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We prove that if the framed instanton homology $I^{\\sharp}(S^3_r(K);\\mathbb{Z})$ is $2$-torsion-free for some $r\\in \\mathbb{Q}_+$, then $K$ is an instanton L-space knot and $r>2g(K)-1$. Leveraging this $2$-torsion perspective, we also obtain new small-surgery obstructions: If either $S^{3}_{5}(K)$ or $S^{3}_{11/2}(K)$ is $SU(2)$-abelian, "},"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":"2508.03394","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-08-05T12:43:05Z","cross_cats_sorted":[],"title_canon_sha256":"e2d76eb56bd5c7cf1d399f48d9cedbbb9c43cc2182b7eea62efa7ff26e83314d","abstract_canon_sha256":"6aeadbc5d79f7b2b8f76376c811465c3850736b7e7345565f03b8096b3a1ed3c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:48:55.635040Z","signature_b64":"YF9G2ll8kOLpMasrLQzjluXLs+gIDiKpftTCKT8hKpxIMt1Oxrfc8ruMeRwOuIoGk2oO9dNRNpZ0rDkzRl2vBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c11ac324a41b00914eae4bdb4afc3e4b7f364e30b24668eeba223b25f404544","last_reissued_at":"2026-07-05T11:48:55.634599Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:48:55.634599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Instanton 2-torsion and Dehn surgeries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Fan Ye, Zhenkun Li","submitted_at":"2025-08-05T12:43:05Z","abstract_excerpt":"In our earlier work on $2$-torsion in instanton Floer homology, we considered only integral surgeries on a knot $K\\subset S^3$ and showed that the absence of $2$-torsion forces $K$ to be fibered. The present paper extends the result to all rational surgeries. We prove that if the framed instanton homology $I^{\\sharp}(S^3_r(K);\\mathbb{Z})$ is $2$-torsion-free for some $r\\in \\mathbb{Q}_+$, then $K$ is an instanton L-space knot and $r>2g(K)-1$. 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