Pith Number

pith:3I2ZUU4Q

pith:2011:3I2ZUU4QOVEV4CYX2RR4EW5OWS

not attested not anchored not stored refs pending

Spectral Statistics of Erd{\H o}s-R\'enyi Graphs II: Eigenvalue Spacing and the Extreme Eigenvalues

Antti Knowles, Horng-Tzer Yau, Jun Yin, Laszlo Erdos

arxiv:1103.3869 v3 · 2011-03-20 · 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{3I2ZUU4QOVEV4CYX2RR4EW5OWS}

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	2026-05-18T02:02:49.139564Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

da359a539075495e0b17d463c25baeb48a16c64481193f558cd024dcce453c61

Aliases

arxiv: 1103.3869 · arxiv_version: 1103.3869v3 · doi: 10.48550/arxiv.1103.3869 · pith_short_12: 3I2ZUU4QOVEV · pith_short_16: 3I2ZUU4QOVEV4CYX · pith_short_8: 3I2ZUU4Q

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/3I2ZUU4QOVEV4CYX2RR4EW5OWS \
  | 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: da359a539075495e0b17d463c25baeb48a16c64481193f558cd024dcce453c61

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "16310e6725268e1dbacc681a66f78200c36a1ac81fe210bd7938057cb5235021",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-03-20T17:59:33Z",
    "title_canon_sha256": "b2000a5236e3bc6b387d7274c382ca0b2e8f02e28608729ed780c38b1870fdbd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.3869",
    "kind": "arxiv",
    "version": 3
  }
}