Pith Number

pith:4YORH7N5

pith:2026:4YORH7N56TDO2UGU5K3PPF3RTL

not attested not anchored not stored refs pending

Variational Formulas for the Spectrum of Block Wishart Matrices

Andrea Montanari, Basil Saeed

arxiv:2606.27774 v1 · 2026-06-26 · math.PR · math.ST · 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{4YORH7N56TDO2UGU5K3PPF3RTL}

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	2026-06-29T01:14:48.008077Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e61d13fdbdf4c6ed50d4eab6f797719ac05d6cb3ac22650e51372a54ad8801ea

Aliases

arxiv: 2606.27774 · arxiv_version: 2606.27774v1 · doi: 10.48550/arxiv.2606.27774 · pith_short_12: 4YORH7N56TDO · pith_short_16: 4YORH7N56TDO2UGU · pith_short_8: 4YORH7N5

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/4YORH7N56TDO2UGU5K3PPF3RTL \
  | 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: e61d13fdbdf4c6ed50d4eab6f797719ac05d6cb3ac22650e51372a54ad8801ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "117037057fad46162c9d16fb3351b3211567c8b88ecfae0f93ab7bfc1e753e24",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-06-26T06:59:52Z",
    "title_canon_sha256": "bcfef35e70436a4345bd34be249f983d20b1447e6e00986322e963f02251657b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.27774",
    "kind": "arxiv",
    "version": 1
  }
}