Pith Number

pith:TADB4FYT

pith:2002:TADB4FYT3Z6O5WBW632ZCKPRDF

not attested not anchored not stored refs pending

Cumulants in noncommutative probability I. Noncommutative Exchangeability Systems

Franz Lehner

arxiv:math/0210442 v3 · 2002-10-29 · 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{TADB4FYT3Z6O5WBW632ZCKPRDF}

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	2026-05-18T03:39:06.575666Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

98061e1713de7ceed836f6f59129f1195e1a1ecf3ce1baa6c892dbd842307bc7

Aliases

arxiv: math/0210442 · arxiv_version: math/0210442v3 · doi: 10.48550/arxiv.math/0210442 · pith_short_12: TADB4FYT3Z6O · pith_short_16: TADB4FYT3Z6O5WBW · pith_short_8: TADB4FYT

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/TADB4FYT3Z6O5WBW632ZCKPRDF \
  | 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: 98061e1713de7ceed836f6f59129f1195e1a1ecf3ce1baa6c892dbd842307bc7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a31ecb2948de05edbedd3207c9b448d04f16a0f8149066c4749bc378cf7b21ce",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2002-10-29T14:24:12Z",
    "title_canon_sha256": "111b5721af86e744e283bf1c515b133f46db693827ad6d2458ba4a9cf4801594"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0210442",
    "kind": "arxiv",
    "version": 3
  }
}