Pith Number

pith:EOWMHZBB

pith:2012:EOWMHZBBQSJ3O67NE3MSXWXSJD

not attested not anchored not stored refs pending

Direct products of finite groups as unions of proper subgroups

Andrea Lucchini, Martino Garonzi

arxiv:1211.5346 v1 · 2012-11-22 · 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{EOWMHZBBQSJ3O67NE3MSXWXSJD}

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	2026-05-18T03:40:04.630152Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

23acc3e4218493b77bed26d92bdaf248e394277282923c867c65e8873ba5f6a1

Aliases

arxiv: 1211.5346 · arxiv_version: 1211.5346v1 · doi: 10.48550/arxiv.1211.5346 · pith_short_12: EOWMHZBBQSJ3 · pith_short_16: EOWMHZBBQSJ3O67N · pith_short_8: EOWMHZBB

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/EOWMHZBBQSJ3O67NE3MSXWXSJD \
  | 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: 23acc3e4218493b77bed26d92bdaf248e394277282923c867c65e8873ba5f6a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a40fb397f2db0c1570731eeea84e3062d5b127009d2a7ad787f55fcb4208647",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-11-22T18:01:13Z",
    "title_canon_sha256": "e86345f0b9cb6411b3651869ce5e39bef221b866213b1d3dc87c7a355df699a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.5346",
    "kind": "arxiv",
    "version": 1
  }
}