Pith Number

pith:4M4QHOO7

pith:2013:4M4QHOO7CQRZ7DFI3V24BYB6FN

not attested not anchored not stored refs pending

Three-coloring triangle-free planar graphs in linear time

Ken-ichi Kawarabayashi, Robin Thomas, Zdenek Dvorak

arxiv:1302.5121 v1 · 2013-02-20 · math.CO · cs.DM · cs.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4M4QHOO7CQRZ7DFI3V24BYB6FN}

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	2026-05-18T03:32:59.633822Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e33903b9df14239f8ca8dd75c0e03e2b4e05b4d40ec439b3bdee5b8dd5087464

Aliases

arxiv: 1302.5121 · arxiv_version: 1302.5121v1 · doi: 10.48550/arxiv.1302.5121 · pith_short_12: 4M4QHOO7CQRZ · pith_short_16: 4M4QHOO7CQRZ7DFI · pith_short_8: 4M4QHOO7

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/4M4QHOO7CQRZ7DFI3V24BYB6FN \
  | 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: e33903b9df14239f8ca8dd75c0e03e2b4e05b4d40ec439b3bdee5b8dd5087464

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1dae853db521bf9b95aef65bf755c9b3b73e491e530c1c19c855256927a9c783",
    "cross_cats_sorted": [
      "cs.DM",
      "cs.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-02-20T21:13:06Z",
    "title_canon_sha256": "49a2a84fe71c29709b88ad542671504397ad9306319fadcd5f0f2eabad1f5bff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.5121",
    "kind": "arxiv",
    "version": 1
  }
}