Pith Number

pith:P4ZIGKZ5

pith:2012:P4ZIGKZ56SAHW74BUZDEVMLTB2

not attested not anchored not stored refs pending

The Brownian plane

Jean-Fran\c{c}ois Le Gall, Nicolas Curien

arxiv:1204.5921 v1 · 2012-04-26 · 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{P4ZIGKZ56SAHW74BUZDEVMLTB2}

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	2026-05-18T03:56:59.044529Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f32832b3df4807b7f81a6464ab1730e8ebadcf20caed9f4498f566ee2b78602

Aliases

arxiv: 1204.5921 · arxiv_version: 1204.5921v1 · doi: 10.48550/arxiv.1204.5921 · pith_short_12: P4ZIGKZ56SAH · pith_short_16: P4ZIGKZ56SAHW74B · pith_short_8: P4ZIGKZ5

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/P4ZIGKZ56SAHW74BUZDEVMLTB2 \
  | 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: 7f32832b3df4807b7f81a6464ab1730e8ebadcf20caed9f4498f566ee2b78602

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "481d73ac6f7b1364cba0bdfc3085e31fe004fb93666a1830537b2cf7d9085240",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-04-26T13:51:17Z",
    "title_canon_sha256": "e1e3dddcdad4ce5bfda637bc9ffd357110415c2ce2539a8d79950c1659e24380"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.5921",
    "kind": "arxiv",
    "version": 1
  }
}