Pith Number

pith:UVKHV32F

pith:2002:UVKHV32F3S77B4UXYK4WOOVZTI

not attested not anchored not stored refs pending

Multinomial identities arising from the free probability theory

Piotr Sniady

arxiv:math/0202077 v2 · 2002-02-08 · math.CO · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UVKHV32F3S77B4UXYK4WOOVZTI}

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	2026-05-17T23:59:18.438781Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a5547aef45dcbff0f297c2b9673ab99a3989891a8c51e9372bf048d5cf429a86

Aliases

arxiv: math/0202077 · arxiv_version: math/0202077v2 · doi: 10.48550/arxiv.math/0202077 · pith_short_12: UVKHV32F3S77 · pith_short_16: UVKHV32F3S77B4UX · pith_short_8: UVKHV32F

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/UVKHV32F3S77B4UXYK4WOOVZTI \
  | 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: a5547aef45dcbff0f297c2b9673ab99a3989891a8c51e9372bf048d5cf429a86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b20f601916dc1b9728a55854ba8e7b5b287f53cbb1b18942c534d4fc0bfd09b",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2002-02-08T21:31:08Z",
    "title_canon_sha256": "47f960b775e6224fc51936162ea9f91175c3bc292821d9ac87feb3ab7c023c7d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0202077",
    "kind": "arxiv",
    "version": 2
  }
}