Pith Number

pith:3CESDXHV

pith:2015:3CESDXHVIC4KAOFX4ZWV2JOJK6

not attested not anchored not stored refs pending

Cliques in the union of $C_4$-free graphs

Abeer Othman, Eli Berger

arxiv:1511.08772 v1 · 2015-11-27 · 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{3CESDXHVIC4KAOFX4ZWV2JOJK6}

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	2026-05-18T01:25:48.137233Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d88921dcf540b8a038b7e66d5d25c957a776ff20968ade2c04940c3ba862aea1

Aliases

arxiv: 1511.08772 · arxiv_version: 1511.08772v1 · doi: 10.48550/arxiv.1511.08772 · pith_short_12: 3CESDXHVIC4K · pith_short_16: 3CESDXHVIC4KAOFX · pith_short_8: 3CESDXHV

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/3CESDXHVIC4KAOFX4ZWV2JOJK6 \
  | 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: d88921dcf540b8a038b7e66d5d25c957a776ff20968ade2c04940c3ba862aea1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71c1c3b765905e4bc9184b95ad10122e4a0cfbc137f64a5ba87709bce6695622",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-11-27T19:39:05Z",
    "title_canon_sha256": "3f12236aa2904805e570782edf4a8ecd318cea269e7e80b6c65f857563e2e813"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.08772",
    "kind": "arxiv",
    "version": 1
  }
}