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We prove the following three main theorems: in two different scenarios (when the height of the coin is small, or when the coin is near-circular) there is a family of KAM curves close to, but not accumulating on, the bound"},"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":"2411.13214","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DS","submitted_at":"2024-11-20T11:20:27Z","cross_cats_sorted":[],"title_canon_sha256":"1877a31a9825235fb644fa4d91b1681ba977d8f5e39f55c30076badd71b26b4d","abstract_canon_sha256":"e3f6db2cd220c40cb1adf406fccd26868ae402a27d1109738e9313662fa32e57"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:41:50.383185Z","signature_b64":"94B2t082V/bN34nFebkVbVGn8n21G+xVjn11n9dfaznLOyfczgIZLY+OH8sAeEK/oGtobpRPk8gMAsmC3CTWCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb31c2bbf7a8faa1829fa9eaa429a353b043a422ecfdf332893723309f586e3a","last_reissued_at":"2026-07-05T10:41:50.382709Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:41:50.382709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence and Nonexistence of Invariant Curves of Coin Billiards","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Andrew Clarke, Santiago Barbieri","submitted_at":"2024-11-20T11:20:27Z","abstract_excerpt":"In this paper we consider the coin billiard introduced by M. 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