Pith Number

pith:5BOX5K3D

pith:2011:5BOX5K3DLD6ERF5POUMDR734K5

not attested not anchored not stored refs pending

Potts model with invisible colours: Random-cluster representation and Pirogov-Sinai analysis

Aernout C.D. van Enter, Giulio Iacobelli, Siamak Taati

arxiv:1109.0189 v1 · 2011-09-01 · math-ph · cond-mat.stat-mech · 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{5BOX5K3DLD6ERF5POUMDR734K5}

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	2026-05-18T02:00:43.300672Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e85d7eab6358fc4897af751838ff7c5766d449ce35cf86d13e866b53d01a8952

Aliases

arxiv: 1109.0189 · arxiv_version: 1109.0189v1 · doi: 10.48550/arxiv.1109.0189 · pith_short_12: 5BOX5K3DLD6E · pith_short_16: 5BOX5K3DLD6ERF5P · pith_short_8: 5BOX5K3D

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/5BOX5K3DLD6ERF5POUMDR734K5 \
  | 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: e85d7eab6358fc4897af751838ff7c5766d449ce35cf86d13e866b53d01a8952

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b21fe609d6000101db2c563673245251a28704e5a21247d112a23fe7e886a62",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-09-01T14:07:00Z",
    "title_canon_sha256": "4811629aee2adbe724c2382a6face1e10447c0c6dd18709b35b4003d01563c06"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.0189",
    "kind": "arxiv",
    "version": 1
  }
}