Pith Number

pith:EK3ZDC5F

pith:2005:EK3ZDC5F6LE6A2PBIJMQBVRLKG

not attested not anchored not stored refs pending

Lifshitz tails for spectra of Erd\H{o}s--R\'{e}nyi random graphs

Oleksiy Khorunzhiy, Peter M\"uller, Werner Kirsch

arxiv:math-ph/0502054 v3 · 2005-02-27 · math-ph · cond-mat.stat-mech · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EK3ZDC5F6LE6A2PBIJMQBVRLKG}

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	2026-05-18T01:08:51.771557Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

22b7918ba5f2c9e069e1425900d62b51b18170239596dfe2c289530bf93517e8

Aliases

arxiv: math-ph/0502054 · arxiv_version: math-ph/0502054v3 · doi: 10.48550/arxiv.math-ph/0502054 · pith_short_12: EK3ZDC5F6LE6 · pith_short_16: EK3ZDC5F6LE6A2PB · pith_short_8: EK3ZDC5F

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/EK3ZDC5F6LE6A2PBIJMQBVRLKG \
  | 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: 22b7918ba5f2c9e069e1425900d62b51b18170239596dfe2c289530bf93517e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "115b72c2a10e4a6ee77fa04373346dd3ad5c44e2b4507657e59f092e7318e5f3",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math.MP",
      "math.PR"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2005-02-27T21:12:48Z",
    "title_canon_sha256": "3b5222a877ae8b06e1e1db6944888daf8db345801825dc4c4cf41f1b02548987"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0502054",
    "kind": "arxiv",
    "version": 3
  }
}