Pith Number

pith:J5U2L23J

pith:2024:J5U2L23JCSKKWEDDS6VHT2J7BZ

not attested not anchored not stored refs pending

Coloring of some $(P_2\cup P_4)$-free graphs

Chen Ran, Zhang xiaowen

arxiv:2412.14524 v1 · 2024-12-19 · 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{J5U2L23JCSKKWEDDS6VHT2J7BZ}

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	2026-07-05T09:51:48.782963Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f69a5eb691494ab106397aa79e93f0e6462117a9f0d01feab7f11bee7b6ed3c

Aliases

arxiv: 2412.14524 · arxiv_version: 2412.14524v1 · doi: 10.48550/arxiv.2412.14524 · pith_short_12: J5U2L23JCSKK · pith_short_16: J5U2L23JCSKKWEDD · pith_short_8: J5U2L23J

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/J5U2L23JCSKKWEDDS6VHT2J7BZ \
  | 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: 4f69a5eb691494ab106397aa79e93f0e6462117a9f0d01feab7f11bee7b6ed3c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4cfe0f3a4322ce1910f9ab7cd58a93c74fa36b872240f1b7b8297a41cc91581",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-12-19T04:43:19Z",
    "title_canon_sha256": "88b16bad78cb6980f10cb388486035dc0f0628a0bc8acb396dd81195d0cccfd4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.14524",
    "kind": "arxiv",
    "version": 1
  }
}