Pith Number

pith:24US3ZCN

pith:2004:24US3ZCNTRXQQUXKO4SEGR3K4G

not attested not anchored not stored refs pending

Cumulants in Noncommutative Probability Theory IV. De Finetti's Theorem and $L^p$-Inequalities

Franz Lehner

arxiv:math/0409025 v2 · 2004-09-02 · math.OA · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{24US3ZCNTRXQQUXKO4SEGR3K4G}

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	2026-05-18T03:04:14.211613Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7292de44d9c6f0852ea772443476ae1afcde9f2432f5e7f04b08c0a940d78f3

Aliases

arxiv: math/0409025 · arxiv_version: math/0409025v2 · doi: 10.48550/arxiv.math/0409025 · pith_short_12: 24US3ZCNTRXQ · pith_short_16: 24US3ZCNTRXQQUXK · pith_short_8: 24US3ZCN

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/24US3ZCNTRXQQUXKO4SEGR3K4G \
  | 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: d7292de44d9c6f0852ea772443476ae1afcde9f2432f5e7f04b08c0a940d78f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13f10fd86a566a8d1f8653682c3b170be1293bfa3a9526f979b9cf4d33b45d5c",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2004-09-02T10:06:13Z",
    "title_canon_sha256": "66c7221e08a9bfea4bf8e561d0b1124660395aa66143a2a4d8ddcba23ace378a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0409025",
    "kind": "arxiv",
    "version": 2
  }
}