Pith Number

pith:S3BMAYB4

pith:2013:S3BMAYB4QJOL76K4PCGZJ6AQYH

not attested not anchored not stored refs pending

A note on the limiting mean distribution of singular values for products of two Wishart random matrices

Lun Zhang

arxiv:1305.0726 v2 · 2013-05-03 · math-ph · math.CA · 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{S3BMAYB4QJOL76K4PCGZJ6AQYH}

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	2026-05-18T01:50:12.725649Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

96c2c0603c825cbff95c788d94f810c1f4f46f83afda1e34f9fb41be832157a0

Aliases

arxiv: 1305.0726 · arxiv_version: 1305.0726v2 · doi: 10.48550/arxiv.1305.0726 · pith_short_12: S3BMAYB4QJOL · pith_short_16: S3BMAYB4QJOL76K4 · pith_short_8: S3BMAYB4

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/S3BMAYB4QJOL76K4PCGZJ6AQYH \
  | 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: 96c2c0603c825cbff95c788d94f810c1f4f46f83afda1e34f9fb41be832157a0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4a52e01fb3ab4b51d9211a33031782e178d18b321a9bf8604d81cda23b36139",
    "cross_cats_sorted": [
      "math.CA",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-05-03T14:43:39Z",
    "title_canon_sha256": "4b5d27a7481b6e0e9b2d70352ea95e7ccb6dd4a0564b16d9aca700d17c53621b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.0726",
    "kind": "arxiv",
    "version": 2
  }
}