Pith Number

pith:4MHXKSDN

pith:2009:4MHXKSDN6SIBXEHC4LQDTRAHVX

not attested not anchored not stored refs pending

Every plane graph of maximum degree 8 has an edge-face 9-colouring

Jean-S\'ebastien Sereni, Mat\v{e}j Stehl\'ik, Ross J. Kang

arxiv:0912.4770 v2 · 2009-12-24 · 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{4MHXKSDN6SIBXEHC4LQDTRAHVX}

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	2026-05-18T03:50:59.422019Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e30f75486df4901b90e2e2e039c407adf80546489be805fdf1018d690be216ea

Aliases

arxiv: 0912.4770 · arxiv_version: 0912.4770v2 · doi: 10.48550/arxiv.0912.4770 · pith_short_12: 4MHXKSDN6SIB · pith_short_16: 4MHXKSDN6SIBXEHC · pith_short_8: 4MHXKSDN

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/4MHXKSDN6SIBXEHC4LQDTRAHVX \
  | 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: e30f75486df4901b90e2e2e039c407adf80546489be805fdf1018d690be216ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b16fabed4c6ab7b4f433dac5f2586f33d633de29981afe56677f3de8cfc06ff5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-12-24T20:24:37Z",
    "title_canon_sha256": "d80296f99c2f119096a3a33ffca1ae9e0d2c0bab31211d5bb00d35dbbfffb273"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.4770",
    "kind": "arxiv",
    "version": 2
  }
}