Pith Number

pith:ATY36KOJ

pith:2010:ATY36KOJEPOSXJHFRYVST4RZOY

not attested not anchored not stored refs pending

Higher commutativity and nilpotency in finite groups

Enrique Torres-Giese

arxiv:1005.3876 v1 · 2010-05-21 · 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{ATY36KOJEPOSXJHFRYVST4RZOY}

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	2026-05-18T02:58:02.156689Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04f1bf29c923dd2ba4e58e2b29f239760a735a5a812a9c0a6ec6fcf9f8d38f5b

Aliases

arxiv: 1005.3876 · arxiv_version: 1005.3876v1 · doi: 10.48550/arxiv.1005.3876 · pith_short_12: ATY36KOJEPOS · pith_short_16: ATY36KOJEPOSXJHF · pith_short_8: ATY36KOJ

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/ATY36KOJEPOSXJHFRYVST4RZOY \
  | 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: 04f1bf29c923dd2ba4e58e2b29f239760a735a5a812a9c0a6ec6fcf9f8d38f5b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0dbfdeea5ce26782ea6b35c505c3e331622ee5d3a7dbfb07de3654e740d32d5e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-05-21T03:12:43Z",
    "title_canon_sha256": "de48c99b98e0640dc3cf887ae16015d3b9748f29bebc37ed4d2f0956cea75e33"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.3876",
    "kind": "arxiv",
    "version": 1
  }
}