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A conjecture of Boyer, Gordon and Watson says that non-reducing surgeries on K can be classified into left-orderable surgeries or L-space surgeries. We introduce a way to provide knots with left-orderable, non-L-space surgeries. As an application we present infinitely many hyperbolic knots on each of which every nontrivial surgery is a hyperbolic, left-orderable, non"},"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":"1301.5729","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-01-24T08:48:49Z","cross_cats_sorted":[],"title_canon_sha256":"231dc039afc79334a8f73a7bc527acd4be534fc08642a627ce4aeb56ade27c02","abstract_canon_sha256":"b829473c04c025db80cd53087ca7bd7fe90c3ff6737bd50a029ff3365f708d25"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:33.896158Z","signature_b64":"VGq6T5oUDn5zlPKrWevIsv8aXXqakmMe3Pm4nPQADFsOVj/aDeSafT2sN2mDhJRA6kRpHlQ+njXUzRffid08AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b01270869c238642adba6f9e85816eb5052e8ef0f148f3722ccb17fb33be3973","last_reissued_at":"2026-05-18T03:09:33.895406Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:33.895406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Left-orderable, non-L-space surgeries on knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kimihiko Motegi, Masakazu Teragaito","submitted_at":"2013-01-24T08:48:49Z","abstract_excerpt":"Let K be a knot in the 3--sphere. 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