Pith Number

pith:L4XOUORP

pith:2012:L4XOUORPOSBMFH7GGSDDPQIK23

not attested not anchored not stored refs pending

On the free convolution with a free multiplicative analogue of the normal distribution

Ping Zhong

arxiv:1211.3160 v3 · 2012-11-13 · math.PR · math.FA · math.OA

Open paper page JSON What is a Pith Number?

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

Receipt and verification

First computed	2026-05-18T02:53:27.262785Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f2eea3a2f7482c29fe6348637c10ad6c0e8ba5cc16d325881700e4451ee095d

Aliases

arxiv: 1211.3160 · arxiv_version: 1211.3160v3 · doi: 10.48550/arxiv.1211.3160

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/L4XOUORPOSBMFH7GGSDDPQIK23 \
  | 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: 5f2eea3a2f7482c29fe6348637c10ad6c0e8ba5cc16d325881700e4451ee095d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "efc011cb017384c583b3a5b90e82251ea90d652b5c878e47617c3ed1e6ff9d4b",
    "cross_cats_sorted": [
      "math.FA",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-11-13T23:26:56Z",
    "title_canon_sha256": "42cc0355ef28252a1a191369f49b74d46096ec58a525865829856ec5e7ff6a60"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.3160",
    "kind": "arxiv",
    "version": 3
  }
}