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We establish the conjecture in case of $|\\omega| \\neq 1$, prove that $\\{K_n\\}$ contains at most three L-space knots if $\\omega = 0$, and address the case where $|\\omega| = 1$ under an additional hypothesis about Seifert surgeries. To that end, we characterize a twisting circle $c$ for which $\\{ (K_n, r_n) \\}$ co"},"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":"1506.04455","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-06-15T01:59:25Z","cross_cats_sorted":[],"title_canon_sha256":"93fed82a6505473892344741192c38f6a404ee7d1c87ba7a57d7ce66fb8102c2","abstract_canon_sha256":"9f2496a0296aef0d18662c95d2cca645d7045663283852f3726ee8200270229c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:26.282847Z","signature_b64":"LDVA7iYhIQA8aD3DtqgYOVywNJzZEWb2Ox7rYe9PvTvX83ZyqoJbspevAHUSg6Y3I89uF7t0whwXsZ4j5sBKCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2eeb6d4750f2c0ee8ed08e3b6e80b3e77b2de258deb227887dae3b0c2e725061","last_reissued_at":"2026-05-18T00:45:26.282376Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:26.282376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Twist families of L-space knots, their genera, and Seifert surgeries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kenneth L. 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