Pith Number

pith:Z3FVF2KH

pith:2016:Z3FVF2KHW2BQXKARNEXLSOE6K6

not attested not anchored not stored refs pending

Improper coloring of graphs with no odd clique minor

Dong Yeap Kang, Sang-il Oum

arxiv:1612.05372 v3 · 2016-12-16 · 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{Z3FVF2KHW2BQXKARNEXLSOE6K6}

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	2026-05-17T23:43:24.024216Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cecb52e947b6830ba811692eb9389e57919725131c195eed30f2abef6fa5e3f1

Aliases

arxiv: 1612.05372 · arxiv_version: 1612.05372v3 · doi: 10.48550/arxiv.1612.05372 · pith_short_12: Z3FVF2KHW2BQ · pith_short_16: Z3FVF2KHW2BQXKAR · pith_short_8: Z3FVF2KH

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/Z3FVF2KHW2BQXKARNEXLSOE6K6 \
  | 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: cecb52e947b6830ba811692eb9389e57919725131c195eed30f2abef6fa5e3f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dfd1c70b9a4baea1f6907813fa2f46328bea9fc28838d1abe09265a13ac6f577",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-12-16T05:30:52Z",
    "title_canon_sha256": "1280155948142077a615329644d918405aa3d23845bdcf8057615940fcd4bb22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.05372",
    "kind": "arxiv",
    "version": 3
  }
}