Pith Number

pith:KAERK54F

pith:2020:KAERK54FA5S2D7MMMKHFNOAOVF

not attested not anchored not stored refs pending

Fluctuations of extreme eigenvalues of sparse Erd\H{o}s-R\'enyi graphs

Antti Knowles, Yukun He

arxiv:2005.02254 v2 · 2020-05-05 · 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{KAERK54FA5S2D7MMMKHFNOAOVF}

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	2026-07-05T02:29:08.913424Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50091577850765a1fd8c628e56b80ea974585fc7054d7047b8ed705e35cb5b82

Aliases

arxiv: 2005.02254 · arxiv_version: 2005.02254v2 · doi: 10.48550/arxiv.2005.02254 · pith_short_12: KAERK54FA5S2 · pith_short_16: KAERK54FA5S2D7MM · pith_short_8: KAERK54F

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/KAERK54FA5S2D7MMMKHFNOAOVF \
  | 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: 50091577850765a1fd8c628e56b80ea974585fc7054d7047b8ed705e35cb5b82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1ba439858d56429a66ff01501690768f494473c7922755ed5fee44659d8397ff",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2020-05-05T14:50:45Z",
    "title_canon_sha256": "adf19c9e7d3fd05d56257477241058394d676088b12b46e0541246c4691b0f32"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2005.02254",
    "kind": "arxiv",
    "version": 2
  }
}