Pith Number

pith:VXA5CKYK

pith:2011:VXA5CKYKHVBDPTMZ3LCXYTQ6HA

not attested not anchored not stored refs pending

C*-algebras with the weak expectation property and a multivariable analogue of Ando's theorem on the numerical radius

Ali S. Kavruk, Douglas Farenick, Vern I. Paulsen

arxiv:1107.0418 v2 · 2011-07-02 · 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{VXA5CKYKHVBDPTMZ3LCXYTQ6HA}

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	2026-05-18T03:59:49.491565Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

adc1d12b0a3d4237cd99dac57c4e1e382fc829460524b791bd99f0040acda6e3

Aliases

arxiv: 1107.0418 · arxiv_version: 1107.0418v2 · doi: 10.48550/arxiv.1107.0418 · pith_short_12: VXA5CKYKHVBD · pith_short_16: VXA5CKYKHVBDPTMZ · pith_short_8: VXA5CKYK

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/VXA5CKYKHVBDPTMZ3LCXYTQ6HA \
  | 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: adc1d12b0a3d4237cd99dac57c4e1e382fc829460524b791bd99f0040acda6e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a15d146c0dfd8765a65e9701e816d48578495484d1b86685036524f120396061",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2011-07-02T23:26:27Z",
    "title_canon_sha256": "d40eea95198b44f5d2f879067f4250700d6c6584720f6a08be9a095e7cb96a8c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.0418",
    "kind": "arxiv",
    "version": 2
  }
}