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Furthermore, the monodromy of a fibered component of any such counterexample has unexpected restrictions.\n  The simplest plausible counterexample to the Generalized Property R Conjecture could be a 2-component link containing the square knot. We characterize all two-component links that contain the square knot and which surger to (S^1 x S^2) # (S^1 x S^2). We exhibit a family of such links that are probably counterexamples to Gener"},"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":"1103.1601","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-03-08T18:54:05Z","cross_cats_sorted":[],"title_canon_sha256":"58cd0601efb9de5917ce524d9f32a4d1c5591a60380b7825167d8be19a3a888c","abstract_canon_sha256":"276a9ffd0e0ba8ed3bccb5698ad5287e8af39fc287dc3ac1773239408d1df6f5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:15.526510Z","signature_b64":"3XpjChC073IW+gNiko6Sk0Hq0wzAJgLj15hZ52uT7glWZeTBshvXEW6pQMInRpbMuOlAUrscT32RhHue7AhPDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a34f82632ee00005713c075c5043981db6b39104e273d213429d008cc5ad2aa6","last_reissued_at":"2026-05-18T04:27:15.526028Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:15.526028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fibered knots and potential counterexamples to the Property 2R and Slice-Ribbon Conjectures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Abigail Thompson, Martin Scharlemann, Robert E. 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