Pith Number

pith:VTYUAKA6

pith:2010:VTYUAKA6HJIQ2CAOC62MOTZ722

not attested not anchored not stored refs pending

Sharp metastability threshold for an anisotropic bootstrap percolation model

A. C. D. van Enter, H. Duminil-Copin

arxiv:1010.4691 v3 · 2010-10-22 · math.PR · math-ph · math.CO · 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{VTYUAKA6HJIQ2CAOC62MOTZ722}

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	2026-05-18T01:18:04.904594Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

acf140281e3a510d080e17b4c74f3fd6bb9aafba9f331c63adbe0fb8ba6d8b56

Aliases

arxiv: 1010.4691 · arxiv_version: 1010.4691v3 · doi: 10.48550/arxiv.1010.4691 · pith_short_12: VTYUAKA6HJIQ · pith_short_16: VTYUAKA6HJIQ2CAO · pith_short_8: VTYUAKA6

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/VTYUAKA6HJIQ2CAOC62MOTZ722 \
  | 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: acf140281e3a510d080e17b4c74f3fd6bb9aafba9f331c63adbe0fb8ba6d8b56

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf23aca72f04d50ae4f9e83eb7c287f0b487d23830a75e174a66594e1accf6c3",
    "cross_cats_sorted": [
      "math-ph",
      "math.CO",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-10-22T12:43:40Z",
    "title_canon_sha256": "9395f1d584099585a876515768c6e8177703c6d555e33e48849d3d34aed43a47"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.4691",
    "kind": "arxiv",
    "version": 3
  }
}