Pith Number

pith:BAEBHPVI

pith:2010:BAEBHPVI5GDQ3UR7F3AEOUV2JF

not attested not anchored not stored refs pending

A Khintchine Decomposition for Free Probability

John D. Williams

arxiv:1009.4955 v2 · 2010-09-24 · 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{BAEBHPVI5GDQ3UR7F3AEOUV2JF}

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	2026-05-18T04:24:45.214734Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

080813bea8e9870dd23f2ec04752ba4966b08546962cee23594ef2497d367877

Aliases

arxiv: 1009.4955 · arxiv_version: 1009.4955v2 · doi: 10.48550/arxiv.1009.4955 · pith_short_12: BAEBHPVI5GDQ · pith_short_16: BAEBHPVI5GDQ3UR7 · pith_short_8: BAEBHPVI

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/BAEBHPVI5GDQ3UR7F3AEOUV2JF \
  | 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: 080813bea8e9870dd23f2ec04752ba4966b08546962cee23594ef2497d367877

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2fa2a9fed2600a7c51fe3f5b5e57e6a55bae37daf5c7376d7b9abafd9a750af0",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2010-09-24T22:12:06Z",
    "title_canon_sha256": "2e674a0d8526804130cb20a2c1d7667d67ea6206551d4c9351a66525a23eb7a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.4955",
    "kind": "arxiv",
    "version": 2
  }
}