Pith Number

pith:2A5CUYSI

pith:2024:2A5CUYSIXMVIU4WKQ7RWSB4V5G

not attested not anchored not stored refs pending

Harmonic analysis of Mandelbrot cascades -- in the context of vector-valued martingales

Xinxin Chen, Yanqi Qiu, Yong Han, Zipeng Wang

arxiv:2409.13164 v3 · 2024-09-20 · math.PR · math-ph · math.FA · math.MP

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2A5CUYSIXMVIU4WKQ7RWSB4V5G}

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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

6 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

Fourier restriction estimates based on $L^q$-dimensions: beyond Stein--Tomas

Receipt and verification

First computed	2026-07-05T11:19:21.072509Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d03a2a6248bb2a8a72ca87e3690795e98286bb54220955119825daa7c72b97b0

Aliases

arxiv: 2409.13164 · arxiv_version: 2409.13164v3 · doi: 10.48550/arxiv.2409.13164 · pith_short_12: 2A5CUYSIXMVI · pith_short_16: 2A5CUYSIXMVIU4WK · pith_short_8: 2A5CUYSI

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/2A5CUYSIXMVIU4WKQ7RWSB4V5G \
  | 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: d03a2a6248bb2a8a72ca87e3690795e98286bb54220955119825daa7c72b97b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "27d43b9bd6c9ef1355cb6e919c3155215a9ffdd9cfeda964c374d17e0565c7b3",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2024-09-20T02:36:23Z",
    "title_canon_sha256": "7167ae376a62e08812356dd9b75ff266b5f76a5046b4dd39fd06e84fbc738726"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2409.13164",
    "kind": "arxiv",
    "version": 3
  }
}