Pith Number

pith:4K3PINVQ

pith:2003:4K3PINVQKIVQOGCUFW4RALKS5Z

not attested not anchored not stored refs pending

Some prime factorization results for type II_1 factors

Narutaka Ozawa, Sorin Popa

arxiv:math/0302240 v2 · 2003-02-19 · 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{4K3PINVQKIVQOGCUFW4RALKS5Z}

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	2026-07-04T16:41:40.109470Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2b6f436b0522b0718542db9102d52ee632bbc7ec37d529c770c9f2d39370e3b

Aliases

arxiv: math/0302240 · arxiv_version: math/0302240v2 · doi: 10.48550/arxiv.math/0302240 · pith_short_12: 4K3PINVQKIVQ · pith_short_16: 4K3PINVQKIVQOGCU · pith_short_8: 4K3PINVQ

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/4K3PINVQKIVQOGCUFW4RALKS5Z \
  | 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: e2b6f436b0522b0718542db9102d52ee632bbc7ec37d529c770c9f2d39370e3b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aeb46063b00a35cf1e1035443f6b36c0b8218c1fd09e91c74395c7d92d08f8e7",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.OA",
    "submitted_at": "2003-02-19T20:02:39Z",
    "title_canon_sha256": "afdc73e92fd1cad4f801845824e3e9d80feff3de8f3d28af892090102b4a4ed6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0302240",
    "kind": "arxiv",
    "version": 2
  }
}