Pith Number

pith:WGE72L7D

pith:2011:WGE72L7DLZNQIVEA4WELKH5OGN

not attested not anchored not stored refs pending

A power law of order 1/4 for critical mean-field Swendsen-Wang dynamics

Asaf Nachmias, Weiyang Ning, Yun Long, Yuval Peres

arxiv:1107.2970 v1 · 2011-07-15 · 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{WGE72L7DLZNQIVEA4WELKH5OGN}

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	2026-05-18T04:18:14.956227Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b189fd2fe35e5b045480e588b51fae335cecd26e91485ef8980237c30cf05295

Aliases

arxiv: 1107.2970 · arxiv_version: 1107.2970v1 · doi: 10.48550/arxiv.1107.2970 · pith_short_12: WGE72L7DLZNQ · pith_short_16: WGE72L7DLZNQIVEA · pith_short_8: WGE72L7D

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/WGE72L7DLZNQIVEA4WELKH5OGN \
  | 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: b189fd2fe35e5b045480e588b51fae335cecd26e91485ef8980237c30cf05295

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69b7fd2bdcc043924a7e85a3fa1e19d4ce452e98953f0d8d1b8d84fff0f99175",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-07-15T00:02:03Z",
    "title_canon_sha256": "c53762f904fe8bf20fc882c76380c4338b493d9a35fadfbc53f542a5271a460c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.2970",
    "kind": "arxiv",
    "version": 1
  }
}