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The random vector-valued Weierstrass function is given by\n  $$\n  f_{\\Theta,\\Lambda}(x)=\n  \\left(\n  \\sum_{n=0}^{\\infty} a^n\\cos\\bigl(2\\pi (b^n x+\\theta_n)\\bigr),\\\n  \\sum_{n=0}^{\\infty} a^n\\sin\\bigl(2\\pi (b^n x+\\lambda_n)\\bigr)\n  \\right), \\; x\\in[0,1],\n  $$ where $0<a<1<b,\\ ab> 1$. The Hausdorff dimension of the graph of this function is proved to be\n  $$\\dim_H G(f_{\\Theta,\\Lambda}) = \\min\\left\\{-\\frac{\\log b}{\\log a}, \\, 3 +2\\frac{\\log a}{\\log b}\\righ"},"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":"2604.13913","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2026-04-15T14:20:03Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"ed00c457ff8125bd755371325e3b7134921c61a5ee8ff485e818184ecb6ff9e1","abstract_canon_sha256":"888f7268208c4f971f132d198a82c8deca9185334bf0172b2f1403cfed9b0962"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T01:05:13.630570Z","signature_b64":"cnSU4oqTbnwpaV6e9j2qK57bbutZodGld8QzoPWWI4x2nzC94XCVkIDloV6Jd/kRpWvBS1i2OywEjZfS4lHKAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"788f7718248d7bfca5c7282ffb04197541c26fe5d746c11e583bc94b9684e45a","last_reissued_at":"2026-06-03T01:05:13.630146Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T01:05:13.630146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Hausdorff dimension of graph of random vector-valued Weierstrass function","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The Hausdorff dimension of the graph of the random vector-valued Weierstrass function equals 3-2β with probability one.","cross_cats":["math.PR"],"primary_cat":"math.CA","authors_text":"Jun Jason Luo, Zi-Rui Zhang","submitted_at":"2026-04-15T14:20:03Z","abstract_excerpt":"Let $\\Theta=\\{\\theta_n\\}, \\Lambda=\\{\\lambda_n\\}$ be two sequences of independent and identically distributed uniform random variables on $[0,1]$. The random vector-valued Weierstrass function is given by\n  $$\n  f_{\\Theta,\\Lambda}(x)=\n  \\left(\n  \\sum_{n=0}^{\\infty} a^n\\cos\\bigl(2\\pi (b^n x+\\theta_n)\\bigr),\\\n  \\sum_{n=0}^{\\infty} a^n\\sin\\bigl(2\\pi (b^n x+\\lambda_n)\\bigr)\n  \\right), \\; x\\in[0,1],\n  $$ where $0<a<1<b,\\ ab> 1$. The Hausdorff dimension of the graph of this function is proved to be\n  $$\\dim_H G(f_{\\Theta,\\Lambda}) = \\min\\left\\{-\\frac{\\log b}{\\log a}, \\, 3 +2\\frac{\\log a}{\\log b}\\righ"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that, with probability one, the Hausdorff dimension of the graph of this function is dim_H G(f_Θ,Λ)=3-2β, extending a result of Hunt in 1998.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The two sequences of phases Θ and Λ consist of independent and identically distributed uniform random variables on [0,1], with the contraction parameter β strictly less than 1/2.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"With probability one, the Hausdorff dimension of the graph of the random vector-valued Weierstrass function is 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