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We then analyze $M_U$ from three complementary viewpoints:\n  (1) finite quotients, where $U/M_U$ is shown to be the universal ``maximal meridionally unramified'' quotient of $U$;\n  (2) profinite completions, where we identify the closed ramification subgroup $\\widehat M_{\\widehat U}$ as the closed normal su"},"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":"2605.20365","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2026-05-19T18:18:11Z","cross_cats_sorted":["math.AT","math.GR"],"title_canon_sha256":"ebf044ffe11036fa9aada0a3b98301a9f24e5036ea694093a7ae099da2bda513","abstract_canon_sha256":"316806771674d2a96a0405c61256a9b35f8584646c5158882f124dddf2331987"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:04:35.165614Z","signature_b64":"dqEP03w15iSHTy8xJ0NUDl6dNvzsan8fPLzOOLaNrMFzt4Xbv1+ndDFtSMl19VHKgnLoqiyE+KZSpzyPwXqrDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e06699a209314823a25dbbbafcb51c60ce6bb6fc05c922b4eabbf7ec09a6d50","last_reissued_at":"2026-05-21T01:04:35.164812Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:04:35.164812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ramification Subgroups of Knot Groups and their Profinite and Cohomological Structure","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT","math.GR"],"primary_cat":"math.GT","authors_text":"Federico W. 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