Pith Number

pith:WX5HIRWL

pith:2012:WX5HIRWL4CYSK2YZLAGUBGTEDD

not attested not anchored not stored refs pending

Domination related parameters in rooted product graphs

Dorota Kuziak, Ismael G. Yero, Magdalena Lemanska

arxiv:1204.0644 v2 · 2012-04-03 · 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{WX5HIRWL4CYSK2YZLAGUBGTEDD}

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	2026-05-18T03:36:36.918898Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5fa7446cbe0b1256b19580d409a6418d8fa98905bc25f05304d0866119bbeea

Aliases

arxiv: 1204.0644 · arxiv_version: 1204.0644v2 · doi: 10.48550/arxiv.1204.0644 · pith_short_12: WX5HIRWL4CYS · pith_short_16: WX5HIRWL4CYSK2YZ · pith_short_8: WX5HIRWL

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/WX5HIRWL4CYSK2YZLAGUBGTEDD \
  | 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: b5fa7446cbe0b1256b19580d409a6418d8fa98905bc25f05304d0866119bbeea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f4c02f98ca4eb0828b1e4aca06f9677144748b1e00235ba1d8c901710d553b5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-04-03T10:20:34Z",
    "title_canon_sha256": "e00001eb85e5f337217754578d7cb208ce75463864c4ceb4309ae0cf1147f35a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.0644",
    "kind": "arxiv",
    "version": 2
  }
}