{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:LAHQA3VVD6X735WVZNVNK7AJTR","short_pith_number":"pith:LAHQA3VV","schema_version":"1.0","canonical_sha256":"580f006eb51faffdf6d5cb6ad57c099c70c5ff81b312509ee065bb2a9b3dc1b9","source":{"kind":"arxiv","id":"1210.4965","version":1},"attestation_state":"computed","paper":{"title":"A characterisation of uniform pro-p groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Benjamin Klopsch, Ilir Snopce","submitted_at":"2012-10-17T21:48:13Z","abstract_excerpt":"Let p be a prime. Uniform pro-p groups play a central role in the theory of p-adic Lie groups. Indeed, a topological group admits the structure of a p-adic Lie group if and only if it contains an open pro-p subgroup which is uniform. Furthermore, uniform pro-p groups naturally correspond to powerful Lie lattices over the p-adic integers and thus constitute a cornerstone of p-adic Lie theory.\n  In the present paper we propose and supply evidence for the following conjecture, aimed at characterising uniform pro-p groups. Suppose that p > 2 and let G be a torsion-free pro-p group of finite rank. "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1210.4965","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-10-17T21:48:13Z","cross_cats_sorted":[],"title_canon_sha256":"a381e7e229bb8a3007a365dd8b10477f322257b3e011ac2ba282b4ca5e30baac","abstract_canon_sha256":"7fa712bdb8b3efc3b86ceeeee9b6f993f358d6b91aa59d7c4361e55198b7b0dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:54.729709Z","signature_b64":"CNmuPCZFb/hRNo5HLrJ5eFhR3eW0A97hM0pQEqCd9DkZijsSf72okvIbpXSRiB01n+8GZKRSyjIut0e8yDn+CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"580f006eb51faffdf6d5cb6ad57c099c70c5ff81b312509ee065bb2a9b3dc1b9","last_reissued_at":"2026-05-18T03:42:54.729058Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:54.729058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A characterisation of uniform pro-p groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Benjamin Klopsch, Ilir Snopce","submitted_at":"2012-10-17T21:48:13Z","abstract_excerpt":"Let p be a prime. Uniform pro-p groups play a central role in the theory of p-adic Lie groups. Indeed, a topological group admits the structure of a p-adic Lie group if and only if it contains an open pro-p subgroup which is uniform. Furthermore, uniform pro-p groups naturally correspond to powerful Lie lattices over the p-adic integers and thus constitute a cornerstone of p-adic Lie theory.\n  In the present paper we propose and supply evidence for the following conjecture, aimed at characterising uniform pro-p groups. Suppose that p > 2 and let G be a torsion-free pro-p group of finite rank. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4965","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1210.4965","created_at":"2026-05-18T03:42:54.729172+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.4965v1","created_at":"2026-05-18T03:42:54.729172+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4965","created_at":"2026-05-18T03:42:54.729172+00:00"},{"alias_kind":"pith_short_12","alias_value":"LAHQA3VVD6X7","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"LAHQA3VVD6X735WV","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"LAHQA3VV","created_at":"2026-05-18T12:27:14.488303+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LAHQA3VVD6X735WVZNVNK7AJTR","json":"https://pith.science/pith/LAHQA3VVD6X735WVZNVNK7AJTR.json","graph_json":"https://pith.science/api/pith-number/LAHQA3VVD6X735WVZNVNK7AJTR/graph.json","events_json":"https://pith.science/api/pith-number/LAHQA3VVD6X735WVZNVNK7AJTR/events.json","paper":"https://pith.science/paper/LAHQA3VV"},"agent_actions":{"view_html":"https://pith.science/pith/LAHQA3VVD6X735WVZNVNK7AJTR","download_json":"https://pith.science/pith/LAHQA3VVD6X735WVZNVNK7AJTR.json","view_paper":"https://pith.science/paper/LAHQA3VV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.4965&json=true","fetch_graph":"https://pith.science/api/pith-number/LAHQA3VVD6X735WVZNVNK7AJTR/graph.json","fetch_events":"https://pith.science/api/pith-number/LAHQA3VVD6X735WVZNVNK7AJTR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LAHQA3VVD6X735WVZNVNK7AJTR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LAHQA3VVD6X735WVZNVNK7AJTR/action/storage_attestation","attest_author":"https://pith.science/pith/LAHQA3VVD6X735WVZNVNK7AJTR/action/author_attestation","sign_citation":"https://pith.science/pith/LAHQA3VVD6X735WVZNVNK7AJTR/action/citation_signature","submit_replication":"https://pith.science/pith/LAHQA3VVD6X735WVZNVNK7AJTR/action/replication_record"}},"created_at":"2026-05-18T03:42:54.729172+00:00","updated_at":"2026-05-18T03:42:54.729172+00:00"}