Pith Number

pith:6OBO5PS5

pith:2014:6OBO5PS55IEOPGV3L6CNR3YBCE

not attested not anchored not stored refs pending

A noncommutative De Finetti theorem for boolean independence

Weihua Liu

arxiv:1403.1772 v3 · 2014-03-07 · 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{6OBO5PS55IEOPGV3L6CNR3YBCE}

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	2026-05-18T02:39:23.829585Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f382eebe5dea08e79abb5f84d8ef011135a072f5ced5daa11cb32fe80a77e639

Aliases

arxiv: 1403.1772 · arxiv_version: 1403.1772v3 · doi: 10.48550/arxiv.1403.1772 · pith_short_12: 6OBO5PS55IEO · pith_short_16: 6OBO5PS55IEOPGV3 · pith_short_8: 6OBO5PS5

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/6OBO5PS55IEOPGV3L6CNR3YBCE \
  | 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: f382eebe5dea08e79abb5f84d8ef011135a072f5ced5daa11cb32fe80a77e639

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad922041d96a2fcb2db3dba5708eeb638ae25c7dd1bd7396f377b0d4feeb775d",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2014-03-07T15:08:23Z",
    "title_canon_sha256": "3b16ab6ed7c828fb942a22710d2ce8bee39fb6ff91299242535a7b2650036194"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1403.1772",
    "kind": "arxiv",
    "version": 3
  }
}