Pith Number

pith:JBBBD7AT

pith:2012:JBBBD7ATQUGRLMLNFCUUMZZHCZ

not attested not anchored not stored refs pending

Rapid mixing of Swendsen-Wang dynamics in two dimensions

Mario Ullrich

arxiv:1212.4908 v2 · 2012-12-20 · 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{JBBBD7ATQUGRLMLNFCUUMZZHCZ}

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	2026-05-18T02:51:57.207917Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

484211fc13850d15b16d28a94667271666305d59ce8e4ced028d3431f8b51aab

Aliases

arxiv: 1212.4908 · arxiv_version: 1212.4908v2 · doi: 10.48550/arxiv.1212.4908 · pith_short_12: JBBBD7ATQUGR · pith_short_16: JBBBD7ATQUGRLMLN · pith_short_8: JBBBD7AT

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/JBBBD7ATQUGRLMLNFCUUMZZHCZ \
  | 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: 484211fc13850d15b16d28a94667271666305d59ce8e4ced028d3431f8b51aab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a0f43e50a1d67132f30bbc1a6b6cb796e381f652a16d00cb3e97705570530f0",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-12-20T02:19:23Z",
    "title_canon_sha256": "9c92001dd7b57703e7a328c1b3232345dccddca1ab929cb72d4efef55e32ecad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.4908",
    "kind": "arxiv",
    "version": 2
  }
}