Pith Number

pith:BZE3QO5Q

pith:2013:BZE3QO5QJE3ZPMVGQM5257CF4J

not attested not anchored not stored refs pending

Large and symmetric: The Khukhro--Makarenko theorem on laws --- without laws

Anton A. Klyachko, Maria V. Milentyeva

arxiv:1309.0571 v4 · 2013-09-03 · math.GR · math.CO · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BZE3QO5QJE3ZPMVGQM5257CF4J}

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	2026-05-18T02:31:36.181371Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e49b83bb0493797b2a6833baefc45e2500204f797a3fbd78a7b217815faf809

Aliases

arxiv: 1309.0571 · arxiv_version: 1309.0571v4 · doi: 10.48550/arxiv.1309.0571 · pith_short_12: BZE3QO5QJE3Z · pith_short_16: BZE3QO5QJE3ZPMVG · pith_short_8: BZE3QO5Q

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/BZE3QO5QJE3ZPMVGQM5257CF4J \
  | 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: 0e49b83bb0493797b2a6833baefc45e2500204f797a3fbd78a7b217815faf809

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20ddda5119c9436b198678319a24f317d1749c3246fa4cec80c41859c1003737",
    "cross_cats_sorted": [
      "math.CO",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-09-03T01:16:36Z",
    "title_canon_sha256": "8e2aa573835243d0cd65539b380d4419978ea820c7c73a3eee243c66be5a8f84"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.0571",
    "kind": "arxiv",
    "version": 4
  }
}