Pith Number

pith:NK5VLU5C

pith:2012:NK5VLU5CFZULU3OJBPWE6646LU

not attested not anchored not stored refs pending

Beyond the Vizing's bound for at most seven colors

{\L}ukasz Kowalik, Marcin Kami\'nski

arxiv:1211.5031 v4 · 2012-11-21 · cs.DS · cs.DM · 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{NK5VLU5CFZULU3OJBPWE6646LU}

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	2026-05-18T02:57:33.838143Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6abb55d3a22e68ba6dc90bec4f7b9e5d3bb98ca79d5a85184c06e38d934d9bd6

Aliases

arxiv: 1211.5031 · arxiv_version: 1211.5031v4 · doi: 10.48550/arxiv.1211.5031 · pith_short_12: NK5VLU5CFZUL · pith_short_16: NK5VLU5CFZULU3OJ · pith_short_8: NK5VLU5C

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/NK5VLU5CFZULU3OJBPWE6646LU \
  | 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: 6abb55d3a22e68ba6dc90bec4f7b9e5d3bb98ca79d5a85184c06e38d934d9bd6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1caa30ab1c1b4eeeaa7df613ce63fd8c4a847e14b14ba0e18044c174367ba8af",
    "cross_cats_sorted": [
      "cs.DM",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2012-11-21T13:52:26Z",
    "title_canon_sha256": "9e3cc58d22496f942c8283690fa89b69aff452a1819e7d385c0000149df73748"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.5031",
    "kind": "arxiv",
    "version": 4
  }
}