Pith Number

pith:WOEH23PV

pith:2009:WOEH23PVPKIHV4W3PBXGU6AEBJ

not attested not anchored not stored refs pending

Convex Hull of N Planar Brownian Motions: Exact Results and an Application to Ecology

Alain Comtet, Julien Randon-Furling, Satya N. Majumdar

arxiv:0907.0921 v2 · 2009-07-06 · cond-mat.stat-mech · math-ph · math.MP · 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{WOEH23PVPKIHV4W3PBXGU6AEBJ}

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	2026-05-18T02:13:05.125291Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3887d6df57a907af2db786e6a78040a7da171c8978e5bb0ffec682f95938dff

Aliases

arxiv: 0907.0921 · arxiv_version: 0907.0921v2 · doi: 10.48550/arxiv.0907.0921 · pith_short_12: WOEH23PVPKIH · pith_short_16: WOEH23PVPKIHV4W3 · pith_short_8: WOEH23PV

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/WOEH23PVPKIHV4W3PBXGU6AEBJ \
  | 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: b3887d6df57a907af2db786e6a78040a7da171c8978e5bb0ffec682f95938dff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a55832793528766f8c17862fd1de6132cac8611a3bf514877b2534bdc29246d4",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2009-07-06T06:49:44Z",
    "title_canon_sha256": "c33bd5837215082b3bcec6fc9155bc087b150e834be4d52506c1fb029f5d37e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.0921",
    "kind": "arxiv",
    "version": 2
  }
}