Pith Number

pith:PCHXOGBE

pith:2026:PCHXOGBERV57ZJOHFAX7WBAZOV

not attested not anchored not stored refs pending

On the Hausdorff dimension of graph of random vector-valued Weierstrass function

Jun Jason Luo, Zi-Rui Zhang

The Hausdorff dimension of the graph of the random vector-valued Weierstrass function equals 3-2β with probability one.

arxiv:2604.13913 v2 · 2026-04-15 · math.CA · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PCHXOGBERV57ZJOHFAX7WBAZOV}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

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.

C2weakest assumption

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.

C3one line summary

With probability one, the Hausdorff dimension of the graph of the random vector-valued Weierstrass function is 3-2β.

Receipt and verification

First computed	2026-06-03T01:05:13.630146Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

788f7718248d7bfca5c7282ffb04197541c26fe5d746c11e583bc94b9684e45a

Aliases

arxiv: 2604.13913 · arxiv_version: 2604.13913v2 · doi: 10.48550/arxiv.2604.13913 · pith_short_12: PCHXOGBERV57 · pith_short_16: PCHXOGBERV57ZJOH · pith_short_8: PCHXOGBE

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PCHXOGBERV57ZJOHFAX7WBAZOV \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 788f7718248d7bfca5c7282ffb04197541c26fe5d746c11e583bc94b9684e45a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "888f7268208c4f971f132d198a82c8deca9185334bf0172b2f1403cfed9b0962",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2026-04-15T14:20:03Z",
    "title_canon_sha256": "ed00c457ff8125bd755371325e3b7134921c61a5ee8ff485e818184ecb6ff9e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.13913",
    "kind": "arxiv",
    "version": 2
  }
}