{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:VDF6SQW7IYBLKWKMHS7IOAIYPV","short_pith_number":"pith:VDF6SQW7","canonical_record":{"source":{"id":"1412.1876","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-05T01:46:55Z","cross_cats_sorted":[],"title_canon_sha256":"44390808f470f49b8eabc098e70267c4af741559d7eea59b2980c825cf157589","abstract_canon_sha256":"e7447b57998f40ec26b507a2314b4d1bed6de3920d14224c58ec480d08164bb8"},"schema_version":"1.0"},"canonical_sha256":"a8cbe942df4602b5594c3cbe8701187d44e3816ed5b86d8185ba96ea85e859f3","source":{"kind":"arxiv","id":"1412.1876","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:VDF6SQW7IYBLKWKMHS7IOAIYPV","target":"record","payload":{"canonical_record":{"source":{"id":"1412.1876","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-05T01:46:55Z","cross_cats_sorted":[],"title_canon_sha256":"44390808f470f49b8eabc098e70267c4af741559d7eea59b2980c825cf157589","abstract_canon_sha256":"e7447b57998f40ec26b507a2314b4d1bed6de3920d14224c58ec480d08164bb8"},"schema_version":"1.0"},"canonical_sha256":"a8cbe942df4602b5594c3cbe8701187d44e3816ed5b86d8185ba96ea85e859f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:05.859115Z","signature_b64":"dWsgwjXZW4GdjExmCg1XYryIWya6IrTmdtuPvTmEoxNSLHacbXGIkM1ieyUiPt4eDACRCW4AiQSkNVmn31EsAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8cbe942df4602b5594c3cbe8701187d44e3816ed5b86d8185ba96ea85e859f3","last_reissued_at":"2026-05-18T02:32:05.858766Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:05.858766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.1876","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:32:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cBbgzUKMqF9H0EKbNWjbdWtBDmzCJDYo/s+ulyG2ZR34GIZ0lxifG15BxjYchEW3vkeyebXtD1gbhbeSohJ2DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:52:59.646470Z"},"content_sha256":"cd43170deab6609ac4cdcc30c6389ba0fb61b1842f93f8a907116ed9a7c4bd6f","schema_version":"1.0","event_id":"sha256:cd43170deab6609ac4cdcc30c6389ba0fb61b1842f93f8a907116ed9a7c4bd6f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:VDF6SQW7IYBLKWKMHS7IOAIYPV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Profinite Groups of Type $\\operatorname{FP}_\\infty$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ged Corob Cook","submitted_at":"2014-12-05T01:46:55Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1876","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:32:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EFfg7Pj8TlGK4SY16exqE7flDCkbvtMEw9RJ6mVjqFCtec49/j9d2xMWO+W7V3yIgEtWFQSofg57x71eXQJWBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:52:59.647098Z"},"content_sha256":"18bcfc90ab9cb0682c04962ea373a6e4c8634e7788115f9eabcf4efff6baff32","schema_version":"1.0","event_id":"sha256:18bcfc90ab9cb0682c04962ea373a6e4c8634e7788115f9eabcf4efff6baff32"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VDF6SQW7IYBLKWKMHS7IOAIYPV/bundle.json","state_url":"https://pith.science/pith/VDF6SQW7IYBLKWKMHS7IOAIYPV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VDF6SQW7IYBLKWKMHS7IOAIYPV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T03:52:59Z","links":{"resolver":"https://pith.science/pith/VDF6SQW7IYBLKWKMHS7IOAIYPV","bundle":"https://pith.science/pith/VDF6SQW7IYBLKWKMHS7IOAIYPV/bundle.json","state":"https://pith.science/pith/VDF6SQW7IYBLKWKMHS7IOAIYPV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VDF6SQW7IYBLKWKMHS7IOAIYPV/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CSvplBUOAf5xJpB/sYDKfgjTvYwgrhGaqxnbnJ/QUgp7RfHjOH7RuQBCC1rc3UnFFR63gDrzPnUTvmsev9AJDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T03:52:59.650144Z","bundle_sha256":"09199f1d3566b532ef593378c247f9e50d0e7d472ade31ac68f9ad6ee10babb1"}}