Pith Number

pith:Y25GWFVE

pith:2026:Y25GWFVE57PO35EQUEZBXRYCWH

not attested not anchored not stored refs pending

ICC property(T) groups without W$^*$-superrigidity

Shuoxing Zhou

arxiv:2608.02327 v1 · 2026-08-03 · 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{Y25GWFVE57PO35EQUEZBXRYCWH}

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	2026-08-04T02:11:49.347790Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c6ba6b16a4efdeedf490a1321bc702b1fc54e8b4ccc9c40163f8beb3ffb2715c

Aliases

arxiv: 2608.02327 · arxiv_version: 2608.02327v1 · doi: 10.48550/arxiv.2608.02327 · pith_short_12: Y25GWFVE57PO · pith_short_16: Y25GWFVE57PO35EQ · pith_short_8: Y25GWFVE

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/Y25GWFVE57PO35EQUEZBXRYCWH \
  | 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: c6ba6b16a4efdeedf490a1321bc702b1fc54e8b4ccc9c40163f8beb3ffb2715c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be0cc727c296980f0e6f878de8dde2d70e3932ae07c1de9e5f63349258d906af",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-08-03T14:50:28Z",
    "title_canon_sha256": "fd378a4ea5bcfe92dba38ba52d4cf2660557769d8ca8516f497fcf6416388ee9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.02327",
    "kind": "arxiv",
    "version": 1
  }
}