Pith Number

pith:OR2B5PSL

pith:2019:OR2B5PSLZJSHO4SYYQXMWKJWE7

not attested not anchored not stored refs pending

Free self-decomposability and unimodality of the Fuss-Catalan distributions

Noriyoshi Sakuma, Wojciech M{\l}otkowski, Yuki Ueda

arxiv:1908.07887 v1 · 2019-08-21 · 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{OR2B5PSLZJSHO4SYYQXMWKJWE7}

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	2026-07-05T04:53:59.628008Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

74741ebe4bca64777258c42ecb293627c4e76d8777039ff775d040cba7bd40ce

Aliases

arxiv: 1908.07887 · arxiv_version: 1908.07887v1 · doi: 10.48550/arxiv.1908.07887 · pith_short_12: OR2B5PSLZJSH · pith_short_16: OR2B5PSLZJSHO4SY · pith_short_8: OR2B5PSL

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/OR2B5PSLZJSHO4SYYQXMWKJWE7 \
  | 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: 74741ebe4bca64777258c42ecb293627c4e76d8777039ff775d040cba7bd40ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "891a88aa34b1734235242d9367e2d5dc157e9cfe97c2f09a79e356491796b339",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-08-21T14:18:44Z",
    "title_canon_sha256": "c2ac713084998dbb9e0d7bb0a56dff306facf2e0d38a7e95a4665cb556c60649"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.07887",
    "kind": "arxiv",
    "version": 1
  }
}