Pith Number

pith:UYHB5O3J

pith:2012:UYHB5O3JQ67GZZEPIS4J36F4WP

not attested not anchored not stored refs pending

Marchenko-Pastur Theorem and Bercovici-Pata bijections for heavy-tailed or localized vectors

CMAP), Florent Benaych-Georges (MAP5, Thierry Cabanal-Duvillard (MAP5)

arxiv:1204.5154 v4 · 2012-04-23 · 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{UYHB5O3JQ67GZZEPIS4J36F4WP}

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	2026-05-18T03:43:42.144771Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a60e1ebb6987be6ce48f44b89df8bcb3dca80df85a16bf45dcdb5a2ffe000175

Aliases

arxiv: 1204.5154 · arxiv_version: 1204.5154v4 · doi: 10.48550/arxiv.1204.5154 · pith_short_12: UYHB5O3JQ67G · pith_short_16: UYHB5O3JQ67GZZEP · pith_short_8: UYHB5O3J

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/UYHB5O3JQ67GZZEPIS4J36F4WP \
  | 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: a60e1ebb6987be6ce48f44b89df8bcb3dca80df85a16bf45dcdb5a2ffe000175

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "34be1f0422bdd710d422280a9f05f606e0b0c411cf722cee3bd8b90e06953fd8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-04-23T19:29:30Z",
    "title_canon_sha256": "bb66fbc433e50bffa407c00d366e63adf18cfcaa44057ee75279013a11539c70"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.5154",
    "kind": "arxiv",
    "version": 4
  }
}