Pith Number

pith:XSPALUM4

pith:2013:XSPALUM4SSSOK42CHA7YPU4ZDZ

not attested not anchored not stored refs pending

The maximum number of complete subgraphs in a graph with given maximum degree

A.J. Radcliffe, Jonathan Cutler

arxiv:1306.1803 v1 · 2013-06-07 · 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{XSPALUM4SSSOK42CHA7YPU4ZDZ}

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	2026-05-18T03:21:32.301603Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc9e05d19c94a4e57342383f87d3991e60df9c8fbde5370b9532051523f77f17

Aliases

arxiv: 1306.1803 · arxiv_version: 1306.1803v1 · doi: 10.48550/arxiv.1306.1803 · pith_short_12: XSPALUM4SSSO · pith_short_16: XSPALUM4SSSOK42C · pith_short_8: XSPALUM4

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/XSPALUM4SSSOK42CHA7YPU4ZDZ \
  | 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: bc9e05d19c94a4e57342383f87d3991e60df9c8fbde5370b9532051523f77f17

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef904514f0d90caa636c373b29697a50bfeadad9a69d9d1ab2056b3b8795ce5d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-06-07T18:29:51Z",
    "title_canon_sha256": "043c38591a325ab266816af73c967c05d508c0a0a6b5aac82fc6900595690240"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.1803",
    "kind": "arxiv",
    "version": 1
  }
}