Pith Number

pith:3GYYIZOP

pith:2018:3GYYIZOPOWVRDABWCC42TKSSQP

not attested not anchored not stored refs pending

Normalized Laplacian spectrum of some generalized subdivision-corona of two regular graphs

Qun Liu, Zhongzhi Zhang

arxiv:1807.03939 v1 · 2018-07-11 · math.CO · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3GYYIZOPOWVRDABWCC42TKSSQP}

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	2026-05-18T00:10:58.594765Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d9b18465cf75ab11803610b9a9aa5283f37f61ab91055d25b5eb1cad3bba0e78

Aliases

arxiv: 1807.03939 · arxiv_version: 1807.03939v1 · doi: 10.48550/arxiv.1807.03939 · pith_short_12: 3GYYIZOPOWVR · pith_short_16: 3GYYIZOPOWVRDABW · pith_short_8: 3GYYIZOP

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/3GYYIZOPOWVRDABWCC42TKSSQP \
  | 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: d9b18465cf75ab11803610b9a9aa5283f37f61ab91055d25b5eb1cad3bba0e78

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e3d61f344dd87b39d98256aa3e1807da7bd81c07e0a995a5f108dbff42fe999",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-07-11T03:16:51Z",
    "title_canon_sha256": "0d3de03fa54e65ded1208b82bf60f0191e5dcb476628fc6ec5aa9868c07084f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.03939",
    "kind": "arxiv",
    "version": 1
  }
}