Pith Number

pith:GJH3VAQ7

pith:2013:GJH3VAQ7CEKJ2K32Y6APOWK7OB

not attested not anchored not stored refs pending

On the free Gamma distributions

Steen Thorbjornsen, Uffe Haagerup

arxiv:1302.3738 v1 · 2013-02-15 · math.PR · math.OA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GJH3VAQ7CEKJ2K32Y6APOWK7OB}

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	2026-05-18T03:33:35.931214Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

324fba821f11149d2b7ac780f7595f707a05e85e0f4eeb4479396c776bcaa7fc

Aliases

arxiv: 1302.3738 · arxiv_version: 1302.3738v1 · doi: 10.48550/arxiv.1302.3738 · pith_short_12: GJH3VAQ7CEKJ · pith_short_16: GJH3VAQ7CEKJ2K32 · pith_short_8: GJH3VAQ7

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/GJH3VAQ7CEKJ2K32Y6APOWK7OB \
  | 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: 324fba821f11149d2b7ac780f7595f707a05e85e0f4eeb4479396c776bcaa7fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e2fc527d5bacca22e2f81d59bf14e0b6837752089362213f67765b47eee6ffc3",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-02-15T12:43:00Z",
    "title_canon_sha256": "6fcf168e3a9c01265a28d707d57175a9e0f94e9b833ff4b9d5e0167208864d4f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.3738",
    "kind": "arxiv",
    "version": 1
  }
}