Pith Number

pith:CMJPHLZ4

pith:2012:CMJPHLZ4W3KYXJ3XFCOH6TH45Z

not attested not anchored not stored refs pending

A multivariate hook formula for labelled trees

I. P. Goulden, Valentin F\'eray

arxiv:1205.0369 v2 · 2012-05-02 · math.CO · math.RT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CMJPHLZ4W3KYXJ3XFCOH6TH45Z}

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	2026-05-18T03:27:34.467031Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1312f3af3cb6d58ba777289c7f4cfcee6cf3a31df732788a8c40259a6e447f6a

Aliases

arxiv: 1205.0369 · arxiv_version: 1205.0369v2 · doi: 10.48550/arxiv.1205.0369 · pith_short_12: CMJPHLZ4W3KY · pith_short_16: CMJPHLZ4W3KYXJ3X · pith_short_8: CMJPHLZ4

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/CMJPHLZ4W3KYXJ3XFCOH6TH45Z \
  | 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: 1312f3af3cb6d58ba777289c7f4cfcee6cf3a31df732788a8c40259a6e447f6a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9db324e25033d7810176bcb7039a58e7828e387a08af3138286ed9131e3d1b5f",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-05-02T10:22:03Z",
    "title_canon_sha256": "e3f6e2b292085ebfbd482f481b08d16d0a1af2c0fc5fb15d96fd141fe5df8d6c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.0369",
    "kind": "arxiv",
    "version": 2
  }
}