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Putting this problem into the context of knot cobordism, we show, using Rasmussen's Invariant that the reconnection number of a positive knot is equal to twice the genus of its Seifert spanning surface. In particular an $(a,b)$ torus knot has $R = (a-1)(b-1).$ For an arbitrary unsplittable"},"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":"2206.03056","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-06-07T07:15:38Z","cross_cats_sorted":[],"title_canon_sha256":"42c861c9841915c0ed01aff3634f460bbdd677253904e6742be03a9dc2705679","abstract_canon_sha256":"cf5528f7b1e3c5a4d701a14e8df38aa72c6ff761fcf015f8b57c5d3e214eb320"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:38:52.835593Z","signature_b64":"2Jtn14HqIVNHnPDuwyVggRDw50urtNxdM0wRQbOa0QunvW66l7aURrUBK7ufYKNr6xEd7RvNnOj08l21x9kVAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97c2cfa587022c297142c7e757a9d9efb9f241976674d89e12f6b6b8669c9ddc","last_reissued_at":"2026-07-05T04:38:52.835166Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:38:52.835166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topology of Vortex Reconnection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Louis H. 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