{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:V7AMM5Z6NTOT7G6UKTFUZF6D3P","short_pith_number":"pith:V7AMM5Z6","schema_version":"1.0","canonical_sha256":"afc0c6773e6cdd3f9bd454cb4c97c3dbe8a27f2bef128dbd5cf47a22ddcb834f","source":{"kind":"arxiv","id":"1105.0253","version":1},"attestation_state":"computed","paper":{"title":"Normalizers of Parabolic Subgroups of Coxeter Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Daniel Allcock","submitted_at":"2011-05-02T07:27:53Z","abstract_excerpt":"We improve a bound of Borcherds on the virtual cohomological dimension of the non-reflection part of the normalizer of a parabolic subgroup of a Coxeter group. Our bound is in terms of the types of the components of the corresponding Coxeter subdiagram rather than the number of nodes. A consequence is an extension of Brink's result that the non-reflection part of a reflection centralizer is free. Namely, the non-reflection part of the normalizer of parabolic subgroup of type D5 or Aodd is either free or has a free subgroup of index 2."},"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":"1105.0253","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-02T07:27:53Z","cross_cats_sorted":[],"title_canon_sha256":"da340a9db2558f152b4073ab016b802ed1104e2068fe4c5e843e21f9dbf51c55","abstract_canon_sha256":"383767b3ab3f621df53725d1706c909876fffe5734dc2c3a2b54e43794c3bb52"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:50.511682Z","signature_b64":"nqMu2u3oescXYyo4/Rng08nnF9ZK8woEhZcoc2wewNhS5xR4unyorW/nwfzoH0g9/SRgJUK1idiP27vnoNKHCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afc0c6773e6cdd3f9bd454cb4c97c3dbe8a27f2bef128dbd5cf47a22ddcb834f","last_reissued_at":"2026-05-18T02:41:50.511108Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:50.511108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Normalizers of Parabolic Subgroups of Coxeter Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Daniel Allcock","submitted_at":"2011-05-02T07:27:53Z","abstract_excerpt":"We improve a bound of Borcherds on the virtual cohomological dimension of the non-reflection part of the normalizer of a parabolic subgroup of a Coxeter group. Our bound is in terms of the types of the components of the corresponding Coxeter subdiagram rather than the number of nodes. A consequence is an extension of Brink's result that the non-reflection part of a reflection centralizer is free. Namely, the non-reflection part of the normalizer of parabolic subgroup of type D5 or Aodd is either free or has a free subgroup of index 2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0253","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":"1105.0253","created_at":"2026-05-18T02:41:50.511191+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.0253v1","created_at":"2026-05-18T02:41:50.511191+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.0253","created_at":"2026-05-18T02:41:50.511191+00:00"},{"alias_kind":"pith_short_12","alias_value":"V7AMM5Z6NTOT","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"V7AMM5Z6NTOT7G6U","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"V7AMM5Z6","created_at":"2026-05-18T12:26:42.757692+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/V7AMM5Z6NTOT7G6UKTFUZF6D3P","json":"https://pith.science/pith/V7AMM5Z6NTOT7G6UKTFUZF6D3P.json","graph_json":"https://pith.science/api/pith-number/V7AMM5Z6NTOT7G6UKTFUZF6D3P/graph.json","events_json":"https://pith.science/api/pith-number/V7AMM5Z6NTOT7G6UKTFUZF6D3P/events.json","paper":"https://pith.science/paper/V7AMM5Z6"},"agent_actions":{"view_html":"https://pith.science/pith/V7AMM5Z6NTOT7G6UKTFUZF6D3P","download_json":"https://pith.science/pith/V7AMM5Z6NTOT7G6UKTFUZF6D3P.json","view_paper":"https://pith.science/paper/V7AMM5Z6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.0253&json=true","fetch_graph":"https://pith.science/api/pith-number/V7AMM5Z6NTOT7G6UKTFUZF6D3P/graph.json","fetch_events":"https://pith.science/api/pith-number/V7AMM5Z6NTOT7G6UKTFUZF6D3P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V7AMM5Z6NTOT7G6UKTFUZF6D3P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V7AMM5Z6NTOT7G6UKTFUZF6D3P/action/storage_attestation","attest_author":"https://pith.science/pith/V7AMM5Z6NTOT7G6UKTFUZF6D3P/action/author_attestation","sign_citation":"https://pith.science/pith/V7AMM5Z6NTOT7G6UKTFUZF6D3P/action/citation_signature","submit_replication":"https://pith.science/pith/V7AMM5Z6NTOT7G6UKTFUZF6D3P/action/replication_record"}},"created_at":"2026-05-18T02:41:50.511191+00:00","updated_at":"2026-05-18T02:41:50.511191+00:00"}