Pith Number

pith:CGA6CTVV

pith:2014:CGA6CTVVO2YVBSEBCATRF3SHSM

not attested not anchored not stored refs pending

Explicit formulae in probability and in statistical physics

Alain Comtet, Yves Tourigny

arxiv:1409.3777 v2 · 2014-09-12 · 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{CGA6CTVVO2YVBSEBCATRF3SHSM}

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	2026-05-18T02:39:40.098019Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1181e14eb576b150c881102712ee47931a81e579c5a5a3c5e5e8b4e2eab4bde8

Aliases

arxiv: 1409.3777 · arxiv_version: 1409.3777v2 · doi: 10.48550/arxiv.1409.3777 · pith_short_12: CGA6CTVVO2YV · pith_short_16: CGA6CTVVO2YVBSEB · pith_short_8: CGA6CTVV

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/CGA6CTVVO2YVBSEBCATRF3SHSM \
  | 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: 1181e14eb576b150c881102712ee47931a81e579c5a5a3c5e5e8b4e2eab4bde8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cdefb3e3accf33c2963bacfc50ccb65826dbeaa950545f4e5c4dc53e69e55c8e",
    "cross_cats_sorted": [
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2014-09-12T15:48:14Z",
    "title_canon_sha256": "d267b7eb778cf3d40d5a96983320e4c37acc964694139038525cd8072b1cc9a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.3777",
    "kind": "arxiv",
    "version": 2
  }
}