Pith Number

pith:ESF6VNYY

pith:2011:ESF6VNYYUFZMIRMGKIWK6XYJGI

not attested not anchored not stored refs pending

On multidimensional Mandelbrot's cascades

Dariusz Buraczewski, Ewa Damek, Sebastian Mentemeier, Yves Guivarc'h

arxiv:1109.1845 v2 · 2011-09-08 · 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{ESF6VNYYUFZMIRMGKIWK6XYJGI}

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	2026-05-18T02:56:33.043088Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

248beab718a172c44586522caf5f093200b25f622f195b7bad5a5ef4f3b8b338

Aliases

arxiv: 1109.1845 · arxiv_version: 1109.1845v2 · doi: 10.48550/arxiv.1109.1845 · pith_short_12: ESF6VNYYUFZM · pith_short_16: ESF6VNYYUFZMIRMG · pith_short_8: ESF6VNYY

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/ESF6VNYYUFZMIRMGKIWK6XYJGI \
  | 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: 248beab718a172c44586522caf5f093200b25f622f195b7bad5a5ef4f3b8b338

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2be8407f8e7ed07122e8cb06b85dc24021054590f29e39de7c6788d34b2d4891",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-09-08T20:59:05Z",
    "title_canon_sha256": "fd5fefdb12c6566b388b7c37b805308f5a26a5c5eec535a5f69cd8d72b322791"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.1845",
    "kind": "arxiv",
    "version": 2
  }
}