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It was recently shown in [Savov, 2014] that almost surely $\\lim_{\\delta\\to0}U(\\delta)N(t,\\delta) = t$, where $N(t,\\delta)$ is the minimal number of boxes of size at most $\\delta$ needed to cover a subordinator's range up to time $t$, and $U(\\delta)$ is the subordinator's renewal function. Our main result is a central limit theorem (CLT) for $N(t,\\delta)$, complementing and refining work in [Savov, 2014].\n  Box-counting dimension is defined in terms of $N(t,\\delta)$, but for subordi"},"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":"1706.06850","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-21T12:09:56Z","cross_cats_sorted":[],"title_canon_sha256":"4ebe9d563efe9b3c022e8b4e93bcaca07de0db41b99e7779c2fdf1781e6283b5","abstract_canon_sha256":"b6543d56df66754a1728d1c3a2bbf436b0ea8811b7b33ae27be7be27a43477dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:37.639280Z","signature_b64":"CV1eFcKkDxg8ne3Oj1IR4h22NUPGROgFDqqS8bswUcbGmiJwL2A7HCXGc3NdZ3kJ0r97LdFQcolgm9jo0pg/CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"653784ef547ca79e61ae3da92a547d4e95c26ce3d1398ca84a00c32344bb8dd0","last_reissued_at":"2026-05-18T00:24:37.638682Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:37.638682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fractal-Dimensional Properties of Subordinators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Adam Barker","submitted_at":"2017-06-21T12:09:56Z","abstract_excerpt":"This work looks at the box-counting dimension of sets related to subordinators (non-decreasing L\\'evy processes). 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