Pith Number

pith:NAYAZLJK

pith:2010:NAYAZLJK4HIDNQBYA7AY4IAQFQ

not attested not anchored not stored refs pending

Laplacian spectral characterization of some graph products

Suijie Wang, Xiaogang Liu

arxiv:1007.2472 v3 · 2010-07-15 · 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{NAYAZLJK4HIDNQBYA7AY4IAQFQ}

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	2026-05-18T00:36:04.370726Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68300cad2ae1d036c03807c18e20102c24f6b37c2e573ab0e2ceba36bf0b6177

Aliases

arxiv: 1007.2472 · arxiv_version: 1007.2472v3 · doi: 10.48550/arxiv.1007.2472 · pith_short_12: NAYAZLJK4HID · pith_short_16: NAYAZLJK4HIDNQBY · pith_short_8: NAYAZLJK

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/NAYAZLJK4HIDNQBYA7AY4IAQFQ \
  | 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: 68300cad2ae1d036c03807c18e20102c24f6b37c2e573ab0e2ceba36bf0b6177

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df6ce1331bf4481ee2554b971986a1610acc5284d1ece61d6741ffae207244ed",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-07-15T04:15:51Z",
    "title_canon_sha256": "360815a3fe54dbd80cf6346323d070243f91a5ea0224a330f3b42b1c27a0be33"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.2472",
    "kind": "arxiv",
    "version": 3
  }
}