Pith Number

pith:LP4CFSJH

pith:2022:LP4CFSJH5P5FASJAN32JSEZAOK

not attested not anchored not stored refs pending

Every graph with no $\mathcal{K}_9^{-6}$ minor is $8$-colorable

Michael Lafferty, Zi-Xia Song

arxiv:2209.05259 v2 · 2022-09-12 · 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{LP4CFSJH5P5FASJAN32JSEZAOK}

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

Every graph with no $K_7^{\vee}$-minor is $6$-colorable

Receipt and verification

First computed	2026-07-05T05:03:39.276900Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5bf822c927ebfa5049206ef499132072be4034c19bbbc02d1a444b06daf2b145

Aliases

arxiv: 2209.05259 · arxiv_version: 2209.05259v2 · doi: 10.48550/arxiv.2209.05259 · pith_short_12: LP4CFSJH5P5F · pith_short_16: LP4CFSJH5P5FASJA · pith_short_8: LP4CFSJH

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/LP4CFSJH5P5FASJAN32JSEZAOK \
  | 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: 5bf822c927ebfa5049206ef499132072be4034c19bbbc02d1a444b06daf2b145

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "abca40e2fdd279efdb604f5083a44db11e6d93a5c10a91b794587a8c6d618a5f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2022-09-12T14:01:23Z",
    "title_canon_sha256": "f4edec8ba7cc26d2884206961703cb57a2c93f847f9f2b768aef9df34f4d5de7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2209.05259",
    "kind": "arxiv",
    "version": 2
  }
}