Pith Number

pith:C72CKME3

pith:2025:C72CKME3YQ5ZJ6MMRF6RQTZU6H

not attested not anchored not stored refs pending

On the $4$-clique cover number of graphs

Jialin He, Tianying Xie, Yihan Chen

arxiv:2506.10478 v1 · 2025-06-12 · 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{C72CKME3YQ5ZJ6MMRF6RQTZU6H}

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	2026-07-05T11:20:24.581479Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

17f425309bc43b94f98c897d184f34f1d4e6b30cdd444c0430e2b1c20cfa5c14

Aliases

arxiv: 2506.10478 · arxiv_version: 2506.10478v1 · doi: 10.48550/arxiv.2506.10478 · pith_short_12: C72CKME3YQ5Z · pith_short_16: C72CKME3YQ5ZJ6MM · pith_short_8: C72CKME3

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/C72CKME3YQ5ZJ6MMRF6RQTZU6H \
  | 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: 17f425309bc43b94f98c897d184f34f1d4e6b30cdd444c0430e2b1c20cfa5c14

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "efae853917fe66d8f458c5c79b30d7de6bce9f2d42939a48ce9c0a4c9d8b0420",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-06-12T08:30:34Z",
    "title_canon_sha256": "a45f2a4eec74dea596daf0b53820736110ef4cb84b43cfe304b1019bd7e30939"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.10478",
    "kind": "arxiv",
    "version": 1
  }
}