Pith Number

pith:V7YFJLLF

pith:2008:V7YFJLLFJJBAHQNDWSDPFS7E5J

not attested not anchored not stored refs pending

Mean field frozen percolation

Balazs Rath

arxiv:0812.2750 v2 · 2008-12-15 · math.PR · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{V7YFJLLFJJBAHQNDWSDPFS7E5J}

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	2026-05-18T02:15:04.821074Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aff054ad654a4203c1a3b486f2cbe4ea6b646a3e3bd888e84a8e10caf13e5021

Aliases

arxiv: 0812.2750 · arxiv_version: 0812.2750v2 · doi: 10.48550/arxiv.0812.2750 · pith_short_12: V7YFJLLFJJBA · pith_short_16: V7YFJLLFJJBAHQND · pith_short_8: V7YFJLLF

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/V7YFJLLFJJBAHQNDWSDPFS7E5J \
  | 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: aff054ad654a4203c1a3b486f2cbe4ea6b646a3e3bd888e84a8e10caf13e5021

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee7471a2f42a746163f3404e1f65d6b895ed14450c26cdf4455ee0fc684d9a8c",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2008-12-15T09:57:02Z",
    "title_canon_sha256": "ec327605486343cf039a21aebe179fabba3b1754c0d22c68531e436005d66045"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.2750",
    "kind": "arxiv",
    "version": 2
  }
}