Pith Number

pith:QNI2QLZT

pith:2015:QNI2QLZTTWYHZHC6ZXUQMBSLCQ

not attested not anchored not stored refs pending

Haagerup approximation property via bimodules

Narutaka Ozawa, Reiji Tomatsu, Rui Okayasu

arxiv:1501.06293 v2 · 2015-01-26 · math.OA · math.GR · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QNI2QLZTTWYHZHC6ZXUQMBSLCQ}

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	2026-05-18T02:27:31.547148Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8351a82f339db07c9c5ecde906064b140f9b53268a0522966ab40709bd99f679

Aliases

arxiv: 1501.06293 · arxiv_version: 1501.06293v2 · doi: 10.48550/arxiv.1501.06293 · pith_short_12: QNI2QLZTTWYH · pith_short_16: QNI2QLZTTWYHZHC6 · pith_short_8: QNI2QLZT

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/QNI2QLZTTWYHZHC6ZXUQMBSLCQ \
  | 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: 8351a82f339db07c9c5ecde906064b140f9b53268a0522966ab40709bd99f679

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3981674a3ffa97d6355801c6dd378cc707b31b3b88de4c58bcf5c8a2cc192fb4",
    "cross_cats_sorted": [
      "math.GR",
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-01-26T09:23:56Z",
    "title_canon_sha256": "45014adb2b95deb6958bb5facae5921c53b1e1bad7b593a8e14311d14c9905ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.06293",
    "kind": "arxiv",
    "version": 2
  }
}