Pith Number

pith:S4IO3D6N

pith:2019:S4IO3D6NPFVUB4MULV746VZIOU

not attested not anchored not stored refs pending

Clustered Coloring of Graphs Excluding a Subgraph and a Minor

Chun-Hung Liu, David R. Wood

arxiv:1905.09495 v4 · 2019-05-23 · 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{S4IO3D6NPFVUB4MULV746VZIOU}

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

3-Colouring Planar Graphs

Receipt and verification

First computed	2026-07-05T03:37:36.881502Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9710ed8fcd796b40f1945d7fcf57287536cdb344852c696b75b48bee426e2bd9

Aliases

arxiv: 1905.09495 · arxiv_version: 1905.09495v4 · doi: 10.48550/arxiv.1905.09495 · pith_short_12: S4IO3D6NPFVU · pith_short_16: S4IO3D6NPFVUB4MU · pith_short_8: S4IO3D6N

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/S4IO3D6NPFVUB4MULV746VZIOU \
  | 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: 9710ed8fcd796b40f1945d7fcf57287536cdb344852c696b75b48bee426e2bd9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f6b2c580db4fe164ccb72b494680c409c2ef166c843388427a09c22a086907dd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-05-23T06:40:54Z",
    "title_canon_sha256": "99a4f9c65b176ac3cc9c99b5b7702e31ec17fa7abe511ccd0206e911d105b8f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.09495",
    "kind": "arxiv",
    "version": 4
  }
}