Pith Number

pith:BNGWA3LG

pith:2012:BNGWA3LGEKUNJZGZPF2TE75ZMD

not attested not anchored not stored refs pending

On the Cartesian product of non well-covered graphs

Bert L. Hartnell, Douglas F. Rall

arxiv:1204.6681 v1 · 2012-04-30 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BNGWA3LGEKUNJZGZPF2TE75ZMD}

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	2026-05-18T03:56:44.132894Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b4d606d6622a8d4e4d97975327fb960c9507c8bd5ee28fbe1094c0431eb8dfa

Aliases

arxiv: 1204.6681 · arxiv_version: 1204.6681v1 · doi: 10.48550/arxiv.1204.6681 · pith_short_12: BNGWA3LGEKUN · pith_short_16: BNGWA3LGEKUNJZGZ · pith_short_8: BNGWA3LG

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/BNGWA3LGEKUNJZGZPF2TE75ZMD \
  | 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: 0b4d606d6622a8d4e4d97975327fb960c9507c8bd5ee28fbe1094c0431eb8dfa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "28e1ef82a198dd6b4fb197c47683417dc08282dae331cd47567913ba237aeb0c",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-04-30T16:09:46Z",
    "title_canon_sha256": "674e4ee1848d4f39e88ffce7baafe96bb7f3c84720bf41b2c2b9e2237a9ae227"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.6681",
    "kind": "arxiv",
    "version": 1
  }
}