Pith Number

pith:DNYCOP7X

pith:2025:DNYCOP7XISMLEZMFLFF2E2YD34

not attested not anchored not stored refs pending

Asymptotic Expansions of Gaussian and Laguerre Ensembles at the Soft Edge III: Generating Functions

Folkmar Bornemann

arxiv:2506.18673 v2 · 2025-06-23 · math.PR · math-ph · math.MP · 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{DNYCOP7XISMLEZMFLFF2E2YD34}

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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.

Cited by

1 paper in Pith

Edge density expansions for the classical Gaussian and Laguerre ensembles

Receipt and verification

First computed	2026-05-20T00:00:21.557019Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1b70273ff74498b26585594ba26b03df0312bfb3b4d5355eb5ee1d6bf15e2a57

Aliases

arxiv: 2506.18673 · arxiv_version: 2506.18673v2 · doi: 10.48550/arxiv.2506.18673 · pith_short_12: DNYCOP7XISML · pith_short_16: DNYCOP7XISMLEZMF · pith_short_8: DNYCOP7X

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/DNYCOP7XISMLEZMFLFF2E2YD34 \
  | 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: 1b70273ff74498b26585594ba26b03df0312bfb3b4d5355eb5ee1d6bf15e2a57

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "266ada75b09a76d845175e63bc8fe7587726aab833493f1a201223292c18a95b",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-06-23T14:17:44Z",
    "title_canon_sha256": "7fcd18f4bfd85d0bd9683a2cc1b0390e5600ebbe7bb7529866b0078c49d96d52"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.18673",
    "kind": "arxiv",
    "version": 2
  }
}