Pith Number

pith:LWGCHPAP

pith:2011:LWGCHPAP3NVBXGETUHT32TGQMF

not attested not anchored not stored refs pending

Extremal incomplete sets in finite abelian groups

Dan Guo, Guoqing Wang, Qinghong Wang, Yongke Qu

arxiv:1101.4715 v3 · 2011-01-25 · math.CO · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LWGCHPAP3NVBXGETUHT32TGQMF}

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	2026-05-18T04:25:27.800178Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5d8c23bc0fdb6a1b9893a1e7bd4cd06147ae336c3ea63e2666b6c6088fda0051

Aliases

arxiv: 1101.4715 · arxiv_version: 1101.4715v3 · doi: 10.48550/arxiv.1101.4715 · pith_short_12: LWGCHPAP3NVB · pith_short_16: LWGCHPAP3NVBXGET · pith_short_8: LWGCHPAP

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/LWGCHPAP3NVBXGETUHT32TGQMF \
  | 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: 5d8c23bc0fdb6a1b9893a1e7bd4cd06147ae336c3ea63e2666b6c6088fda0051

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1804824f3d93ebe537fccb7e5000cad038ab4583de7a078f01cef8c2d12baec4",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-01-25T04:12:31Z",
    "title_canon_sha256": "8a879084cf98b41e2130cdbe2a6c287f64de7044b05b6dbbffe5f67c42e34051"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.4715",
    "kind": "arxiv",
    "version": 3
  }
}