Pith Number

pith:FBUOXLSW

pith:2013:FBUOXLSWYBW3VK55SJLP4BQCWQ

not attested not anchored not stored refs pending

Crossing probabilities in topological rectangles for the critical planar FK-Ising model

Cl\'ement Hongler, Dmitry Chelkak, Hugo Duminil-Copin

arxiv:1312.7785 v1 · 2013-12-30 · 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{FBUOXLSWYBW3VK55SJLP4BQCWQ}

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	2026-05-18T03:03:33.710893Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2868ebae56c06dbaabbd9256fe0602b4192bd6c00b9fa5b711973df1e1fcdb4e

Aliases

arxiv: 1312.7785 · arxiv_version: 1312.7785v1 · doi: 10.48550/arxiv.1312.7785 · pith_short_12: FBUOXLSWYBW3 · pith_short_16: FBUOXLSWYBW3VK55 · pith_short_8: FBUOXLSW

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/FBUOXLSWYBW3VK55SJLP4BQCWQ \
  | 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: 2868ebae56c06dbaabbd9256fe0602b4192bd6c00b9fa5b711973df1e1fcdb4e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4978b1640a796107fa236d6a60fb5acdd7b4ba09ec674cad3dcf571da37564f7",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-12-30T17:16:36Z",
    "title_canon_sha256": "0de0b6633d5e3d13c09ff81ab8076c17a876fd79e0dfe3c2c27966a175ab51e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.7785",
    "kind": "arxiv",
    "version": 1
  }
}