Pith Number

pith:PZHZDORJ

pith:2011:PZHZDORJDDERACAS7COUZDUTEM

not attested not anchored not stored refs pending

2-Groups that factorise as products of cyclic groups, and regular embeddings of complete bipartite graphs

Gareth Jones, Jin Ho Kwak, Martin Skoviera, Roman Nedela, Shaofei Du

arxiv:1112.2376 v1 · 2011-12-11 · math.GR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PZHZDORJDDERACAS7COUZDUTEM}

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	2026-05-18T04:06:34.611604Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e4f91ba2918c9100812f89d4c8e93233f9381567df74d8a0b632d4a80791419

Aliases

arxiv: 1112.2376 · arxiv_version: 1112.2376v1 · doi: 10.48550/arxiv.1112.2376 · pith_short_12: PZHZDORJDDER · pith_short_16: PZHZDORJDDERACAS · pith_short_8: PZHZDORJ

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/PZHZDORJDDERACAS7COUZDUTEM \
  | 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: 7e4f91ba2918c9100812f89d4c8e93233f9381567df74d8a0b632d4a80791419

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71e2f99acd16de2df122af82df181659865b52b6109d8a60903be78cd8ac877d",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-12-11T17:29:51Z",
    "title_canon_sha256": "329ba147b6eb4bbd4fec878ae5299d5b2996cc5d193d2db537f0c5c5e501354d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.2376",
    "kind": "arxiv",
    "version": 1
  }
}