Pith Number

pith:BO6WPGVK

pith:2011:BO6WPGVKGM5GLX4FE6G33LJ3SY

not attested not anchored not stored refs pending

Unique Cartan decomposition for II_1 factors arising from arbitrary actions of free groups

Sorin Popa, Stefaan Vaes

arxiv:1111.6951 v3 · 2011-11-29 · math.OA · math.DS · 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{BO6WPGVKGM5GLX4FE6G33LJ3SY}

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	2026-05-18T02:56:04.144830Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0bbd679aaa333a65df85278dbdad3b962705a4a10cfe6d5373f1db51da87759b

Aliases

arxiv: 1111.6951 · arxiv_version: 1111.6951v3 · doi: 10.48550/arxiv.1111.6951 · pith_short_12: BO6WPGVKGM5G · pith_short_16: BO6WPGVKGM5GLX4F · pith_short_8: BO6WPGVK

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/BO6WPGVKGM5GLX4FE6G33LJ3SY \
  | 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: 0bbd679aaa333a65df85278dbdad3b962705a4a10cfe6d5373f1db51da87759b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "302431d5d9700211389b9925458e3a26c06a375ccc5d004c7d2a112c6f1df348",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2011-11-29T20:01:08Z",
    "title_canon_sha256": "1206a53bdf40efb629a077d44758afdb70170748e53a98c3068c3b3c1b4b5e56"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.6951",
    "kind": "arxiv",
    "version": 3
  }
}