Pith Number

pith:7RXXMQRY

pith:2013:7RXXMQRY6QESNJNNX5O2YX7EEL

not attested not anchored not stored refs pending

Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits

Arno B.J. Kuijlaars, Lun Zhang

arxiv:1308.1003 v2 · 2013-08-05 · 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{7RXXMQRY6QESNJNNX5O2YX7EEL}

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	2026-05-18T01:48:23.749091Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc6f764238f40926a5adbf5dac5fe422d769a36bb73a799bb65b69b3b3d2ea0b

Aliases

arxiv: 1308.1003 · arxiv_version: 1308.1003v2 · doi: 10.48550/arxiv.1308.1003 · pith_short_12: 7RXXMQRY6QES · pith_short_16: 7RXXMQRY6QESNJNN · pith_short_8: 7RXXMQRY

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/7RXXMQRY6QESNJNNX5O2YX7EEL \
  | 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: fc6f764238f40926a5adbf5dac5fe422d769a36bb73a799bb65b69b3b3d2ea0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c5edccc8e1f42d6157cb733a9dfb66529df1fbd8801b8aa1731b62e8178814e",
    "cross_cats_sorted": [
      "math.CA",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-08-05T15:05:18Z",
    "title_canon_sha256": "946d405dddf753178f3e9e550eaacdc11ab1111c5566142648e46e811c986304"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.1003",
    "kind": "arxiv",
    "version": 2
  }
}