Pith Number

pith:NESK5AMM

pith:2022:NESK5AMMVA2XQQER5LUXFWZMYJ

not attested not anchored not stored refs pending

Every graph with no $\mathcal{K}_8^{-4}$ minor is $7$-colorable

Michael Lafferty, Zi-Xia Song

arxiv:2208.07338 v2 · 2022-08-15 · 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{NESK5AMMVA2XQQER5LUXFWZMYJ}

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	2026-07-05T04:50:19.889080Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6924ae818ca835784091eae972db2cc240cbe66aa9e46b32e1c4f446bf30fbf0

Aliases

arxiv: 2208.07338 · arxiv_version: 2208.07338v2 · doi: 10.48550/arxiv.2208.07338 · pith_short_12: NESK5AMMVA2X · pith_short_16: NESK5AMMVA2XQQER · pith_short_8: NESK5AMM

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/NESK5AMMVA2XQQER5LUXFWZMYJ \
  | 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: 6924ae818ca835784091eae972db2cc240cbe66aa9e46b32e1c4f446bf30fbf0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9837c9cdd0844bee346b51f91373b0951bdeaef39ff5186e9d98932a80d17b31",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2022-08-15T17:08:01Z",
    "title_canon_sha256": "8efb0de3b215dab185491feb259e25b25a5118771d0c02664ff37a5cf18146fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2208.07338",
    "kind": "arxiv",
    "version": 2
  }
}