Pith Number

pith:EZABFM5I

pith:2002:EZABFM5I6VP2PKZCICQOIMQOE2

not attested not anchored not stored refs pending

On the Fundamental Group of Type II$_1$ Factors

Sorin Popa

arxiv:math/0210467 v1 · 2002-10-30 · 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{EZABFM5I6VP2PKZCICQOIMQOE2}

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	2026-07-04T14:36:41.276970Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

264012b3a8f55fa7ab2240a0e4320e269e0bce51c9d4c81bba90b99c566e0826

Aliases

arxiv: math/0210467 · arxiv_version: math/0210467v1 · doi: 10.48550/arxiv.math/0210467 · pith_short_12: EZABFM5I6VP2 · pith_short_16: EZABFM5I6VP2PKZC · pith_short_8: EZABFM5I

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/EZABFM5I6VP2PKZCICQOIMQOE2 \
  | 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: 264012b3a8f55fa7ab2240a0e4320e269e0bce51c9d4c81bba90b99c566e0826

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f7b09cc1e3ab9301d461d01d3cf4670a9e90f3139157399e36b75bddc7e56ef8",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.OA",
    "submitted_at": "2002-10-30T19:02:07Z",
    "title_canon_sha256": "e63032a17ac8a0682812bb3a7404cd015574d71d7876a1223f8147a6d6d0b0aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0210467",
    "kind": "arxiv",
    "version": 1
  }
}