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We prove a functional large deviation principle, a functional moderate deviation principle, and a Strassen-type functional law of the iterated logarithm for the process $(\\log L_{\\lfloor{nt}\\rfloor})_{0\\le t\\le1}$. The large deviation rate function is given by an entropy contraction for geometric marks, while the moderate deviation rate function and LIL cluster set are described by the reproduc"},"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":"2607.08129","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-09T06:00:18Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"105f42dc0393d12ae2dbfc0a4440adee5e90d645c874b8aba42c45c5a372741d","abstract_canon_sha256":"61ab730b001ca99d6852a54952fc9f5e2db309fad6c2bfbd8a0aceb64f202c2f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-10T01:19:27.451423Z","signature_b64":"DCg5G5AIi1IscTIAnOeRC18OjZ7EMOtnMk13Pan5/tgqSUR/Uz2m1gNEEVyF6OHT7ds43A0kHwM6e1JrwO9DBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0e26a41216d2e7b60f6fa74ce41d273d37418b946c167e3982c8ba9ee75588b","last_reissued_at":"2026-07-10T01:19:27.451016Z","signature_status":"signed_v1","first_computed_at":"2026-07-10T01:19:27.451016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Functional Limit Theorems for Random Least Common Multiples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.PR","authors_text":"Guangyu Yang, Shaochen Wang, Wang Zhou","submitted_at":"2026-07-09T06:00:18Z","abstract_excerpt":"Let $A_n$ be a subset of $\\{1,2,\\ldots,n\\}$ obtained by retaining each integer independently with fixed probability $\\theta\\in(0,1)$, and let $L_n$ be the least common multiple of the integers in $A_n$. 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