0fdd906e325e695b2aac68d08ff6f1c1f2f80246e487aa6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b98cd99f8d9d056e0fdd906e325e695b2aac68d08ff6f1c1f2f80246e487aa6","first_computed_at":"2026-05-18T02:40:17.263699Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:17.263699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5iG8C5H4VO8uhWboknE0N4ye6f3VfLKvcgBaoQX2xg2uaCH7AGh7c8uIcSAFaoZkxzBuI5P6/oLk9OB9pBGXDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:17.264156Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.3007","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a35f4cead385f5ebbecea2ecde1f21e42409a8558d8bb75380b638872d815ba","sha256:46b357d89b479301e254345b0d5d4329a0e3476a44bd0c87a97b4b8fea5b6e10"],"state_sha256":"dbf0f46d5b74809ad794c5c8f6e7e9c2ba042cd5d934c1ac8ef4d70631fb2e27"}