Pith Number

pith:FGYNXGZK

pith:2011:FGYNXGZKFC32JZ2VN3HSIH33EU

not attested not anchored not stored refs pending

Groups generated by a finite Engel set

Alireza Abdollahi, Antonio Tortora, Rolf Brandl

arxiv:1109.5439 v1 · 2011-09-26 · 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{FGYNXGZKFC32JZ2VN3HSIH33EU}

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	2026-05-18T04:12:19.795871Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

29b0db9b2a28b7a4e7556ecf241f7b251b6290a593f624a483e9647719ffdbbb

Aliases

arxiv: 1109.5439 · arxiv_version: 1109.5439v1 · doi: 10.48550/arxiv.1109.5439 · pith_short_12: FGYNXGZKFC32 · pith_short_16: FGYNXGZKFC32JZ2V · pith_short_8: FGYNXGZK

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/FGYNXGZKFC32JZ2VN3HSIH33EU \
  | 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: 29b0db9b2a28b7a4e7556ecf241f7b251b6290a593f624a483e9647719ffdbbb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5eb0ed9aba4e56ca3136771878041fd01e3a05a396431a4feb0417b72cc5c405",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-09-26T04:01:21Z",
    "title_canon_sha256": "9337ac2a4ef33bd06194e333faf6b0ddb3f724f9ed733bc44d8b3767f5a9a00b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.5439",
    "kind": "arxiv",
    "version": 1
  }
}