{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7EEICLLR5XXY4SS3AZLGVTJWJ6","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":"2007c0c778598c2f3e9916fec14f1d292c0476bc1534ae73c3f182dd84a2f82c","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-06-14T13:49:48Z","title_canon_sha256":"24826ad3948bff1487f2352a44d3cad574441ea7dc5117422c0953e46c7f3188"},"schema_version":"1.0","source":{"id":"1406.3731","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3731","created_at":"2026-05-18T02:30:31Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3731v3","created_at":"2026-05-18T02:30:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3731","created_at":"2026-05-18T02:30:31Z"},{"alias_kind":"pith_short_12","alias_value":"7EEICLLR5XXY","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7EEICLLR5XXY4SS3","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7EEICLLR","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:8f2e97c379d7d2acbe684a9dfacbff7eafddec1291c7a5f3d48f4a94ad4f30e9","target":"graph","created_at":"2026-05-18T02:30:31Z","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 define a class $\\mathcal{U}$ of solvable groups of finite abelian section rank which includes all such groups that are virtually torsion-free as well as those that are finitely generated. Assume that $G$ is a group in $\\mathcal{U}$ and $A$ a $\\mathbb ZG$-module. If $A$ is $\\mathbb Z$-torsion-free and has finite $\\mathbb Z$-rank, we stipulate a condition on $A$ that guarantees that $H^n(G,A)$ and $H_n(G,A)$ must be finite for $n\\geq 0$. Moreover, if the underlying abelian group of $A$ is a \\v{C}ernikov group, we identify a similar condition on $A$ that ensures that $H^n(G,A)$ must be a \\v{C}","authors_text":"Karl Lorensen","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-06-14T13:49:48Z","title":"Torsion cohomology for solvable groups of finite rank"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3731","kind":"arxiv","version":3},"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":"sha256:0217e4e9f96d6c50e64a1d13fa48021bd405e5df19a02f0164184ee281ee7a07","target":"record","created_at":"2026-05-18T02:30:31Z","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":"2007c0c778598c2f3e9916fec14f1d292c0476bc1534ae73c3f182dd84a2f82c","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-06-14T13:49:48Z","title_canon_sha256":"24826ad3948bff1487f2352a44d3cad574441ea7dc5117422c0953e46c7f3188"},"schema_version":"1.0","source":{"id":"1406.3731","kind":"arxiv","version":3}},"canonical_sha256":"f908812d71edef8e4a5b06566acd364f8e7b23587a237cc6cff09725bfb9497d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f908812d71edef8e4a5b06566acd364f8e7b23587a237cc6cff09725bfb9497d","first_computed_at":"2026-05-18T02:30:31.937130Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:31.937130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v2rvOoavaXgnR5qp7061N2Zl/nJMS/2vC+vsqlOBh5RrQJnX9Ha/RGCAcPbHzUu9CdMWOCQCDfIX04eKURUcBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:31.937703Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.3731","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0217e4e9f96d6c50e64a1d13fa48021bd405e5df19a02f0164184ee281ee7a07","sha256:8f2e97c379d7d2acbe684a9dfacbff7eafddec1291c7a5f3d48f4a94ad4f30e9"],"state_sha256":"e6a6d796ed1ee193990ab04e025b8430988fd48dc7369c12651ea7449d87e2cb"}