Pith Number

pith:GUU5O5TK

pith:2011:GUU5O5TKVLWZM5C3TSDFZAJ3M3

not attested not anchored not stored refs pending

Three theorems in discrete random geometry

Geoffrey Grimmett

arxiv:1110.2395 v2 · 2011-10-11 · math.PR · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GUU5O5TKVLWZM5C3TSDFZAJ3M3}

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	2026-05-18T04:03:45.073375Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3529d7766aaaed96745b9c865c813b66d64ea9b79a5aec3644b031396aef3364

Aliases

arxiv: 1110.2395 · arxiv_version: 1110.2395v2 · doi: 10.48550/arxiv.1110.2395 · pith_short_12: GUU5O5TKVLWZ · pith_short_16: GUU5O5TKVLWZM5C3 · pith_short_8: GUU5O5TK

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/GUU5O5TKVLWZM5C3TSDFZAJ3M3 \
  | 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: 3529d7766aaaed96745b9c865c813b66d64ea9b79a5aec3644b031396aef3364

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "974d37b808f2c4b17354f381259f5b58cb9db29945e3642ada553e155e3dc56d",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-10-11T15:18:08Z",
    "title_canon_sha256": "3c721eedffc82d23c4bcb1b59771cd2c46f80c9435be215ffb50eaa6a9723ad2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.2395",
    "kind": "arxiv",
    "version": 2
  }
}