Pith Number

pith:I3OECVKC

pith:2025:I3OECVKC4BBKKH4L2ALMJKLWUG

not attested not anchored not stored refs pending

Graphs with girth $2\ell$ and without longer even holes are $3$-colorable

Rong chen

arxiv:2509.01137 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{I3OECVKC4BBKKH4L2ALMJKLWUG}

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	2026-07-05T12:02:54.530689Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46dc415542e042a51f8bd016c4a976a1adbc6fb98861982d24846155fc0703dc

Aliases

arxiv: 2509.01137 · arxiv_version: 2509.01137v1 · doi: 10.48550/arxiv.2509.01137 · pith_short_12: I3OECVKC4BBK · pith_short_16: I3OECVKC4BBKKH4L · pith_short_8: I3OECVKC

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/I3OECVKC4BBKKH4L2ALMJKLWUG \
  | 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: 46dc415542e042a51f8bd016c4a976a1adbc6fb98861982d24846155fc0703dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dbda8ffaab971fd53d16e95e79eab972f41a3e8ccf73276b309ec72796eab44f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-09-01T05:13:24Z",
    "title_canon_sha256": "a1cf3e2add9eef62db7d37ec306d086a5cc3d150e29532b953ac88f12ddc7e7e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.01137",
    "kind": "arxiv",
    "version": 1
  }
}