Pith Number

pith:GKBQSN6R

pith:2011:GKBQSN6RPSG4JL3BUSW5MF263M

not attested not anchored not stored refs pending

The Lukacs theorem and the Olkin-Baker equation

Jacek Wesolowski, Jolanta Misiewicz, Roman Ger

arxiv:1112.1226 v2 · 2011-12-06 · 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{GKBQSN6RPSG4JL3BUSW5MF263M}

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	2026-05-18T03:55:46.705842Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32830937d17c8dc4af61a4add6175edb0cc13b6abcd4a607ea7e43ef146c9279

Aliases

arxiv: 1112.1226 · arxiv_version: 1112.1226v2 · doi: 10.48550/arxiv.1112.1226 · pith_short_12: GKBQSN6RPSG4 · pith_short_16: GKBQSN6RPSG4JL3B · pith_short_8: GKBQSN6R

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/GKBQSN6RPSG4JL3BUSW5MF263M \
  | 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: 32830937d17c8dc4af61a4add6175edb0cc13b6abcd4a607ea7e43ef146c9279

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79adcd9ef1abfad162cebed0eb51f506e9931606adc1f92012ba61f29af01703",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-12-06T10:47:56Z",
    "title_canon_sha256": "71fbfea0bfbbd9d05bb59134eaaadb02e6f36a42ca03835512f8d2128678217d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.1226",
    "kind": "arxiv",
    "version": 2
  }
}