Pith Number

pith:I2I27KJZ

pith:2008:I2I27KJZQIU3QAQJ77RSBP42BZ

not attested not anchored not stored refs pending

On a class of II_1 factors with at most one Cartan subalgebra II

Narutaka Ozawa, Sorin Popa

arxiv:0807.4270 v2 · 2008-07-27 · 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{I2I27KJZQIU3QAQJ77RSBP42BZ}

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	2026-07-04T15:13:13.335429Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4691afa9398229b80209ffe320bf9a0e565d55efee6d067603c4fc2a46aa9a28

Aliases

arxiv: 0807.4270 · arxiv_version: 0807.4270v2 · doi: 10.48550/arxiv.0807.4270 · pith_short_12: I2I27KJZQIU3 · pith_short_16: I2I27KJZQIU3QAQJ · pith_short_8: I2I27KJZ

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/I2I27KJZQIU3QAQJ77RSBP42BZ \
  | 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: 4691afa9398229b80209ffe320bf9a0e565d55efee6d067603c4fc2a46aa9a28

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dcb13ef8dd38f40c51eedb0095aff95571e000f1bab24e17a045d88952e78366",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2008-07-27T03:29:06Z",
    "title_canon_sha256": "8efec8a09a6f78eb259328cffa6634dfe53284e20c298cde310d83388673ee7a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0807.4270",
    "kind": "arxiv",
    "version": 2
  }
}