Pith Number

pith:CFLZKCZW

pith:2025:CFLZKCZWI7EV24OXEEPVHYQCHW

not attested not anchored not stored refs pending

Harmonic analysis of multiplicative chaos Part II: a unified approach to Fourier dimensions

Mingjie Tan, Yanqi Qiu, Zhaofeng Lin

arxiv:2505.03298 v4 · 2025-05-06 · math.PR · math-ph · math.DS · math.FA · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CFLZKCZWI7EV24OXEEPVHYQCHW}

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.

Cited by

3 papers in Pith

Exact Fourier dimensions of dyadic Mandelbrot cascades on curves of nonvanishing curvature under minimal integrability

Fourier Dimensions of Mandelbrot Cascades under Minimal Integrability

Exact Fourier dimensions of dyadic Mandelbrot cascades under minimal integrability

Receipt and verification

First computed	2026-07-05T11:22:39.816410Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1157950b3647c95d71d7211f53e2023dac73710d278bef3a161427092ea55222

Aliases

arxiv: 2505.03298 · arxiv_version: 2505.03298v4 · doi: 10.48550/arxiv.2505.03298 · pith_short_12: CFLZKCZWI7EV · pith_short_16: CFLZKCZWI7EV24OX · pith_short_8: CFLZKCZW

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/CFLZKCZWI7EV24OXEEPVHYQCHW \
  | 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: 1157950b3647c95d71d7211f53e2023dac73710d278bef3a161427092ea55222

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd3d8717b7134adad89811b689c5c1fef43e31b9d90b86cca2f077c922da35b2",
    "cross_cats_sorted": [
      "math-ph",
      "math.DS",
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-05-06T08:28:11Z",
    "title_canon_sha256": "5e5825f655c746d21336fa6c2d01098c79edbc54bef1da97154f686c3fe2576e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.03298",
    "kind": "arxiv",
    "version": 4
  }
}