Pith Number

pith:5LZLOTRL

pith:2015:5LZLOTRLD66IKELB5IVU4BX3SR

not attested not anchored not stored refs pending

Kummer and gamma laws through independences on trees - another parallel with the Matsumoto-Yor property

Agnieszka Piliszek, Jacek Weso{\l}owski

arxiv:1511.00116 v2 · 2015-10-31 · 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{5LZLOTRLD66IKELB5IVU4BX3SR}

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	2026-05-18T00:43:36.013405Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eaf2b74e2b1fbc851161ea2b4e06fb945cb62b53e6ac15f1c057e31b6cf300e0

Aliases

arxiv: 1511.00116 · arxiv_version: 1511.00116v2 · doi: 10.48550/arxiv.1511.00116 · pith_short_12: 5LZLOTRLD66I · pith_short_16: 5LZLOTRLD66IKELB · pith_short_8: 5LZLOTRL

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/5LZLOTRLD66IKELB5IVU4BX3SR \
  | 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: eaf2b74e2b1fbc851161ea2b4e06fb945cb62b53e6ac15f1c057e31b6cf300e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc24acbb3aa1bf4662fc2fdee5b5b3f89724930d03176d157d8bdb3a7218c7c8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-10-31T12:03:49Z",
    "title_canon_sha256": "b61e299bce81d0a11366909dcf80e10199471ba48579ab38c0396ff42a889884"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.00116",
    "kind": "arxiv",
    "version": 2
  }
}