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We generalize the notion of tst links to \"surgerized tst links\": recall that when performing $\\Phi^\\mu(n(\\tau), d(\\tau), M)$ on a tst $\\langle \\tau \\rangle$ where $M$ is odd, we obtain the tst link, $[\\Phi^\\mu(n(\\tau), d(\\tau), M)]$ that contains a trivial knot as one of its components. We then perform another operation $\\Phi^{\\mu'}(n(\\tau '), d(\\tau '), M')$ on that trivial knot to create a new link, which we call a \"surgerized tst link\" (stst li"},"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":"1902.05756","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-02-15T10:33:37Z","cross_cats_sorted":["math-ph","math.GN","math.MP"],"title_canon_sha256":"8ccc3193832e4bff1ea317b02975d5a1db8c0340fe14a9aa7ab940f0b53a7f6a","abstract_canon_sha256":"aef0588363d3992b12081af2e77fa5b82d1b8dbad9f96ea3db9177fc041834f2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:40.961659Z","signature_b64":"nJwH702cNdZnCpvf37QS78tDkWMA+O4FjuTWSY+/7tKUx44nYXUyGOmamyJCWPbixdZANfuq0WBHn36nBZ9/Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"336d3cef78d34f8d769ce22c468368d8f06462924c07e0dc359062b87586ac2b","last_reissued_at":"2026-05-17T23:53:40.961262Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:40.961262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Alexander and Jones polynomials of surgerized tst links","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.GN","math.MP"],"primary_cat":"math.GT","authors_text":"Franky Mok, Wilson Wong","submitted_at":"2019-02-15T10:33:37Z","abstract_excerpt":"This paper is a continuation on the 2012 paper on \"Cutting Twisted Solid Tori (TSTs)\", in which we considered twisted solid torus links (tst links). 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