{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:AF26A2QVAS2BE3XCKE4VHRFDQE","short_pith_number":"pith:AF26A2QV","schema_version":"1.0","canonical_sha256":"0175e06a1504b4126ee2513953c4a38107381cd6cd1cc8337b6948639730862a","source":{"kind":"arxiv","id":"1402.2134","version":1},"attestation_state":"computed","paper":{"title":"Complete Bredon cohomology and its applications to hierarchically defined groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GR","authors_text":"Brita E.A. Nucinkis, Nansen Petrosyan","submitted_at":"2014-02-10T13:15:02Z","abstract_excerpt":"By considering the Bredon analogue of complete cohomology of a group, we show that every group in the class $\\LHFF$ of type Bredon-$\\FP_\\infty$ admits a finite dimensional model for $\\EFG$.\n  We also show that abelian-by-infinite cyclic groups admit a $3$-dimensional model for the classifying space for the family of virtually nilpotent subgroups. This allows us to prove that for $\\mF,$ the class of virtually cyclic groups, the class of $\\LHFF$-groups contains all locally virtually soluble groups and all linear groups over $\\mathbb C$ of integral characteristic."},"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":"1402.2134","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-02-10T13:15:02Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"b80ea23ce475f221aa6d14cba97ef4b30dce89efeea8228cab07bbffbea99be5","abstract_canon_sha256":"ed3bcaa505c491b1df75c911483132ca60705987b1ffd452ce8452a1536c8ef7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:17.047365Z","signature_b64":"D2y1nWQMdeQ47+xYwQhquh2vz2LLgGIEIV0cRdt7WucVFVA3WYB7dZ1j9qZNTrL/2C+zC/3WVp0ZtWSCWPciDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0175e06a1504b4126ee2513953c4a38107381cd6cd1cc8337b6948639730862a","last_reissued_at":"2026-05-18T01:13:17.046939Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:17.046939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complete Bredon cohomology and its applications to hierarchically defined groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GR","authors_text":"Brita E.A. Nucinkis, Nansen Petrosyan","submitted_at":"2014-02-10T13:15:02Z","abstract_excerpt":"By considering the Bredon analogue of complete cohomology of a group, we show that every group in the class $\\LHFF$ of type Bredon-$\\FP_\\infty$ admits a finite dimensional model for $\\EFG$.\n  We also show that abelian-by-infinite cyclic groups admit a $3$-dimensional model for the classifying space for the family of virtually nilpotent subgroups. This allows us to prove that for $\\mF,$ the class of virtually cyclic groups, the class of $\\LHFF$-groups contains all locally virtually soluble groups and all linear groups over $\\mathbb C$ of integral characteristic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2134","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":"1402.2134","created_at":"2026-05-18T01:13:17.046998+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.2134v1","created_at":"2026-05-18T01:13:17.046998+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2134","created_at":"2026-05-18T01:13:17.046998+00:00"},{"alias_kind":"pith_short_12","alias_value":"AF26A2QVAS2B","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"AF26A2QVAS2BE3XC","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"AF26A2QV","created_at":"2026-05-18T12:28:19.803747+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/AF26A2QVAS2BE3XCKE4VHRFDQE","json":"https://pith.science/pith/AF26A2QVAS2BE3XCKE4VHRFDQE.json","graph_json":"https://pith.science/api/pith-number/AF26A2QVAS2BE3XCKE4VHRFDQE/graph.json","events_json":"https://pith.science/api/pith-number/AF26A2QVAS2BE3XCKE4VHRFDQE/events.json","paper":"https://pith.science/paper/AF26A2QV"},"agent_actions":{"view_html":"https://pith.science/pith/AF26A2QVAS2BE3XCKE4VHRFDQE","download_json":"https://pith.science/pith/AF26A2QVAS2BE3XCKE4VHRFDQE.json","view_paper":"https://pith.science/paper/AF26A2QV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.2134&json=true","fetch_graph":"https://pith.science/api/pith-number/AF26A2QVAS2BE3XCKE4VHRFDQE/graph.json","fetch_events":"https://pith.science/api/pith-number/AF26A2QVAS2BE3XCKE4VHRFDQE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AF26A2QVAS2BE3XCKE4VHRFDQE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AF26A2QVAS2BE3XCKE4VHRFDQE/action/storage_attestation","attest_author":"https://pith.science/pith/AF26A2QVAS2BE3XCKE4VHRFDQE/action/author_attestation","sign_citation":"https://pith.science/pith/AF26A2QVAS2BE3XCKE4VHRFDQE/action/citation_signature","submit_replication":"https://pith.science/pith/AF26A2QVAS2BE3XCKE4VHRFDQE/action/replication_record"}},"created_at":"2026-05-18T01:13:17.046998+00:00","updated_at":"2026-05-18T01:13:17.046998+00:00"}