Pith Number

pith:YNN3AGYO

pith:2015:YNN3AGYO3AZXGWWBJWIIP4TQMI

not attested not anchored not stored refs pending

The normalized Laplacian spectrum of subdivisions of a graph

Francesc Comellas, Pinchen Xie, Zhongzhi Zhang

arxiv:1510.02394 v1 · 2015-10-07 · math.CO · cond-mat.stat-mech · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YNN3AGYO3AZXGWWBJWIIP4TQMI}

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	2026-05-18T01:14:29.226132Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c35bb01b0ed833735ac14d9087f2706201d408f760e25d125689f49b97608e53

Aliases

arxiv: 1510.02394 · arxiv_version: 1510.02394v1 · doi: 10.48550/arxiv.1510.02394 · pith_short_12: YNN3AGYO3AZX · pith_short_16: YNN3AGYO3AZXGWWB · pith_short_8: YNN3AGYO

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/YNN3AGYO3AZXGWWBJWIIP4TQMI \
  | 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: c35bb01b0ed833735ac14d9087f2706201d408f760e25d125689f49b97608e53

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "48f0e16c7a604bdf179dd8a9552157708276a5bf34ebc18b47d2a9b1482cc4c5",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-10-07T04:34:32Z",
    "title_canon_sha256": "47f3341877cb1df4261fc32c2ce0bb1d304c638aac1d155a0264020a676b5161"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.02394",
    "kind": "arxiv",
    "version": 1
  }
}