Pith Number

pith:B4ODT57U

pith:2012:B4ODT57UDXRQD5SNFJSYTGBRVY

not attested not anchored not stored refs pending

Groups associated to $II_1$-factors

Nathanial P. Brown, Valerio Capraro

arxiv:1205.2862 v3 · 2012-05-13 · math.OA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B4ODT57UDXRQD5SNFJSYTGBRVY}

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	2026-05-18T03:13:10.921745Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f1c39f7f41de301f64d2a65899831ae3e74109c54c9399e730037d466eace07

Aliases

arxiv: 1205.2862 · arxiv_version: 1205.2862v3 · doi: 10.48550/arxiv.1205.2862 · pith_short_12: B4ODT57UDXRQ · pith_short_16: B4ODT57UDXRQD5SN · pith_short_8: B4ODT57U

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/B4ODT57UDXRQD5SNFJSYTGBRVY \
  | 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: 0f1c39f7f41de301f64d2a65899831ae3e74109c54c9399e730037d466eace07

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c25068393aa4d5a161c21152a25184af323ab3bc4decfc39414c7f724f37f8c",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2012-05-13T14:08:55Z",
    "title_canon_sha256": "9c8b7f24a309173fb6bce4335894f8408b3da21ec714909e6ff0b6f9350774b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.2862",
    "kind": "arxiv",
    "version": 3
  }
}