Pith Number

pith:5DDKILTE

pith:2015:5DDKILTEFAXIMN7AB6DTSSBH3G

not attested not anchored not stored refs pending

Products of normal, beta and gamma random variables: Stein operators and distributional theory

Robert E. Gaunt

arxiv:1507.07696 v4 · 2015-07-28 · 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{5DDKILTEFAXIMN7AB6DTSSBH3G}

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	2026-05-18T00:18:27.176084Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e8c6a42e64282e8637e00f87394827d9a38ebf2486656572a4a04b8f6de6697f

Aliases

arxiv: 1507.07696 · arxiv_version: 1507.07696v4 · doi: 10.48550/arxiv.1507.07696 · pith_short_12: 5DDKILTEFAXI · pith_short_16: 5DDKILTEFAXIMN7A · pith_short_8: 5DDKILTE

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/5DDKILTEFAXIMN7AB6DTSSBH3G \
  | 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: e8c6a42e64282e8637e00f87394827d9a38ebf2486656572a4a04b8f6de6697f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e2c3806c3f34759a7e317dbc207032df98f9221f5d545945a6647489f28a408",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-07-28T09:35:10Z",
    "title_canon_sha256": "1763beaa062cc43880082ed0cba360a020816d3bd7fd3dc0e5896d5656f6b99f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.07696",
    "kind": "arxiv",
    "version": 4
  }
}