Pith Number

pith:BFOW5XBR

pith:2026:BFOW5XBRML5QSGXXBFAWE4JKFN

not attested not anchored not stored refs pending

Marchenko-Pastur law for tensor powers of exchangeable unconditional vectors

Dan Mikulincer, Feng Cheng

arxiv:2607.21759 v1 · 2026-07-23 · 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{BFOW5XBRML5QSGXXBFAWE4JKFN}

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	2026-07-27T00:20:19.520074Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

095d6edc3162fb091af7094162712a2b73de87c9b16e2ece18c205ca1c17ab7a

Aliases

arxiv: 2607.21759 · arxiv_version: 2607.21759v1 · doi: 10.48550/arxiv.2607.21759 · pith_short_12: BFOW5XBRML5Q · pith_short_16: BFOW5XBRML5QSGXX · pith_short_8: BFOW5XBR

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/BFOW5XBRML5QSGXXBFAWE4JKFN \
  | 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: 095d6edc3162fb091af7094162712a2b73de87c9b16e2ece18c205ca1c17ab7a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82db3af88bdb35ef9e5fddf25242ba1c4725ca64796ad7e45be2991d53a0b96b",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-23T19:20:28Z",
    "title_canon_sha256": "93d4a2312fae88a8ede3772872f8ce9c3c7520621cce6374e02e9ffb96685b73"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.21759",
    "kind": "arxiv",
    "version": 1
  }
}