Pith Number

pith:PFRSYDAJ

pith:2009:PFRSYDAJV7PET67CZENUG5DJFD

not attested not anchored not stored refs pending

Product between ultrafilters and applications to the Connes' embedding problem

L. Paunescu, V. Capraro

arxiv:0911.4978 v6 · 2009-11-25 · math.OA · 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{PFRSYDAJV7PET67CZENUG5DJFD}

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	2026-05-18T03:13:11.225372Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79632c0c09afde49fbe2c91b43746928c5d1e84cdde0f9a4b6c80d400ea9feba

Aliases

arxiv: 0911.4978 · arxiv_version: 0911.4978v6 · doi: 10.48550/arxiv.0911.4978 · pith_short_12: PFRSYDAJV7PE · pith_short_16: PFRSYDAJV7PET67C · pith_short_8: PFRSYDAJ

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/PFRSYDAJV7PET67CZENUG5DJFD \
  | 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: 79632c0c09afde49fbe2c91b43746928c5d1e84cdde0f9a4b6c80d400ea9feba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b51c86c82a5c9236b2190567e165250199df5058063cec9a2fa24220d2d68b2d",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2009-11-25T23:05:26Z",
    "title_canon_sha256": "a0c6fc2cae34ab93df16c5cfd3e1cbf3f72108d263402e1af52ddd4975e8fdf3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.4978",
    "kind": "arxiv",
    "version": 6
  }
}