Pith Number

pith:P45W7CKY

pith:2012:P45W7CKYEK6IPEE63DNBJRJ6B3

not attested not anchored not stored refs pending

Invariant $\beta$-Wishart ensembles, crossover densities and asymptotic corrections to the Marchenko-Pastur law

Jean-Philippe Bouchaud, Pierpaolo Vivo, Romain Allez, Satya N. Majumdar

arxiv:1209.6171 v1 · 2012-09-27 · cond-mat.stat-mech · 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{P45W7CKYEK6IPEE63DNBJRJ6B3}

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	2026-05-18T03:35:25.431049Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f3b6f895822bc87909ed8da14c53e0ed91778edd3b1f71aded5b8b3a7c93d25

Aliases

arxiv: 1209.6171 · arxiv_version: 1209.6171v1 · doi: 10.48550/arxiv.1209.6171 · pith_short_12: P45W7CKYEK6I · pith_short_16: P45W7CKYEK6IPEE6 · pith_short_8: P45W7CKY

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/P45W7CKYEK6IPEE63DNBJRJ6B3 \
  | 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: 7f3b6f895822bc87909ed8da14c53e0ed91778edd3b1f71aded5b8b3a7c93d25

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b98cfbf20f4f892a727dad67d6b97f172964f22a95efb86eceefd29494a0868",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2012-09-27T09:26:53Z",
    "title_canon_sha256": "02aebe667426979511aa2f4f6dd4c22c8de46a63c2a2f82c8c5ccfc6bb6852f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.6171",
    "kind": "arxiv",
    "version": 1
  }
}