Pith Number

pith:TLUVJ54E

pith:2017:TLUVJ54EXAEFJE7SHM6PDHJUBJ

not attested not anchored not stored refs pending

The square of a planar cubic graph is $7$-colorable

Carsten Thomassen

arxiv:1708.04406 v1 · 2017-08-15 · 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{TLUVJ54EXAEFJE7SHM6PDHJUBJ}

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	2026-05-18T00:37:59.396846Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ae954f784b8085493f23b3cf19d340a5120b06c15cf5374353133dd7830f86d

Aliases

arxiv: 1708.04406 · arxiv_version: 1708.04406v1 · doi: 10.48550/arxiv.1708.04406 · pith_short_12: TLUVJ54EXAEF · pith_short_16: TLUVJ54EXAEFJE7S · pith_short_8: TLUVJ54E

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/TLUVJ54EXAEFJE7SHM6PDHJUBJ \
  | 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: 9ae954f784b8085493f23b3cf19d340a5120b06c15cf5374353133dd7830f86d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "91079de6a0f56a6d66b5469ef6b291f4ac44e94249f5fc925c6462661028ba69",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-08-15T06:02:54Z",
    "title_canon_sha256": "25a7687f2f6db3bc2a0024497ea18a693d3fe981894596f87dd23f7eb3ff7992"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.04406",
    "kind": "arxiv",
    "version": 1
  }
}