Pith Number

pith:FIM6YM73

pith:2010:FIM6YM73FCIRD77UHPOI24S6SN

not attested not anchored not stored refs pending

Joint cumulants for natural independence

Hayato Saigo, Takahiro Hasebe

arxiv:1005.3900 v3 · 2010-05-21 · math.OA · 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{FIM6YM73FCIRD77UHPOI24S6SN}

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	2026-05-18T03:05:45.215480Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2a19ec33fb289111fff43bdc8d725e93597410a1a6bcc002380aad141a68609a

Aliases

arxiv: 1005.3900 · arxiv_version: 1005.3900v3 · doi: 10.48550/arxiv.1005.3900 · pith_short_12: FIM6YM73FCIR · pith_short_16: FIM6YM73FCIRD77U · pith_short_8: FIM6YM73

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/FIM6YM73FCIRD77UHPOI24S6SN \
  | 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: 2a19ec33fb289111fff43bdc8d725e93597410a1a6bcc002380aad141a68609a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2476d0579145db156972104c6401c9f528f73d9fdb6c6c17430f0d2ba6ce32bd",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2010-05-21T07:53:37Z",
    "title_canon_sha256": "bf452de78d8b430f2017c049af1ef14f6e9ee1e43d9a61b6a87b72817cc3bb69"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.3900",
    "kind": "arxiv",
    "version": 3
  }
}