Pith Number

pith:LO6ZAIV4

pith:2013:LO6ZAIV4WM7VFTNNZHBMF4WAYM

not attested not anchored not stored refs pending

The $b$-Chromatic Number and $f$-Chromatic Vertex Number of Regular Graphs

Amine El Sahili, Hamamache Kheddouci, Mekkia Kouider, Miadoun Mortada

arxiv:1302.4214 v1 · 2013-02-18 · 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{LO6ZAIV4WM7VFTNNZHBMF4WAYM}

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	2026-05-18T03:33:23.700869Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5bbd9022bcb33f52cdadc9c2c2f2c0c31152bf820804a476686fb885280bd630

Aliases

arxiv: 1302.4214 · arxiv_version: 1302.4214v1 · doi: 10.48550/arxiv.1302.4214 · pith_short_12: LO6ZAIV4WM7V · pith_short_16: LO6ZAIV4WM7VFTNN · pith_short_8: LO6ZAIV4

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/LO6ZAIV4WM7VFTNNZHBMF4WAYM \
  | 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: 5bbd9022bcb33f52cdadc9c2c2f2c0c31152bf820804a476686fb885280bd630

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "90ba9ce5cabd0c8537ef3eaae12b3fa3e00f54405778cb3578342a5b25260e09",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-02-18T10:25:28Z",
    "title_canon_sha256": "ec84dcaeed2e0855e2d1d00f8eb660ddd02a52e8e5d9052d71d4c33c36306356"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.4214",
    "kind": "arxiv",
    "version": 1
  }
}