Pith Number

pith:3NGY4TU7

pith:2013:3NGY4TU776Q3OEQF6MYJKAB427

not attested not anchored not stored refs pending

Laplacian spectra of recursive treelike small-world polymer networks: Analytical solutions and applications

Hongxiao Liu, Zhongzhi Zhang

arxiv:1303.2188 v1 · 2013-03-09 · cond-mat.stat-mech · physics.chem-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3NGY4TU776Q3OEQF6MYJKAB427}

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	2026-05-18T03:30:25.086837Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db4d8e4e9fffa1b71205f33095003cd7e32de208ea74d18a1d246489c972e32d

Aliases

arxiv: 1303.2188 · arxiv_version: 1303.2188v1 · doi: 10.48550/arxiv.1303.2188 · pith_short_12: 3NGY4TU776Q3 · pith_short_16: 3NGY4TU776Q3OEQF · pith_short_8: 3NGY4TU7

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/3NGY4TU776Q3OEQF6MYJKAB427 \
  | 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: db4d8e4e9fffa1b71205f33095003cd7e32de208ea74d18a1d246489c972e32d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43fc6bc7ecf60de8def67ec4225d3930df819e31a07b5e983aea6999e673198b",
    "cross_cats_sorted": [
      "physics.chem-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2013-03-09T09:29:00Z",
    "title_canon_sha256": "f7ef4f3843387a893059a312e51991c8be76381dc7aa18ad179ce770dfd2202b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.2188",
    "kind": "arxiv",
    "version": 1
  }
}