Pith Number

pith:4IBBHCLB

pith:2010:4IBBHCLB3V5GYKGRCI7OGY5MYI

not attested not anchored not stored refs pending

On Explicit Probability Densities Associated with Fuss-Catalan Numbers

Chunwei Song, Dang-Zheng Liu, Zheng-Dong Wang

arxiv:1008.0271 v1 · 2010-08-02 · math.PR · 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{4IBBHCLB3V5GYKGRCI7OGY5MYI}

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	2026-05-18T04:42:43.634102Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e202138961dd7a6c28d1123ee363acc216e2d6b55d677c0f0b38a97fce468201

Aliases

arxiv: 1008.0271 · arxiv_version: 1008.0271v1 · doi: 10.48550/arxiv.1008.0271 · pith_short_12: 4IBBHCLB3V5G · pith_short_16: 4IBBHCLB3V5GYKGR · pith_short_8: 4IBBHCLB

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/4IBBHCLB3V5GYKGRCI7OGY5MYI \
  | 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: e202138961dd7a6c28d1123ee363acc216e2d6b55d677c0f0b38a97fce468201

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "68b5de0a39394034ddffb67d7165cce80998dfed9838164999986b256dca2997",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-08-02T10:06:29Z",
    "title_canon_sha256": "c8edff4f3272043404d6666dfc13beb9e68217313a10f482e1e8cc8dab194134"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.0271",
    "kind": "arxiv",
    "version": 1
  }
}