Pith Number

pith:7XVR25HN

pith:2013:7XVR25HNDFHJES4XXIXYGHNAN2

not attested not anchored not stored refs pending

A L\'evy-Khinchin formula for free groups

S{\o}ren Knudby, Uffe Haagerup

arxiv:1304.5763 v2 · 2013-04-21 · math.GR · math.FA · math.OA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7XVR25HNDFHJES4XXIXYGHNAN2}

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	2026-05-18T01:04:33.698892Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fdeb1d74ed194e924b97ba2f831da06ea17f3b8ff8467cd464865b858122fa8f

Aliases

arxiv: 1304.5763 · arxiv_version: 1304.5763v2 · doi: 10.48550/arxiv.1304.5763 · pith_short_12: 7XVR25HNDFHJ · pith_short_16: 7XVR25HNDFHJES4X · pith_short_8: 7XVR25HN

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/7XVR25HNDFHJES4XXIXYGHNAN2 \
  | 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: fdeb1d74ed194e924b97ba2f831da06ea17f3b8ff8467cd464865b858122fa8f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "16600e5afe0d8455b14c09b554022030be6afd3b4ae3a38497bd62402b066c98",
    "cross_cats_sorted": [
      "math.FA",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-04-21T16:32:28Z",
    "title_canon_sha256": "a5f96d3547779cd6b7a447f45894fb902afc368247c24953e507205bed805a43"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.5763",
    "kind": "arxiv",
    "version": 2
  }
}