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Let \\[ S=\\{t \\in (0,1): a_{i+1}(t) \\geq \\phi^{d_{i}(t)} \\text{infinitely often}\\}, \\] where $\\phi = (\\sqrt{5}+1)/2$. Let $Y_{S} =\\{\\exp(2 \\pi i t): t \\in S \\}$. It is shown that if $y \\in Y_{S}$ then the Rogers-Ramanujan continued fraction, R(y), diverges at y. S is an uncountable set of measure zero. It is also shown that there is an uncountable set of points, $G \\subset Y_{S}$,"},"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":"math/0107043","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2001-07-06T04:14:18Z","cross_cats_sorted":[],"title_canon_sha256":"5eac64156ad9fefd22545acf668f0586f787a5711841a6b91666d4bcf6b8ac5e","abstract_canon_sha256":"3b8779576dace2955c73609576dd9b048ae00cdec00c406c5b30b605aab47f27"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:19.924747Z","signature_b64":"n0Fd+YRaRh++49U72MPhId/6NIGzUlD9bI7wCuGx9tMxqZjifA+eg7apHb6vsTGDeKQxm2eUR/bCSKJrRfECAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"392ba5f6b30b0f067ee4b8a500d90a466d46da76184669e29c8d9b4ebf21796c","last_reissued_at":"2026-05-17T23:57:19.924071Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:19.924071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Divergence of the Rogers-Ramanujan Continued Fraction on the Unit Circle","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Doug Bowman, Jimmy Mc Laughlin","submitted_at":"2001-07-06T04:14:18Z","abstract_excerpt":"Let the continued fraction expansion of any irrational number $t \\in (0,1)$ be denoted by $[0,a_{1}(t),a_{2}(t),...]$ and let the i-th convergent of this continued fraction expansion be denoted by $c_{i}(t)/d_{i}(t)$. Let \\[ S=\\{t \\in (0,1): a_{i+1}(t) \\geq \\phi^{d_{i}(t)} \\text{infinitely often}\\}, \\] where $\\phi = (\\sqrt{5}+1)/2$. Let $Y_{S} =\\{\\exp(2 \\pi i t): t \\in S \\}$. It is shown that if $y \\in Y_{S}$ then the Rogers-Ramanujan continued fraction, R(y), diverges at y. S is an uncountable set of measure zero. 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