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This proves in particular that sequences like $((-1)^{v_2(n)+v_3(n)})_n$ are not $k$-automatic for $k\\geq 2$."},"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":"1605.09403","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-30T20:17:27Z","cross_cats_sorted":[],"title_canon_sha256":"1146c0f302246dee97b22870548e0e0a1faadbb2074d5e4caae5d5360f2ee4e8","abstract_canon_sha256":"66f56c4686c0be12eb0d3712f1a28ea0d73ed8b546e04e5d222f44d56b0d637a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:17.413505Z","signature_b64":"LzbJJo3eEg8EFVBmvjc54bLGIbLWuu78nN8WDjYOskKMqfryeRWofTyYNej2y3cqMiOU6QX5QpxPRlwipGoNCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d6583ca0dd922bd8a232bf86eed3bb7da9ed2fb399cf83dc812e13d7996f93a","last_reissued_at":"2026-05-18T01:13:17.412993Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:17.412993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Subword Complexity and (non)-automaticity of certain completely multiplicative functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Yining Hu","submitted_at":"2016-05-30T20:17:27Z","abstract_excerpt":"In this article, we prove that for a completely multiplicative function $f$ from $\\mathbb{N}^*$ to a field $K$ such that the set $$\\{p \\;|\\; f(p)\\neq 1_K \\;\\mbox{and }p \\mbox{ is prime}\\}$$ is finite, the asymptotic subword complexity of $f$ is $\\Theta(n^t)$, where $t$ is the number of primes $p$ that $f(p)\\neq 0_K, 1_K$. 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