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We prove that a quasiconvex subgroup of a negatively curved group has finite weak width in the ambient group. We also give examples demonstrating that height, width, and weak width are different invariants of a subgroup."},"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":"1512.09185","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-31T00:00:46Z","cross_cats_sorted":[],"title_canon_sha256":"7ad23f46b9604e016007f3f90f3c5c4b77ca2a283af42990c182b503de22c42f","abstract_canon_sha256":"92c00f648ac2bfa028e80b9f09e1d09431b7da303daeff7d95a9ba24ce1e858e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:33.083231Z","signature_b64":"XvfDK4DlqcC+YyDe91Rd7ocHMvwTYiItL/HRY/xTzcG1DhXJ3lP2HqDXCqvbyIoi4boMX2HzU7i05TQetIZwCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98151b208c66a0c179b9b00a5dff82c53a40a0d49320988db68730052ecad46b","last_reissued_at":"2026-05-18T01:23:33.082743Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:33.082743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weak Width of Subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Rita Gitik","submitted_at":"2015-12-31T00:00:46Z","abstract_excerpt":"We say that the weak width of an infinite subgroup $H$ of $G$ in $G$ is $n$ if there exists a collection of $n$ strongly essentially distinct conjugates\n  $\\{ H, g_1^{-1} H g_1,\\cdots, g_{n-1}^{-1} H g_{n-1} \\}$ of $H$ in $G$ such that the intersection $H \\cap g_i^{-1} H g_i$ is infinite for all $1 \\leq i \\leq n-1$ and $n$ is maximal possible. We prove that a quasiconvex subgroup of a negatively curved group has finite weak width in the ambient group. 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