Pith Number

pith:PWXNQ22J

pith:2012:PWXNQ22JFSWSGHWCQR5PV2NREY

not attested not anchored not stored refs pending

Ultraproducts of von Neumann algebras

Hiroshi Ando, Uffe Haagerup

arxiv:1212.5457 v3 · 2012-12-21 · 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{PWXNQ22JFSWSGHWCQR5PV2NREY}

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	2026-05-18T02:55:49.981122Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7daed86b492cad231ec2847afae9b12628bd87b5d36fd50ad8dcda8e0a9a3154

Aliases

arxiv: 1212.5457 · arxiv_version: 1212.5457v3 · doi: 10.48550/arxiv.1212.5457 · pith_short_12: PWXNQ22JFSWS · pith_short_16: PWXNQ22JFSWSGHWC · pith_short_8: PWXNQ22J

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/PWXNQ22JFSWSGHWCQR5PV2NREY \
  | 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: 7daed86b492cad231ec2847afae9b12628bd87b5d36fd50ad8dcda8e0a9a3154

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6eb94cad18479372a070d8442653313e57dce8c7ba7784f0c5384dbde2a72cf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2012-12-21T14:23:36Z",
    "title_canon_sha256": "6ff7647e9714807bed70b5ae6a0f915f46e7765badf6e070e8e515ca29ac16a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.5457",
    "kind": "arxiv",
    "version": 3
  }
}