Pith Number

pith:PW2VCPQC

pith:2025:PW2VCPQCMRRK25AJWBFB52HP4R

not attested not anchored not stored refs pending

Optimal $\chi$-boundness of $\ell$-holed graphs

Rong Wu, Yan Wang

arxiv:2508.07034 v1 · 2025-08-09 · 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{PW2VCPQCMRRK25AJWBFB52HP4R}

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

Graphs with girth 8 and without longer even holes are 3-colorable

Receipt and verification

First computed	2026-07-05T11:51:39.707724Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7db5513e026462ad7409b04a1ee8efe464764a7ea005e32ff8b7c88775930d71

Aliases

arxiv: 2508.07034 · arxiv_version: 2508.07034v1 · doi: 10.48550/arxiv.2508.07034 · pith_short_12: PW2VCPQCMRRK · pith_short_16: PW2VCPQCMRRK25AJ · pith_short_8: PW2VCPQC

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/PW2VCPQCMRRK25AJWBFB52HP4R \
  | 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: 7db5513e026462ad7409b04a1ee8efe464764a7ea005e32ff8b7c88775930d71

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26666f3ee99d9e100685422b0e7ead1f3c9e75ccbb743f82fd30796862c7ac86",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-08-09T16:13:21Z",
    "title_canon_sha256": "89882a766afb15668c4bbbd66878073c0dcdb8d7e6bdc175113f514dc2eefb53"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.07034",
    "kind": "arxiv",
    "version": 1
  }
}