Pith Number

pith:XAB7KHB4

pith:2025:XAB7KHB445FLJ2GBGBSIX7E4WK

not attested not anchored not stored refs pending

Mixing rate exponent of planar Fortuin-Kasteleyn percolation

Baojun Wu, Haoyu Liu, Zijie Zhuang

arxiv:2502.09950 v2 · 2025-02-14 · 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{XAB7KHB445FLJ2GBGBSIX7E4WK}

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	2026-07-05T10:18:49.921123Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b803f51c3ce74ab4e8c130648bfc9cb28fa43e38909d19fec9012f943e179595

Aliases

arxiv: 2502.09950 · arxiv_version: 2502.09950v2 · doi: 10.48550/arxiv.2502.09950 · pith_short_12: XAB7KHB445FL · pith_short_16: XAB7KHB445FLJ2GB · pith_short_8: XAB7KHB4

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/XAB7KHB445FLJ2GBGBSIX7E4WK \
  | 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: b803f51c3ce74ab4e8c130648bfc9cb28fa43e38909d19fec9012f943e179595

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c83d5ea395e00d87efe14004954008db3d7e22331c5b126c0bde893a6e4d3dd4",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-02-14T07:09:20Z",
    "title_canon_sha256": "b9ec6b211b1b91178b98b622cc1a268e6431f8fcdcec7b45d69b1d7599789897"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.09950",
    "kind": "arxiv",
    "version": 2
  }
}