Pith Number

pith:HM44EFFR

pith:2009:HM44EFFRWS5X2WSBQ7EOYECUAQ

not attested not anchored not stored refs pending

Group measure space decomposition of II_1 factors and W*-superrigidity

Sorin Popa, Stefaan Vaes

arxiv:0906.2765 v2 · 2009-06-15 · 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{HM44EFFRWS5X2WSBQ7EOYECUAQ}

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	2026-05-18T02:13:19.989189Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3b39c214b1b4bb7d5a4187c8ec1054040aa22402851bf23cdea645b6ef8bd7b7

Aliases

arxiv: 0906.2765 · arxiv_version: 0906.2765v2 · doi: 10.48550/arxiv.0906.2765 · pith_short_12: HM44EFFRWS5X · pith_short_16: HM44EFFRWS5X2WSB · pith_short_8: HM44EFFR

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/HM44EFFRWS5X2WSBQ7EOYECUAQ \
  | 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: 3b39c214b1b4bb7d5a4187c8ec1054040aa22402851bf23cdea645b6ef8bd7b7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b9f0e9c477cdc774ebce398ea3f6448f4527224928dd9abc1d52e065651ade91",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2009-06-15T19:04:54Z",
    "title_canon_sha256": "15ebadc5a390e4ea30c64922ae34c46cce32edea143efb2b2bdbeb7d944f7e67"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.2765",
    "kind": "arxiv",
    "version": 2
  }
}