Pith Number

pith:AKHTOTWK

pith:2012:AKHTOTWKGO3PCILDM3USLJYUDQ

not attested not anchored not stored refs pending

The critical temperature for the Ising model on planar doubly periodic graphs

David Cimasoni, Hugo Duminil-Copin

arxiv:1209.0951 v1 · 2012-09-05 · math-ph · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AKHTOTWKGO3PCILDM3USLJYUDQ}

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	2026-05-18T02:31:09.170946Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

028f374eca33b6f1216366e925a7141c34f75f4073d51922841c4d5686c24b8d

Aliases

arxiv: 1209.0951 · arxiv_version: 1209.0951v1 · doi: 10.48550/arxiv.1209.0951 · pith_short_12: AKHTOTWKGO3P · pith_short_16: AKHTOTWKGO3PCILD · pith_short_8: AKHTOTWK

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/AKHTOTWKGO3PCILDM3USLJYUDQ \
  | 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: 028f374eca33b6f1216366e925a7141c34f75f4073d51922841c4d5686c24b8d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20301e6785938e38f1eb8faf3f85f738f304cb6d1870fbc45ad766ffc1ee93cb",
    "cross_cats_sorted": [
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-09-05T12:48:21Z",
    "title_canon_sha256": "3b209ef916c40c12c3988a4bf158d720580831a7a2f0d318f97283c0e3a7ac62"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.0951",
    "kind": "arxiv",
    "version": 1
  }
}