Pith Number

pith:FZP2EYTH

pith:2018:FZP2EYTHN7YWZZDWHCQDGUAAR2

not attested not anchored not stored refs pending

Another proof of $p_c = \frac{\sqrt{q}}{1+\sqrt{q}}$ on $\mathbb{Z}^2$ with $q \in [1,4]$ for random-cluster model

D. Smirnova, E. Mukoseeva

arxiv:1812.03487 v1 · 2018-12-09 · 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{FZP2EYTHN7YWZZDWHCQDGUAAR2}

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	2026-05-17T23:58:46.159074Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2e5fa262676ff16ce47638a03350008e9c2d1b92af27535f0588f7d3b93cb047

Aliases

arxiv: 1812.03487 · arxiv_version: 1812.03487v1 · doi: 10.48550/arxiv.1812.03487 · pith_short_12: FZP2EYTHN7YW · pith_short_16: FZP2EYTHN7YWZZDW · pith_short_8: FZP2EYTH

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/FZP2EYTHN7YWZZDWHCQDGUAAR2 \
  | 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: 2e5fa262676ff16ce47638a03350008e9c2d1b92af27535f0588f7d3b93cb047

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e006bff7dca33eab19d98e1f35f3b72c299e878e0c2873363d6539c3cfde7db6",
    "cross_cats_sorted": [
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2018-12-09T13:32:36Z",
    "title_canon_sha256": "ea42e3187d9e293d0b328673a8fa9b165a3dee6722a528442ae6a570e95cbcb0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.03487",
    "kind": "arxiv",
    "version": 1
  }
}