Pith Number

pith:27UKEB4X

pith:2012:27UKEB4XZH6XVLSTQKIPMQ3RK3

not attested not anchored not stored refs pending

Local Marchenko-Pastur Law at the Hard Edge of Sample Covariance Matrices

Anna Maltsev, Benjamin Schlein, Claudio Cacciapuoti

arxiv:1206.1730 v3 · 2012-06-08 · math-ph · math.MP · 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{27UKEB4XZH6XVLSTQKIPMQ3RK3}

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	2026-05-18T01:57:00.666800Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7e8a20797c9fd7aae538290f6437156ffaa565b5f28b0adf66cdfe6673a6b2b

Aliases

arxiv: 1206.1730 · arxiv_version: 1206.1730v3 · doi: 10.48550/arxiv.1206.1730 · pith_short_12: 27UKEB4XZH6X · pith_short_16: 27UKEB4XZH6XVLST · pith_short_8: 27UKEB4X

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/27UKEB4XZH6XVLSTQKIPMQ3RK3 \
  | 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: d7e8a20797c9fd7aae538290f6437156ffaa565b5f28b0adf66cdfe6673a6b2b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea5135357ee5cd1b6476ebee6f59ac99c3d0d83907532f830e0c26c091725de9",
    "cross_cats_sorted": [
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-06-08T11:21:54Z",
    "title_canon_sha256": "27c279ebde17d1eaf44d1fa9059a95c21f485e4231a0c554bd5ada66cf0abe69"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.1730",
    "kind": "arxiv",
    "version": 3
  }
}