Pith Number

pith:MLHJWRQX

pith:2012:MLHJWRQXB2FSSWKU6O2BQQXZUW

not attested not anchored not stored refs pending

Unimodular Random Trees

Itai Benjamini, Oded Schramm, Russell Lyons

arxiv:1207.1752 v2 · 2012-07-07 · 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{MLHJWRQXB2FSSWKU6O2BQQXZUW}

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	2026-05-17T23:53:18.589480Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62ce9b46170e8b295954f3b41842f9a598f017834fc3afc093d64bacd84ed8e1

Aliases

arxiv: 1207.1752 · arxiv_version: 1207.1752v2 · doi: 10.48550/arxiv.1207.1752 · pith_short_12: MLHJWRQXB2FS · pith_short_16: MLHJWRQXB2FSSWKU · pith_short_8: MLHJWRQX

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/MLHJWRQXB2FSSWKU6O2BQQXZUW \
  | 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: 62ce9b46170e8b295954f3b41842f9a598f017834fc3afc093d64bacd84ed8e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "84cef87dfcfbc8f75b00e186e3d38e3d0f5752afe3dbbfbaec77b9ca2f7dc575",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-07-07T01:31:08Z",
    "title_canon_sha256": "a7c760d4e5afe3875bf033693c75785936f675ca1797a374babef7880c9bdfb2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.1752",
    "kind": "arxiv",
    "version": 2
  }
}