Pith Number

pith:BO7CLJS5

pith:2018:BO7CLJS5LR6IMF7UTA3UXIBUYB

not attested not anchored not stored refs pending

Conjectured lower bound for the clique number of a graph

Clive Elphick, Pawel Wocjan

arxiv:1804.03752 v2 · 2018-04-10 · 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{BO7CLJS5LR6IMF7UTA3UXIBUYB}

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	2026-05-18T00:08:31.059208Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0bbe25a65d5c7c8617f498374ba034c07c6a1c57be87c3eed4919b6fd6bc4eb3

Aliases

arxiv: 1804.03752 · arxiv_version: 1804.03752v2 · doi: 10.48550/arxiv.1804.03752 · pith_short_12: BO7CLJS5LR6I · pith_short_16: BO7CLJS5LR6IMF7U · pith_short_8: BO7CLJS5

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/BO7CLJS5LR6IMF7UTA3UXIBUYB \
  | 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: 0bbe25a65d5c7c8617f498374ba034c07c6a1c57be87c3eed4919b6fd6bc4eb3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d380b49252a2d73bf06bd4668fd0cfb73a40a33f847a81c3ec48a5dd244f2dd5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-04-10T23:49:56Z",
    "title_canon_sha256": "1b17b5e19d498263924e6dc926a4dab46d029436ec109bf1683d6b1b42bb2ca4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.03752",
    "kind": "arxiv",
    "version": 2
  }
}