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A folklore argument shows that at least one of these $2^n$ diagrams is unknot, from which it follows that every diagram has finite unknotting number. It is easy to see that this argument can be used to show that actually ${\\mathcal D}$ has more than one unknot diagram, but it cannot yield more than $4n$ unknot diagrams. We improve this linear bound to a superpolynomial bound, by showing that a"},"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":"1710.06470","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-17T18:56:21Z","cross_cats_sorted":[],"title_canon_sha256":"e97c9b87a771790041e85c4b948b76c3c94082ea747b99510e5817ed89230fe9","abstract_canon_sha256":"30cc98c20b604a4dfdefd3bd22ed286abb3f7ea54b8d4185f0b64de122835606"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:33.601175Z","signature_b64":"ZBFZJssEO60rfMCYafE+aahJFLBzNe3CCh6jL4OrS1o6xKhBDs6HflU9KI2k2YnqYZNxEgCXppz0H4b3Md9jDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53004b0c4190c682568b5256c089e89d5d8f9e229edadadc12f4830886eb9cc2","last_reissued_at":"2026-05-18T00:32:33.600544Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:33.600544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the number of unknot diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carolina Medina, Gelasio Salazar, Jorge Ram\\'irez-Alfons\\'in","submitted_at":"2017-10-17T18:56:21Z","abstract_excerpt":"Let $D$ be a knot diagram, and let ${\\mathcal D}$ denote the set of diagrams that can be obtained from $D$ by crossing exchanges. 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