{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VDF6SQW7IYBLKWKMHS7IOAIYPV","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":"e7447b57998f40ec26b507a2314b4d1bed6de3920d14224c58ec480d08164bb8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-05T01:46:55Z","title_canon_sha256":"44390808f470f49b8eabc098e70267c4af741559d7eea59b2980c825cf157589"},"schema_version":"1.0","source":{"id":"1412.1876","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1876","created_at":"2026-05-18T02:32:05Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1876v1","created_at":"2026-05-18T02:32:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1876","created_at":"2026-05-18T02:32:05Z"},{"alias_kind":"pith_short_12","alias_value":"VDF6SQW7IYBL","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"VDF6SQW7IYBLKWKM","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"VDF6SQW7","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:18bcfc90ab9cb0682c04962ea373a6e4c8634e7788115f9eabcf4efff6baff32","target":"graph","created_at":"2026-05-18T02:32:05Z","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":"Suppose $R$ is a profinite ring. We construct a large class of profinite groups $\\widehat{{\\scriptstyle\\bf L}'{\\scriptstyle\\bf H}_R}\\mathfrak{F}$, including all soluble profinite groups and profinite groups of finite cohomological dimension over $R$. We show that, if $G \\in \\widehat{{\\scriptstyle\\bf L}'{\\scriptstyle\\bf H}_R}\\mathfrak{F}$ is of type $\\operatorname{FP}_\\infty$ over $R$, then there is some $n$ such that $H_R^n(G,R [[ G ]]) \\neq 0$, and deduce that torsion-free soluble pro-$p$ groups of type $\\operatorname{FP}_\\infty$ over $\\mathbb{Z}_p$ have finite rank, thus answering the torsio","authors_text":"Ged Corob Cook","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-05T01:46:55Z","title":"On Profinite Groups of Type $\\operatorname{FP}_\\infty$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1876","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:cd43170deab6609ac4cdcc30c6389ba0fb61b1842f93f8a907116ed9a7c4bd6f","target":"record","created_at":"2026-05-18T02:32:05Z","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":"e7447b57998f40ec26b507a2314b4d1bed6de3920d14224c58ec480d08164bb8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-05T01:46:55Z","title_canon_sha256":"44390808f470f49b8eabc098e70267c4af741559d7eea59b2980c825cf157589"},"schema_version":"1.0","source":{"id":"1412.1876","kind":"arxiv","version":1}},"canonical_sha256":"a8cbe942df4602b5594c3cbe8701187d44e3816ed5b86d8185ba96ea85e859f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8cbe942df4602b5594c3cbe8701187d44e3816ed5b86d8185ba96ea85e859f3","first_computed_at":"2026-05-18T02:32:05.858766Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:05.858766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dWsgwjXZW4GdjExmCg1XYryIWya6IrTmdtuPvTmEoxNSLHacbXGIkM1ieyUiPt4eDACRCW4AiQSkNVmn31EsAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:05.859115Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.1876","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd43170deab6609ac4cdcc30c6389ba0fb61b1842f93f8a907116ed9a7c4bd6f","sha256:18bcfc90ab9cb0682c04962ea373a6e4c8634e7788115f9eabcf4efff6baff32"],"state_sha256":"3596945ac15938f83ebc9a5bdc5ccf71691fdf59849a31818dbe85c190944ac4"}