Pith Number

pith:KWQ3KBUE

pith:2013:KWQ3KBUEUFWOEBCHLEH3ICB3MJ

not attested not anchored not stored refs pending

On the number of $K_4$-saturating edges

Hong Liu, J\'ozsef Balogh

arxiv:1312.5248 v2 · 2013-12-18 · 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{KWQ3KBUEUFWOEBCHLEH3ICB3MJ}

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	2026-05-18T02:35:52.233873Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

55a1b50684a16ce20447590fb4083b6240aba1fa3784fd6d4140526bb95e9e53

Aliases

arxiv: 1312.5248 · arxiv_version: 1312.5248v2 · doi: 10.48550/arxiv.1312.5248 · pith_short_12: KWQ3KBUEUFWO · pith_short_16: KWQ3KBUEUFWOEBCH · pith_short_8: KWQ3KBUE

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/KWQ3KBUEUFWOEBCHLEH3ICB3MJ \
  | 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: 55a1b50684a16ce20447590fb4083b6240aba1fa3784fd6d4140526bb95e9e53

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee0a3aa8ef91dd5cdb70609374a8c848389e86294906e950e2480ccb484a28f0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-12-18T18:00:48Z",
    "title_canon_sha256": "4cb856883ee05902e32e0186b9c61e528dc5b82f66891255acbcf5a4bbb1813f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.5248",
    "kind": "arxiv",
    "version": 2
  }
}