Pith Number

pith:VPFYEGIB

pith:2015:VPFYEGIBMXF24BABLAKQNBMZOD

not attested not anchored not stored refs pending

Choosability and paintability of the lexicographic product of graphs

Bal\'azs Keszegh, Xuding Zhu

arxiv:1502.03977 v2 · 2015-02-13 · 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{VPFYEGIBMXF24BABLAKQNBMZOD}

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	2026-05-18T01:25:15.909312Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abcb82190165cbae0401581506859970c2bf27adcc721632f13a33e7304da0a4

Aliases

arxiv: 1502.03977 · arxiv_version: 1502.03977v2 · doi: 10.48550/arxiv.1502.03977 · pith_short_12: VPFYEGIBMXF2 · pith_short_16: VPFYEGIBMXF24BAB · pith_short_8: VPFYEGIB

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/VPFYEGIBMXF24BABLAKQNBMZOD \
  | 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: abcb82190165cbae0401581506859970c2bf27adcc721632f13a33e7304da0a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c5273873e9e9cd97dfdff64da32b061e39084e0a1ee840966aac85366f16ea36",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-02-13T13:13:11Z",
    "title_canon_sha256": "c25669f3ba001f13a84575b8f2d8feab46756b1fbed90396d603c3cfb3af4386"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.03977",
    "kind": "arxiv",
    "version": 2
  }
}