Pith Number

pith:G7WMPYGA

pith:2011:G7WMPYGAQREAUHZU67XXJMPSSQ

not attested not anchored not stored refs pending

On the Ornstein-Zernike behaviour for the Bernoulli bond percolation on $\mathbb{Z}^{d},d\geq3,$ in the supercitical regime

Massimo Campanino, Michele Gianfelice

arxiv:1104.1595 v2 · 2011-04-08 · 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{G7WMPYGAQREAUHZU67XXJMPSSQ}

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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	2026-05-18T03:42:32.351044Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

37ecc7e0c084480a1f34f7ef74b1f2940a9948352ba68ebaf82d09e09455c874

Aliases

arxiv: 1104.1595 · arxiv_version: 1104.1595v2 · doi: 10.48550/arxiv.1104.1595 · pith_short_12: G7WMPYGAQREA · pith_short_16: G7WMPYGAQREAUHZU · pith_short_8: G7WMPYGA

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/G7WMPYGAQREAUHZU67XXJMPSSQ \
  | 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: 37ecc7e0c084480a1f34f7ef74b1f2940a9948352ba68ebaf82d09e09455c874

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "409ff726c9be3bdc4640e2df318a0e6c8f73cbbff78ba393738b07517b1e6508",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-04-08T15:03:12Z",
    "title_canon_sha256": "32c3dbabdd92b6e43e82b4d798e04d541856c4e2b3355282fe66b757d8264158"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.1595",
    "kind": "arxiv",
    "version": 2
  }
}