Pith Number

pith:WKOSDIVQ

pith:2025:WKOSDIVQT2UBYVB2VVESTR3EVR

not attested not anchored not stored refs pending

Perfect divisions in ($P_2 \cup P_4$, bull)-free graphs

Hongyang Wang, Lizhong Chen

arxiv:2507.18506 v2 · 2025-07-24 · 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{WKOSDIVQT2UBYVB2VVESTR3EVR}

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	2026-07-05T11:51:32.703928Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b29d21a2b09ea81c543aad4929c764ac52b9902cbd6dde0ad5b4eddeebf1ac41

Aliases

arxiv: 2507.18506 · arxiv_version: 2507.18506v2 · doi: 10.48550/arxiv.2507.18506 · pith_short_12: WKOSDIVQT2UB · pith_short_16: WKOSDIVQT2UBYVB2 · pith_short_8: WKOSDIVQ

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/WKOSDIVQT2UBYVB2VVESTR3EVR \
  | 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: b29d21a2b09ea81c543aad4929c764ac52b9902cbd6dde0ad5b4eddeebf1ac41

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8632b6216655ef73eae4963aeda25ec693dcc1e1462367313477355455a9dff8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-24T15:24:59Z",
    "title_canon_sha256": "e63f48c2a3be5ee04abe38b027534271b83a8059b8d2704aeb7ca55d3e483235"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.18506",
    "kind": "arxiv",
    "version": 2
  }
}