Pith Number

pith:QJERJ4C6

pith:2011:QJERJ4C6WFDQUHD44TR4BFAG5O

not attested not anchored not stored refs pending

Spectral statistics of Erd\H{o}s-R\'{e}nyi graphs I: Local semicircle law

Antti Knowles, Horng-Tzer Yau, Jun Yin, L\'aszl\'o Erd\H{o}s

arxiv:1103.1919 v5 · 2011-03-09 · math.PR · 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{QJERJ4C6WFDQUHD44TR4BFAG5O}

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	2026-05-18T03:18:50.017697Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

824914f05eb1470a1c7ce4e3c09406eb9502177096e17adc1e39b22f4de185de

Aliases

arxiv: 1103.1919 · arxiv_version: 1103.1919v5 · doi: 10.48550/arxiv.1103.1919 · pith_short_12: QJERJ4C6WFDQ · pith_short_16: QJERJ4C6WFDQUHD4 · pith_short_8: QJERJ4C6

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/QJERJ4C6WFDQUHD44TR4BFAG5O \
  | 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: 824914f05eb1470a1c7ce4e3c09406eb9502177096e17adc1e39b22f4de185de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b8721b4022378e5bb772426824bf701264cee0cb357d8dd28429dd3ff9d4ed2",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-03-09T23:39:53Z",
    "title_canon_sha256": "d8ef106d1aafc3eb26d18af60c3fc06716625c53e9994d0efcff6740b09be6c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.1919",
    "kind": "arxiv",
    "version": 5
  }
}