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For $\\lambda \\ge 3$, we determine completely when a finite slope surgery along $M_{\\lambda}$ yields a lens space including $S^3$ and $S^1\\times S^2$, where {\\it finite slope surgery} implies that a surgery coefficient of every component is not $\\infty$. For $\\lambda =3$ (i.e.\\ the Borromean rings), there are three infinite sequences of finite slope surgeries yielding lens spaces. For $\\lambda \\ge 4$, any finite slope surgery does not yield a lens space. As a corollary, $M_{\\lambda}$ for $\\lambda \\ge 3$ does not yield both $S^3$ and $S^1"},"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":"1504.01321","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-04-06T17:09:55Z","cross_cats_sorted":[],"title_canon_sha256":"87058a1ad99f54713021f72fe77e6627dfdadc373f236f66d748d6826437db81","abstract_canon_sha256":"bdcc31bd5b00b1e8b2b9cb2c73d28aa7dd53dff487d4438c85512f2b296c376d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:40.235689Z","signature_b64":"4VUGQOTCpGL8GGNHQZgvQSvaM7g3CULe+cxflxQ+TaK3t9xYH8gAJMU5LR3QZ+ERDuRDcbaa71w+LgrQ8kjSBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fb12d0c3d6f5bdf0feabbc85cfa3109771194da628ddf8309d370179be743ef","last_reissued_at":"2026-05-18T02:18:40.235172Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:40.235172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite slope cyclic surgeries along toroidal Brunnian links and generalized Properties P and R","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Teruhisa Kadokami","submitted_at":"2015-04-06T17:09:55Z","abstract_excerpt":"Let $M_{\\lambda}$ be the $\\lambda$-component Milnor link. For $\\lambda \\ge 3$, we determine completely when a finite slope surgery along $M_{\\lambda}$ yields a lens space including $S^3$ and $S^1\\times S^2$, where {\\it finite slope surgery} implies that a surgery coefficient of every component is not $\\infty$. For $\\lambda =3$ (i.e.\\ the Borromean rings), there are three infinite sequences of finite slope surgeries yielding lens spaces. For $\\lambda \\ge 4$, any finite slope surgery does not yield a lens space. 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