{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:4GBGNWALZVHHDHKASGLTVHKWRN","short_pith_number":"pith:4GBGNWAL","schema_version":"1.0","canonical_sha256":"e18266d80bcd4e719d4091973a9d568b6a9bf1cd8121c45e1c56808b710e9e90","source":{"kind":"arxiv","id":"1508.04865","version":6},"attestation_state":"computed","paper":{"title":"Subgroups of Relatively Hyperbolic Groups of Bredon Cohomological Dimension 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GT"],"primary_cat":"math.GR","authors_text":"Eduardo Martinez-Pedroza","submitted_at":"2015-08-20T03:26:43Z","abstract_excerpt":"A remarkable result of Gersten states that the class of hyperbolic groups of cohomological dimension $2$ is closed under taking finitely presented (or more generally $FP_2$) subgroups. We prove the analogous result for relatively hyperbolic groups of Bredon cohomological dimension $2$ with respect to the family of parabolic subgroups. A class of groups where our result applies consists of $C'(1/6)$ small cancellation products. The proof relies on an algebraic approach to relative homological Dehn functions, and a characterization of relative hyperbolicity in the framework of finiteness propert"},"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":"1508.04865","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-08-20T03:26:43Z","cross_cats_sorted":["math.AT","math.GT"],"title_canon_sha256":"db0433bc9a58b214806e680b259756c1078c270923fbfe3ba9d0d664fe50aeae","abstract_canon_sha256":"977f131b6816edbb1268b7eabd9e919ba067a562ef5f1f3c14ed512afd9e8fd2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:30.893032Z","signature_b64":"pDCiF32GprLRy8SK8ynyBjIbihr2EJ0Jzr/wR7AgdLM9FDVVAICCMOUCgewho3CUj6DMEFSxOJCp9aedGl7jCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e18266d80bcd4e719d4091973a9d568b6a9bf1cd8121c45e1c56808b710e9e90","last_reissued_at":"2026-05-18T00:43:30.892441Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:30.892441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Subgroups of Relatively Hyperbolic Groups of Bredon Cohomological Dimension 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GT"],"primary_cat":"math.GR","authors_text":"Eduardo Martinez-Pedroza","submitted_at":"2015-08-20T03:26:43Z","abstract_excerpt":"A remarkable result of Gersten states that the class of hyperbolic groups of cohomological dimension $2$ is closed under taking finitely presented (or more generally $FP_2$) subgroups. We prove the analogous result for relatively hyperbolic groups of Bredon cohomological dimension $2$ with respect to the family of parabolic subgroups. A class of groups where our result applies consists of $C'(1/6)$ small cancellation products. The proof relies on an algebraic approach to relative homological Dehn functions, and a characterization of relative hyperbolicity in the framework of finiteness propert"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04865","kind":"arxiv","version":6},"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":"1508.04865","created_at":"2026-05-18T00:43:30.892533+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.04865v6","created_at":"2026-05-18T00:43:30.892533+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04865","created_at":"2026-05-18T00:43:30.892533+00:00"},{"alias_kind":"pith_short_12","alias_value":"4GBGNWALZVHH","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"4GBGNWALZVHHDHKA","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"4GBGNWAL","created_at":"2026-05-18T12:29:05.191682+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/4GBGNWALZVHHDHKASGLTVHKWRN","json":"https://pith.science/pith/4GBGNWALZVHHDHKASGLTVHKWRN.json","graph_json":"https://pith.science/api/pith-number/4GBGNWALZVHHDHKASGLTVHKWRN/graph.json","events_json":"https://pith.science/api/pith-number/4GBGNWALZVHHDHKASGLTVHKWRN/events.json","paper":"https://pith.science/paper/4GBGNWAL"},"agent_actions":{"view_html":"https://pith.science/pith/4GBGNWALZVHHDHKASGLTVHKWRN","download_json":"https://pith.science/pith/4GBGNWALZVHHDHKASGLTVHKWRN.json","view_paper":"https://pith.science/paper/4GBGNWAL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.04865&json=true","fetch_graph":"https://pith.science/api/pith-number/4GBGNWALZVHHDHKASGLTVHKWRN/graph.json","fetch_events":"https://pith.science/api/pith-number/4GBGNWALZVHHDHKASGLTVHKWRN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4GBGNWALZVHHDHKASGLTVHKWRN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4GBGNWALZVHHDHKASGLTVHKWRN/action/storage_attestation","attest_author":"https://pith.science/pith/4GBGNWALZVHHDHKASGLTVHKWRN/action/author_attestation","sign_citation":"https://pith.science/pith/4GBGNWALZVHHDHKASGLTVHKWRN/action/citation_signature","submit_replication":"https://pith.science/pith/4GBGNWALZVHHDHKASGLTVHKWRN/action/replication_record"}},"created_at":"2026-05-18T00:43:30.892533+00:00","updated_at":"2026-05-18T00:43:30.892533+00:00"}