Pith Number

pith:4JIXPTOW

pith:2013:4JIXPTOW5P56ICAUV2I4GFRNLO

not attested not anchored not stored refs pending

Haagerup approximation property for arbitrary von Neumann algebras

Reiji Tomatsu, Rui Okayasu

arxiv:1312.1033 v7 · 2013-12-04 · 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{4JIXPTOW5P56ICAUV2I4GFRNLO}

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	2026-05-18T02:18:50.004145Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e25177cdd6ebfbe40814ae91c3162d5b84f6b4f284c6c7743b7e066263b192c7

Aliases

arxiv: 1312.1033 · arxiv_version: 1312.1033v7 · doi: 10.48550/arxiv.1312.1033 · pith_short_12: 4JIXPTOW5P56 · pith_short_16: 4JIXPTOW5P56ICAU · pith_short_8: 4JIXPTOW

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/4JIXPTOW5P56ICAUV2I4GFRNLO \
  | 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: e25177cdd6ebfbe40814ae91c3162d5b84f6b4f284c6c7743b7e066263b192c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1e20009de3c363f35d8ae0089d6d8a203ea9e614c76de2d2ad9a70c04d90859",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2013-12-04T06:04:11Z",
    "title_canon_sha256": "c9dc5e4baeaa0665d56038db6b12180254001c906113595acdd77151ce248d57"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.1033",
    "kind": "arxiv",
    "version": 7
  }
}