Pith Number

pith:JW5UOSXL

pith:2002:JW5UOSXLCQWI5C3NL56NDBPK7V

not attested not anchored not stored refs pending

On a Class of Type II$_1$ Factors with Betti Numbers Invariants

Sorin Popa

arxiv:math/0209130 v6 · 2002-09-11 · math.OA · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JW5UOSXLCQWI5C3NL56NDBPK7V}

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	2026-07-04T14:36:26.129276Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4dbb474aeb142c8e8b6d5f7cd185eafd540d38decb1dec4b15354e770cd1b6fd

Aliases

arxiv: math/0209130 · arxiv_version: math/0209130v6 · doi: 10.48550/arxiv.math/0209130 · pith_short_12: JW5UOSXLCQWI · pith_short_16: JW5UOSXLCQWI5C3N · pith_short_8: JW5UOSXL

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/JW5UOSXLCQWI5C3NL56NDBPK7V \
  | 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: 4dbb474aeb142c8e8b6d5f7cd185eafd540d38decb1dec4b15354e770cd1b6fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c47841511fd0014e64406bd34a12e5b3ebe534b6c45c6ba25f144f6a5e66bfa",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.OA",
    "submitted_at": "2002-09-11T16:17:55Z",
    "title_canon_sha256": "312417eae8c384c10d01491055578f474889a47d37eaf55452d54702d6043917"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0209130",
    "kind": "arxiv",
    "version": 6
  }
}