Pith Number

pith:BZEVCU5U

pith:2018:BZEVCU5UXQCCEO4G4Q5F47NBLQ

not attested not anchored not stored refs pending

A spectral characterization of the s-clique extension of the square grid graphs

Jack H. Koolen, Muhammad Riaz, Sakander Hayat

arxiv:1806.03593 v1 · 2018-06-10 · 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{BZEVCU5UXQCCEO4G4Q5F47NBLQ}

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	2026-05-18T00:13:42.839659Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e495153b4bc04223b86e43a5e7da15c3a028f172c865fa213c972f3593f93b8

Aliases

arxiv: 1806.03593 · arxiv_version: 1806.03593v1 · doi: 10.48550/arxiv.1806.03593 · pith_short_12: BZEVCU5UXQCC · pith_short_16: BZEVCU5UXQCCEO4G · pith_short_8: BZEVCU5U

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/BZEVCU5UXQCCEO4G4Q5F47NBLQ \
  | 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: 0e495153b4bc04223b86e43a5e7da15c3a028f172c865fa213c972f3593f93b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a760b57d3d4c2b228f3a1d33fc99df86bbbc70a6e86dc5e60f913e52d1a9ca6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-06-10T06:34:01Z",
    "title_canon_sha256": "e0f75d8bd12a9334f8fb6df97bac1072f85bb4be93921bc24c892bbd6f6c4324"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.03593",
    "kind": "arxiv",
    "version": 1
  }
}