Pith Number

pith:HHAUHZCT

pith:2012:HHAUHZCTEFJ3VHFOWTMIOLY2UU

not attested not anchored not stored refs pending

Percolation since Saint-Flour

Geoffrey R. Grimmett, Harry Kesten

arxiv:1207.0373 v1 · 2012-07-02 · 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{HHAUHZCTEFJ3VHFOWTMIOLY2UU}

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	2026-05-18T03:51:59.480123Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

39c143e4532153ba9caeb4d8872f1aa52bbb3ec1d313f8a346086241ef96efd4

Aliases

arxiv: 1207.0373 · arxiv_version: 1207.0373v1 · doi: 10.48550/arxiv.1207.0373 · pith_short_12: HHAUHZCTEFJ3 · pith_short_16: HHAUHZCTEFJ3VHFO · pith_short_8: HHAUHZCT

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/HHAUHZCTEFJ3VHFOWTMIOLY2UU \
  | 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: 39c143e4532153ba9caeb4d8872f1aa52bbb3ec1d313f8a346086241ef96efd4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd8cf1e78024f8fd4b548c4d07a30984f967b8a59f11d0a470fbbc1ea4710ab2",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-07-02T13:28:36Z",
    "title_canon_sha256": "54d05a7f62bc958de2f27b1750efb6e150d0b1961c7a3f1fd9fe08ab7f79ae40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.0373",
    "kind": "arxiv",
    "version": 1
  }
}