Pith Number

pith:ZEYVQJJS

pith:2013:ZEYVQJJSNR6AFPFANUY7HU4FLS

not attested not anchored not stored refs pending

Groups having complete bipartite divisor graphs for their conjugacy class sizes

Pablo Spiga, Roghayeh Hafezieh

arxiv:1309.5629 v1 · 2013-09-22 · 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{ZEYVQJJSNR6AFPFANUY7HU4FLS}

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	2026-05-18T03:12:35.724265Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9315825326c7c02bca06d31f3d3855c95ab6fecbe3a7e78dee25489d648f837

Aliases

arxiv: 1309.5629 · arxiv_version: 1309.5629v1 · doi: 10.48550/arxiv.1309.5629 · pith_short_12: ZEYVQJJSNR6A · pith_short_16: ZEYVQJJSNR6AFPFA · pith_short_8: ZEYVQJJS

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/ZEYVQJJSNR6AFPFANUY7HU4FLS \
  | 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: c9315825326c7c02bca06d31f3d3855c95ab6fecbe3a7e78dee25489d648f837

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b5b81d6d93a6469c0e105d592a65368eb7a190aa28e1f21e26a07a19941d9b4",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-09-22T18:48:07Z",
    "title_canon_sha256": "4b32a88997f2b0d390ad9ea0c32af8cb320e803fd7d4fa4d106ad6cd8369a0ab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.5629",
    "kind": "arxiv",
    "version": 1
  }
}