Pith Number

pith:6ZYTCNPF

pith:2013:6ZYTCNPF3GTARP25JLVHVJCWE6

not attested not anchored not stored refs pending

Large cliques in sparse random intersection graphs

Mindaugas Bloznelis, Valentas Kurauskas

arxiv:1302.4627 v2 · 2013-02-19 · math.CO · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6ZYTCNPF3GTARP25JLVHVJCWE6}

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	2026-05-18T00:28:03.073427Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f6713135e5d9a608bf5d4aea7aa456279e86083f1d86952ccddfc373f3c0bf37

Aliases

arxiv: 1302.4627 · arxiv_version: 1302.4627v2 · doi: 10.48550/arxiv.1302.4627 · pith_short_12: 6ZYTCNPF3GTA · pith_short_16: 6ZYTCNPF3GTARP25 · pith_short_8: 6ZYTCNPF

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/6ZYTCNPF3GTARP25JLVHVJCWE6 \
  | 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: f6713135e5d9a608bf5d4aea7aa456279e86083f1d86952ccddfc373f3c0bf37

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f29c46a8c1f6dee422604e12a26d9de84b372d34f9f2812c63daee4d380510d",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-02-19T14:50:30Z",
    "title_canon_sha256": "d1c7675ab72ba00f654ad1adb3a04cbbaa18c3e172e91df69d54102f0d9314d3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.4627",
    "kind": "arxiv",
    "version": 2
  }
}