Pith Number

pith:QP3QYVXS

pith:2008:QP3QYVXSC5STYRXKVLHP73H2I3

not attested not anchored not stored refs pending

Convergence of complex multiplicative cascades

Beno\^{{\i}}t Mandelbrot, Julien Barral, Xiong Jin

arxiv:0812.4557 v3 · 2008-12-24 · 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{QP3QYVXSC5STYRXKVLHP73H2I3}

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.

Receipt and verification

First computed	2026-05-18T04:38:59.395937Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83f70c56f217653c46eaaaceffecfa46edceb1736c8ef3bb7207d2e78b4ee3cf

Aliases

arxiv: 0812.4557 · arxiv_version: 0812.4557v3 · doi: 10.48550/arxiv.0812.4557 · pith_short_12: QP3QYVXSC5ST · pith_short_16: QP3QYVXSC5STYRXK · pith_short_8: QP3QYVXS

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/QP3QYVXSC5STYRXKVLHP73H2I3 \
  | 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: 83f70c56f217653c46eaaaceffecfa46edceb1736c8ef3bb7207d2e78b4ee3cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb1429dc752db305eb766bdbcd4aa2fe2cadca4710af53bd9ee3990ff57ec668",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2008-12-24T17:45:41Z",
    "title_canon_sha256": "b105873eb2b7c8784b7a5e7daeec52de86a4ff485080814f6971e47e375982d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.4557",
    "kind": "arxiv",
    "version": 3
  }
}