Pith Number

pith:GTCDUR7L

pith:2018:GTCDUR7LPYDCIEMCRQTVXQUL4P

not attested not anchored not stored refs pending

Local law and complete eigenvector delocalization for supercritical Erd\H{o}s-R\'enyi graphs

Antti Knowles, Matteo Marcozzi, Yukun He

arxiv:1808.09437 v2 · 2018-08-28 · 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{GTCDUR7LPYDCIEMCRQTVXQUL4P}

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	2026-05-17T23:56:23.218977Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34c43a47eb7e062411828c275bc28be3c00a8218d33179a945be60e03240408f

Aliases

arxiv: 1808.09437 · arxiv_version: 1808.09437v2 · doi: 10.48550/arxiv.1808.09437 · pith_short_12: GTCDUR7LPYDC · pith_short_16: GTCDUR7LPYDCIEMC · pith_short_8: GTCDUR7L

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/GTCDUR7LPYDCIEMCRQTVXQUL4P \
  | 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: 34c43a47eb7e062411828c275bc28be3c00a8218d33179a945be60e03240408f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "00942a14e423ab55c69832d2135b0b29bc2f735a517e9e6e090db3b81cabcc8b",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-08-28T17:53:33Z",
    "title_canon_sha256": "c828431d8d4ce8590d5e17e08e1799787249af20beb04b98baddbf1871f8d55a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.09437",
    "kind": "arxiv",
    "version": 2
  }
}