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We show that any slope $\\frac pq$ which is larger than the number $\\frac{30(r^2-1)(s^2-1)}{67}$ is a characterizing slope for $T_{r,s}$. The proof uses Heegaard Floer homology and Agol--Lackenby's 6--Theorem. In the case of $T_{5,2}$, we obtain more specific information"},"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":"1206.5577","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-06-25T05:36:43Z","cross_cats_sorted":[],"title_canon_sha256":"34d002e0474af9591fff0720bbe9fa2d818f07dbfea0ca54aa9961046438e236","abstract_canon_sha256":"ad9fb1a1ff6301b859ae96c72155e2d8aedbc14ad78491b4d4a0e66ed05684d8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:43.074254Z","signature_b64":"ASFwvHy+W91Of6LWuwQCjuFyvQ80Cu+IQIY9iSvWcjO/lzQaEgL81RDBR78BzCn9hxePuSG+UOdWQQ4cF1LiAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e240987e51331d1f33e77a693a20fd1ba6aa48d933c7898d3bd8e44f1e5cd45","last_reissued_at":"2026-05-18T02:41:43.073555Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:43.073555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterizing slopes for torus knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Xingru Zhang, Yi Ni","submitted_at":"2012-06-25T05:36:43Z","abstract_excerpt":"A slope $\\frac pq$ is called a characterizing slope for a given knot $K_0$ in $S^3$ if whenever the $\\frac pq$-surgery on a knot $K$ in $S^3$ is homeomorphic to the $\\frac pq$-surgery on $K_0$ via an orientation preserving homeomorphism, then $K=K_0$. In this paper we try to find characterizing slopes for torus knots $T_{r,s}$. We show that any slope $\\frac pq$ which is larger than the number $\\frac{30(r^2-1)(s^2-1)}{67}$ is a characterizing slope for $T_{r,s}$. The proof uses Heegaard Floer homology and Agol--Lackenby's 6--Theorem. 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