Pith Number

pith:LH5OGA24

pith:2025:LH5OGA24JMIRK6T77NMEGJWWF2

not attested not anchored not stored refs pending

On $k$-colorability of $(bull, H)$-free graphs

Ingo Schiermeyer, Magdalena Prorok, Monika Pil\'sniak, Nadzieja Hodur

arxiv:2509.01698 v1 · 2025-09-01 · 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{LH5OGA24JMIRK6T77NMEGJWWF2}

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	2026-07-05T12:03:06.296407Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

59fae3035c4b11157a7ffb584326d62ebfdc52288a228e0e313f940b9ea29822

Aliases

arxiv: 2509.01698 · arxiv_version: 2509.01698v1 · doi: 10.48550/arxiv.2509.01698 · pith_short_12: LH5OGA24JMIR · pith_short_16: LH5OGA24JMIRK6T7 · pith_short_8: LH5OGA24

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/LH5OGA24JMIRK6T77NMEGJWWF2 \
  | 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: 59fae3035c4b11157a7ffb584326d62ebfdc52288a228e0e313f940b9ea29822

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "624e0d89e9c451f4c00b1692f88aa18bca1113ab36e5d5bdcb628e9dcc7c64c6",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-09-01T18:17:45Z",
    "title_canon_sha256": "ad6458423a992177f270bad936d4a81a77719d8c15d9bb5681e969d3c04d5e41"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.01698",
    "kind": "arxiv",
    "version": 1
  }
}