Pith Number

pith:63ZY6LMC

pith:2026:63ZY6LMCNHTUKUKIW5XS3ISTRB

not attested not anchored not stored refs pending

The Balanced Four-Color Theorem

Hirotaka Yoneda, Ken-ichi Kawarabayashi, Masataka Yoneda

arxiv:2607.13025 v1 · 2026-07-14 · cs.DS · 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{63ZY6LMCNHTUKUKIW5XS3ISTRB}

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	2026-07-15T01:22:32.078762Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f6f38f2d8269e7455148b76f2da253884dd29e2bab2e13af8fdb0fd959b53510

Aliases

arxiv: 2607.13025 · arxiv_version: 2607.13025v1 · doi: 10.48550/arxiv.2607.13025 · pith_short_12: 63ZY6LMCNHTU · pith_short_16: 63ZY6LMCNHTUKUKI · pith_short_8: 63ZY6LMC

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/63ZY6LMCNHTUKUKIW5XS3ISTRB \
  | 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: f6f38f2d8269e7455148b76f2da253884dd29e2bab2e13af8fdb0fd959b53510

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f24070b7d6ec5d5503b99ba878082a58fbcb4d2ff3556bab083ceeb403694527",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-07-14T17:58:34Z",
    "title_canon_sha256": "df3106d8fe7fb342aceb1914a65008acd40a2713cbfff4f2e09e41e7b45b14f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.13025",
    "kind": "arxiv",
    "version": 1
  }
}