Pith Number

pith:7GUTR2KD

pith:2016:7GUTR2KDWFVDFSHJKLAIEET6G2

not attested not anchored not stored refs pending

A new computation of the critical point for the planar random-cluster model with $q\ge1$

Aran Raoufi, Hugo Duminil-Copin, Vincent Tassion

arxiv:1604.03702 v1 · 2016-04-13 · 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{7GUTR2KDWFVDFSHJKLAIEET6G2}

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	2026-05-18T01:17:11.896065Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9a938e943b16a32c8e952c082127e369205c896a1da9801ff1245aa8154da48

Aliases

arxiv: 1604.03702 · arxiv_version: 1604.03702v1 · doi: 10.48550/arxiv.1604.03702 · pith_short_12: 7GUTR2KDWFVD · pith_short_16: 7GUTR2KDWFVDFSHJ · pith_short_8: 7GUTR2KD

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/7GUTR2KDWFVDFSHJKLAIEET6G2 \
  | 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: f9a938e943b16a32c8e952c082127e369205c896a1da9801ff1245aa8154da48

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8f2f6652aae265173c3131bf90da4b08126cbcdd420076a903a718d20d79458",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-04-13T09:34:23Z",
    "title_canon_sha256": "b33096fc11cbcea17d5ca87b04f1d61b33771af33de34bfe6e4f64be4755fb4f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.03702",
    "kind": "arxiv",
    "version": 1
  }
}