Pith Number

pith:Z42UQF2Y

pith:2013:Z42UQF2YIQUPOAOQ56XOHLROW2

not attested not anchored not stored refs pending

On finite groups in which coprime commutators are covered by few cyclic subgroups

Cristina Acciarri, Pavel Shumyatsky

arxiv:1311.6148 v2 · 2013-11-24 · 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{Z42UQF2YIQUPOAOQ56XOHLROW2}

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	2026-05-18T02:59:18.009740Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf354817584428f701d0efaee3ae2eb692cff791484761feb665a222fc7787fc

Aliases

arxiv: 1311.6148 · arxiv_version: 1311.6148v2 · doi: 10.48550/arxiv.1311.6148 · pith_short_12: Z42UQF2YIQUP · pith_short_16: Z42UQF2YIQUPOAOQ · pith_short_8: Z42UQF2Y

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/Z42UQF2YIQUPOAOQ56XOHLROW2 \
  | 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: cf354817584428f701d0efaee3ae2eb692cff791484761feb665a222fc7787fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4180e30b515d7c7cad23e407e94df18b804e8e0dda4919e7aaedf2bdd69fb9f5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-11-24T17:49:27Z",
    "title_canon_sha256": "7ad8b437aa4d0abe661e99036e54caf85560b64591d6db56786b052ba7afa1ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.6148",
    "kind": "arxiv",
    "version": 2
  }
}