Pith Number

pith:WCYCGHRF

pith:2008:WCYCGHRFYMTYOOZEJBEQYCJM6S

not attested not anchored not stored refs pending

A Unified Approach to Distance-Two Colouring of Graphs on Surfaces

Jan van den Heuvel, Louis Esperet, Omid Amini

arxiv:0812.1345 v4 · 2008-12-07 · 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{WCYCGHRFYMTYOOZEJBEQYCJM6S}

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.

Cited by

1 paper in Pith

Coloring, List Coloring, and Painting Squares of Graphs (and other related problems)

Receipt and verification

First computed	2026-05-18T01:32:08.766008Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0b0231e25c327873b2448490c092cf4a7f440fb93171ca10fa6aa1cb303ca77

Aliases

arxiv: 0812.1345 · arxiv_version: 0812.1345v4 · doi: 10.48550/arxiv.0812.1345 · pith_short_12: WCYCGHRFYMTY · pith_short_16: WCYCGHRFYMTYOOZE · pith_short_8: WCYCGHRF

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/WCYCGHRFYMTYOOZEJBEQYCJM6S \
  | 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: b0b0231e25c327873b2448490c092cf4a7f440fb93171ca10fa6aa1cb303ca77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2fbba220185418b33d24dc12fc69c1c8161c008403e583c044b22676c697c913",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2008-12-07T13:38:29Z",
    "title_canon_sha256": "378a3b6977fa7d441cb3aab298d47618c6d45999ef70c1380184f811aabb82e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.1345",
    "kind": "arxiv",
    "version": 4
  }
}