Pith Number

pith:3K3IZVC5

pith:2020:3K3IZVC5XJGSNEXXR66YJEHUSF

not attested not anchored not stored refs pending

Explicit formulas for the joint third and fourth central moments of the multinomial distribution

Fr\'ed\'eric Ouimet

arxiv:2006.09059 v2 · 2020-06-16 · stat.OT · 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{3K3IZVC5XJGSNEXXR66YJEHUSF}

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	2026-07-05T02:02:04.074894Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dab68cd45dba4d2692f78fbd8490f49144e98232d4d2feba23d87a784784e6e8

Aliases

arxiv: 2006.09059 · arxiv_version: 2006.09059v2 · doi: 10.48550/arxiv.2006.09059 · pith_short_12: 3K3IZVC5XJGS · pith_short_16: 3K3IZVC5XJGSNEXX · pith_short_8: 3K3IZVC5

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/3K3IZVC5XJGSNEXXR66YJEHUSF \
  | 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: dab68cd45dba4d2692f78fbd8490f49144e98232d4d2feba23d87a784784e6e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "854581e93a2aa00a498dade5a3c9f65330703298c5eb5df79e2eb448064e8c1c",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.OT",
    "submitted_at": "2020-06-16T10:36:06Z",
    "title_canon_sha256": "3a477403cca8718416a0d0a7a0a7cfc5d0c66ce3b2f2ba3968028a7fea263859"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2006.09059",
    "kind": "arxiv",
    "version": 2
  }
}