Pith Number

pith:VCWRGER6

pith:2018:VCWRGER6EOF3MAGU3EGNCZJRW6

not attested not anchored not stored refs pending

Concentration of the spectral norm of Erd\H{o}s-R\'enyi random graphs

G\'abor Lugosi, Nikita Zhivotovskiy, Shahar Mendelson

arxiv:1801.02157 v3 · 2018-01-07 · 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{VCWRGER6EOF3MAGU3EGNCZJRW6}

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	2026-05-18T00:00:22.123984Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8ad13123e238bb600d4d90cd16531b7ae735857674e096ad5d244a5b495b1e7

Aliases

arxiv: 1801.02157 · arxiv_version: 1801.02157v3 · doi: 10.48550/arxiv.1801.02157 · pith_short_12: VCWRGER6EOF3 · pith_short_16: VCWRGER6EOF3MAGU · pith_short_8: VCWRGER6

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/VCWRGER6EOF3MAGU3EGNCZJRW6 \
  | 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: a8ad13123e238bb600d4d90cd16531b7ae735857674e096ad5d244a5b495b1e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7cbf9c26ff02d3f251859637221256033df5b8e743d1fa8ff100bf5003495fb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-01-07T08:23:15Z",
    "title_canon_sha256": "d4465128e37819c46ce6e1b959b6baf7b65ca20b45e205877e80d8024e5f4d0d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.02157",
    "kind": "arxiv",
    "version": 3
  }
}