Pith Number

pith:5ZXOCTV4

pith:2009:5ZXOCTV4LNPZJCGGIN6NKZDHH2

not attested not anchored not stored refs pending

An inner amenable group whose von Neumann algebra does not have property Gamma

Stefaan Vaes

arxiv:0909.1485 v1 · 2009-09-08 · math.OA · math.GR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5ZXOCTV4LNPZJCGGIN6NKZDHH2}

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	2026-05-18T03:52:53.605264Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee6ee14ebc5b5f9488c6437cd564673eb579d4dc9e92db61dc89c358d2eab14a

Aliases

arxiv: 0909.1485 · arxiv_version: 0909.1485v1 · doi: 10.48550/arxiv.0909.1485 · pith_short_12: 5ZXOCTV4LNPZ · pith_short_16: 5ZXOCTV4LNPZJCGG · pith_short_8: 5ZXOCTV4

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/5ZXOCTV4LNPZJCGGIN6NKZDHH2 \
  | 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: ee6ee14ebc5b5f9488c6437cd564673eb579d4dc9e92db61dc89c358d2eab14a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7eb9f73f79f48e3923c3f533222e8c543da66dea9571f758fd91b89d52aa60bc",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2009-09-08T13:16:31Z",
    "title_canon_sha256": "6b59ae8590b1565cadeb25156152620aa0f512e5ff2295b88c9dd3f5d4ff60ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.1485",
    "kind": "arxiv",
    "version": 1
  }
}