Pith Number

pith:CV4KSDYP

pith:2015:CV4KSDYPM6YMOSXMH23GOBAU4N

not attested not anchored not stored refs pending

General de Finetti type theorems in noncommutative probability

Weihua Liu

arxiv:1511.05651 v2 · 2015-11-18 · 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{CV4KSDYPM6YMOSXMH23GOBAU4N}

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	2026-05-17T23:47:49.470347Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1578a90f0f67b0c74aec3eb6670414e36348f7c669204f8dd261517958d9cd09

Aliases

arxiv: 1511.05651 · arxiv_version: 1511.05651v2 · doi: 10.48550/arxiv.1511.05651 · pith_short_12: CV4KSDYPM6YM · pith_short_16: CV4KSDYPM6YMOSXM · pith_short_8: CV4KSDYP

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/CV4KSDYPM6YMOSXMH23GOBAU4N \
  | 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: 1578a90f0f67b0c74aec3eb6670414e36348f7c669204f8dd261517958d9cd09

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "276fc05848d65eb92389f9d73341d45a06c8c8a60b82bbbe24944603eee139c0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-11-18T03:34:54Z",
    "title_canon_sha256": "a59ceb5d56f472069922b0485cea90641e45c6d0d910dfc7e94b0d0a7f73cd59"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.05651",
    "kind": "arxiv",
    "version": 2
  }
}