Pith Number

pith:CIGRGETF

pith:2009:CIGRGETFHA2JMXI5D3ZYY6CPIO

not attested not anchored not stored refs pending

The critical Z-invariant Ising model via dimers: locality property

B\'eatrice de Tili\`ere, C\'edric Boutillier

arxiv:0902.1882 v1 · 2009-02-11 · 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{CIGRGETFHA2JMXI5D3ZYY6CPIO}

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	2026-05-18T02:14:48.348060Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

120d1312653834965d1d1ef38c784f43ad2d96f9906568bfe42f1f1998e0f07a

Aliases

arxiv: 0902.1882 · arxiv_version: 0902.1882v1 · doi: 10.48550/arxiv.0902.1882 · pith_short_12: CIGRGETFHA2J · pith_short_16: CIGRGETFHA2JMXI5 · pith_short_8: CIGRGETF

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/CIGRGETFHA2JMXI5D3ZYY6CPIO \
  | 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: 120d1312653834965d1d1ef38c784f43ad2d96f9906568bfe42f1f1998e0f07a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "da260bb7afaf0bf245a1c3c832fd101c4ff328ea7b720dc5141d776a0939322d",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-02-11T13:17:06Z",
    "title_canon_sha256": "e83ee5e60a2290d897caab2638022d4606cd68a5f9afe2212fa24b72106b8bc8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.1882",
    "kind": "arxiv",
    "version": 1
  }
}