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We prove that the box dimension of $\\Lambda$ exists if and only if \\[\n  \\overline{\\dim}_{\\mathrm B} F\\leq \\max \\{\\dim_{\\mathrm H} \\Lambda, \\underline{\\dim}_{\\mathrm B} F\\}. \\] In particular, this provides the first examples of sets of continued fraction expansions with restricted digits for which the box dimension does not exist.\n  More generally, we establish an explicit asymptotic formula for the covering numbers $N_r(\\Lambda)$ in terms of $\\dim_{\\mathrm H}"},"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":"2406.12821","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2024-06-18T17:43:32Z","cross_cats_sorted":["math.CA","math.MG"],"title_canon_sha256":"bebd4b5c52854e10fc8c26ae71a4b5c77d305ccb1cdcc8f203d9eab3ada5d71d","abstract_canon_sha256":"b9f759310e6eeb36a0644e317ddc0fc727f92ea1a642d0872440bf3a5fb6aa52"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:54:14.737641Z","signature_b64":"SxI9mN/3SOojU3sEi3Z44HISSvIaZ9pe2qPTFS4X2wX0sWqZ7n1BDQa6mG2xUV4wpvDnFyTDkSE3+u3flrn0Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e3ea6202e195c8a3f98f9454bd1b70a23cda11cb1f91aa453c54c7ac20b3138","last_reissued_at":"2026-07-05T08:54:14.737242Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:54:14.737242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lower box dimension of infinitely generated self-conformal sets","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.CA","math.MG"],"primary_cat":"math.DS","authors_text":"Alex Rutar, Amlan Banaji","submitted_at":"2024-06-18T17:43:32Z","abstract_excerpt":"Let $\\Lambda$ be the limit set of an infinite conformal iterated function system and let $F$ denote the set of fixed points of the maps. 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