Pith Number

pith:NRGA3UP2

pith:2010:NRGA3UP2CIJN7JKXWVAFOLHFHH

not attested not anchored not stored refs pending

Universality and the circular law for sparse random matrices

Philip Matchett Wood

arxiv:1010.1726 v2 · 2010-10-08 · 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{NRGA3UP2CIJN7JKXWVAFOLHFHH}

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	2026-05-18T03:43:40.676674Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c4c0dd1fa1212dfa557b540572ce539d459acd830f06fdefdbbc47593d49394

Aliases

arxiv: 1010.1726 · arxiv_version: 1010.1726v2 · doi: 10.48550/arxiv.1010.1726 · pith_short_12: NRGA3UP2CIJN · pith_short_16: NRGA3UP2CIJN7JKX · pith_short_8: NRGA3UP2

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/NRGA3UP2CIJN7JKXWVAFOLHFHH \
  | 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: 6c4c0dd1fa1212dfa557b540572ce539d459acd830f06fdefdbbc47593d49394

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1825cce4193763623fa28aa956c838ab6d41792f3dc3010698831390c2c5c914",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-10-08T16:03:58Z",
    "title_canon_sha256": "69537e6fe9340095778deb34546b5f20d63bbcfeb460a019a535fc0a4ac3339d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.1726",
    "kind": "arxiv",
    "version": 2
  }
}