Pith Number

pith:ZBE4WRZM

pith:2013:ZBE4WRZMXOEKZO7JC6E6OJ4M45

not attested not anchored not stored refs pending

Independence properties in subalgebras of ultraproduct II$_1$ factors

Sorin Popa

arxiv:1308.3982 v3 · 2013-08-19 · 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{ZBE4WRZMXOEKZO7JC6E6OJ4M45}

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	2026-05-18T03:00:39.316290Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c849cb472cbb88acbbe91789e7278ce7743e6753d1fe44920191c621c4273cd6

Aliases

arxiv: 1308.3982 · arxiv_version: 1308.3982v3 · doi: 10.48550/arxiv.1308.3982 · pith_short_12: ZBE4WRZMXOEK · pith_short_16: ZBE4WRZMXOEKZO7J · pith_short_8: ZBE4WRZM

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/ZBE4WRZMXOEKZO7JC6E6OJ4M45 \
  | 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: c849cb472cbb88acbbe91789e7278ce7743e6753d1fe44920191c621c4273cd6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61ff2e547fbfbcc4e9e241fdcf66868e0b17dec64ac9c70068edeb6b661848f2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2013-08-19T11:06:15Z",
    "title_canon_sha256": "3a1fbfb35425c1bb93bae7334da363d02ec2142e64b650e2fd2c24bb47cb09a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.3982",
    "kind": "arxiv",
    "version": 3
  }
}