Pith Number

pith:I5UVCW5K

pith:2013:I5UVCW5KZ4E7YYGD2PBTZGPOYN

not attested not anchored not stored refs pending

Notes on C_0-representations and the Haagerup property

Paul Jolissaint

arxiv:1304.6193 v5 · 2013-04-23 · 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{I5UVCW5KZ4E7YYGD2PBTZGPOYN}

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	2026-05-18T03:15:05.953991Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4769515baacf09fc60c3d3c33c99eec36c1463234b763e956344e583478d04e0

Aliases

arxiv: 1304.6193 · arxiv_version: 1304.6193v5 · doi: 10.48550/arxiv.1304.6193 · pith_short_12: I5UVCW5KZ4E7 · pith_short_16: I5UVCW5KZ4E7YYGD · pith_short_8: I5UVCW5K

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/I5UVCW5KZ4E7YYGD2PBTZGPOYN \
  | 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: 4769515baacf09fc60c3d3c33c99eec36c1463234b763e956344e583478d04e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "642e7977caf0ee2ba7a4288c69043ab1a049e41809cc6af1ba24d83d777332a3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-04-23T07:52:42Z",
    "title_canon_sha256": "8f57b00dced37878459e633ef9ab82868f3f3c08754d734f6de764422cb704df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.6193",
    "kind": "arxiv",
    "version": 5
  }
}