Pith Number

pith:QJNBJ6QJ

pith:2016:QJNBJ6QJPLCM3SYE2UVXDMBIHJ

not attested not anchored not stored refs pending

Large gap asymptotics at the hard edge for product random matrices and Muttalib-Borodin ensembles

Dries Stivigny, Manuela Girotti, Tom Claeys

arxiv:1612.01916 v1 · 2016-12-06 · math-ph · math.CV · 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{QJNBJ6QJPLCM3SYE2UVXDMBIHJ}

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	2026-05-18T00:55:47.363563Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

825a14fa097ac4cdcb04d52b71b0283a6f91bcf35eb8ec9b3e89de4fef19f759

Aliases

arxiv: 1612.01916 · arxiv_version: 1612.01916v1 · doi: 10.48550/arxiv.1612.01916 · pith_short_12: QJNBJ6QJPLCM · pith_short_16: QJNBJ6QJPLCM3SYE · pith_short_8: QJNBJ6QJ

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/QJNBJ6QJPLCM3SYE2UVXDMBIHJ \
  | 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: 825a14fa097ac4cdcb04d52b71b0283a6f91bcf35eb8ec9b3e89de4fef19f759

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ae6566af8f86b0a20c2b6927b2ed148f14abca1a6c15d0a4d6990cdf3b7f67e5",
    "cross_cats_sorted": [
      "math.CV",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2016-12-06T17:16:40Z",
    "title_canon_sha256": "9048a7e6d2bfe348140ef3f9b198f8b7924669a6de38bc12501c4f0b3b758cb4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.01916",
    "kind": "arxiv",
    "version": 1
  }
}