Pith Number

pith:7VBLRP3L

pith:2012:7VBLRP3LC42KFFQ45VMLTOPWOK

not attested not anchored not stored refs pending

Minimum Number of k-Cliques in Graphs with Bounded Independence Number

Emil R. Vaughan, Oleg Pikhurko

arxiv:1203.4393 v4 · 2012-03-20 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7VBLRP3LC42KFFQ45VMLTOPWOK}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T02:21:16.942092Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd42b8bf6b1734a2961ced58b9b9f672b66c443fa4f07eacb42777ae9043d62e

Aliases

arxiv: 1203.4393 · arxiv_version: 1203.4393v4 · doi: 10.48550/arxiv.1203.4393 · pith_short_12: 7VBLRP3LC42K · pith_short_16: 7VBLRP3LC42KFFQ4 · pith_short_8: 7VBLRP3L

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/7VBLRP3LC42KFFQ45VMLTOPWOK \
  | 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: fd42b8bf6b1734a2961ced58b9b9f672b66c443fa4f07eacb42777ae9043d62e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a0d2029221c11400d9b2ca5e55c3176becd2b2ffb3e998781d808ff24e93aa0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-03-20T11:11:40Z",
    "title_canon_sha256": "08726b9eeb93110e5e87c0ffea4d42c0421e5280419d242b8ecb433bc3b33267"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.4393",
    "kind": "arxiv",
    "version": 4
  }
}