Pith Number

pith:XYFWN7Q3

pith:2012:XYFWN7Q3YNYEHA7HLGRLRIXYLB

not attested not anchored not stored refs pending

On The Critical Number of Finite Groups (II)

Qinghong Wang, Yongke Qu

arxiv:1212.0595 v1 · 2012-12-04 · math.NT · 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{XYFWN7Q3YNYEHA7HLGRLRIXYLB}

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	2026-05-18T03:39:15.653877Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be0b66fe1bc3704383e759a2b8a2f85854215b482715a92e29d67a7d9db30c2d

Aliases

arxiv: 1212.0595 · arxiv_version: 1212.0595v1 · doi: 10.48550/arxiv.1212.0595 · pith_short_12: XYFWN7Q3YNYE · pith_short_16: XYFWN7Q3YNYEHA7H · pith_short_8: XYFWN7Q3

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/XYFWN7Q3YNYEHA7HLGRLRIXYLB \
  | 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: be0b66fe1bc3704383e759a2b8a2f85854215b482715a92e29d67a7d9db30c2d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "33f818b49394718a74427e0ce1520455806d35472d2231e76457dc46dff44a9a",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-12-04T01:26:02Z",
    "title_canon_sha256": "faddcfc9347ba6595b551459d7c2491df0c6a9ccf9d754fc15c2d738ed386501"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.0595",
    "kind": "arxiv",
    "version": 1
  }
}