Pith Number

pith:E3VELSLO

pith:2012:E3VELSLOYGAVJRLOM36U4GH2HV

not attested not anchored not stored refs pending

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

Sorin Popa, Stefaan Vaes

arxiv:1201.2824 v3 · 2012-01-12 · 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{E3VELSLOYGAVJRLOM36U4GH2HV}

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	2026-05-18T02:43:00.976485Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

26ea45c96ec18154c56e66fd4e18fa3d68e0d217b126cdc595562075cb1e85e5

Aliases

arxiv: 1201.2824 · arxiv_version: 1201.2824v3 · doi: 10.48550/arxiv.1201.2824 · pith_short_12: E3VELSLOYGAV · pith_short_16: E3VELSLOYGAVJRLO · pith_short_8: E3VELSLO

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/E3VELSLOYGAVJRLOM36U4GH2HV \
  | 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: 26ea45c96ec18154c56e66fd4e18fa3d68e0d217b126cdc595562075cb1e85e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "560a2c5acd6743903284198596a7068c5490097c889ba8386b3e4d4ddf599ad7",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2012-01-12T08:09:27Z",
    "title_canon_sha256": "9b637c4ab22d85a472d2eb1103fb6869801caf0d69205761ea8a90edcada0510"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.2824",
    "kind": "arxiv",
    "version": 3
  }
}