Pith Number

pith:P4JZHCIB

pith:2010:P4JZHCIBRBT3R3DSFH7W3ZV7KG

not attested not anchored not stored refs pending

Infinite divisibility and a non-commutative Boolean-to-free Bercovici-Pata bijection

Mihai Popa, Serban T. Belinschi, Victor Vinnikov

arxiv:1007.0058 v3 · 2010-07-01 · math.OA · 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{P4JZHCIBRBT3R3DSFH7W3ZV7KG}

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	2026-05-18T04:07:52.743480Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f139389018867b8ec7229ff6de6bf51ab25aef5a4bbebe1fe89d606e495c203

Aliases

arxiv: 1007.0058 · arxiv_version: 1007.0058v3 · doi: 10.48550/arxiv.1007.0058 · pith_short_12: P4JZHCIBRBT3 · pith_short_16: P4JZHCIBRBT3R3DS · pith_short_8: P4JZHCIB

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/P4JZHCIBRBT3R3DSFH7W3ZV7KG \
  | 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: 7f139389018867b8ec7229ff6de6bf51ab25aef5a4bbebe1fe89d606e495c203

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4b55a1607ac282a7622476affb9f00b6ca3e67e934b76b73dd16e66af6b4daf",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2010-07-01T02:29:26Z",
    "title_canon_sha256": "d3430e9a02bec43718437682e28b0708c9c16536000ad3c9c3fca77003eec979"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.0058",
    "kind": "arxiv",
    "version": 3
  }
}