Pith Number

pith:RQILXGKN

pith:2008:RQILXGKNO2MIW2O2GSSJNVELJJ

not attested not anchored not stored refs pending

On the fundamental group of II_1 factors and equivalence relations arising from group actions

Sorin Popa, Stefaan Vaes

arxiv:0810.0706 v4 · 2008-10-03 · 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{RQILXGKNO2MIW2O2GSSJNVELJJ}

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	2026-05-18T04:00:49.737735Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8c10bb994d76988b69da34a496d48b4a6c2ccd4010af430403dc75f6828dc2d8

Aliases

arxiv: 0810.0706 · arxiv_version: 0810.0706v4 · doi: 10.48550/arxiv.0810.0706 · pith_short_12: RQILXGKNO2MI · pith_short_16: RQILXGKNO2MIW2O2 · pith_short_8: RQILXGKN

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/RQILXGKNO2MIW2O2GSSJNVELJJ \
  | 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: 8c10bb994d76988b69da34a496d48b4a6c2ccd4010af430403dc75f6828dc2d8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de5cf489db7cf16ad854734d91c92340f6dc8080181e8e6b1db19488b8c99de5",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2008-10-03T20:00:03Z",
    "title_canon_sha256": "bdf187e7181299c72865a97308074c09c26b1365f3dd5c99a1e0c62b7745dfc5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0810.0706",
    "kind": "arxiv",
    "version": 4
  }
}