Pith Number

pith:XHE5MIII

pith:2011:XHE5MIIIG5OX54UFGHRWYHZIAX

not attested not anchored not stored refs pending

Universality of sample covariance matrices: CLT of the smoothed empirical spectral distribution

Guangming Pan, Qi-Man Shao, Wang Zhou

arxiv:1111.5420 v1 · 2011-11-23 · math.ST · math.PR · stat.TH

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XHE5MIIIG5OX54UFGHRWYHZIAX}

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	2026-05-18T04:07:43.743661Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b9c9d62108375d7ef28531e36c1f2805c85f6c532525a749f9540946f7cf3fb9

Aliases

arxiv: 1111.5420 · arxiv_version: 1111.5420v1 · doi: 10.48550/arxiv.1111.5420 · pith_short_12: XHE5MIIIG5OX · pith_short_16: XHE5MIIIG5OX54UF · pith_short_8: XHE5MIII

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/XHE5MIIIG5OX54UFGHRWYHZIAX \
  | 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: b9c9d62108375d7ef28531e36c1f2805c85f6c532525a749f9540946f7cf3fb9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f01b04297f86120fdfa681d84c6d768166476d8110b8f50ad8ed0171843fcdcd",
    "cross_cats_sorted": [
      "math.PR",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2011-11-23T07:23:48Z",
    "title_canon_sha256": "1d74497faaba92d8c546b6f35025b96e6d997765e68c40855cf4aaa68abcadbe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.5420",
    "kind": "arxiv",
    "version": 1
  }
}