Pith Number

pith:ZND42GDO

pith:2013:ZND42GDO64NHXJ2WWUP4U65NFR

not attested not anchored not stored refs pending

Moments of the Gaussian $\beta$ Ensembles and the large-$N$ expansion of the densities

N.S. Witte, P.J. Forrester

arxiv:1310.8498 v2 · 2013-10-31 · math.CA · hep-th · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZND42GDO64NHXJ2WWUP4U65NFR}

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	2026-05-18T02:38:26.575608Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb47cd186ef71a7ba756b51fca7bad2c56de6745da4b3eed6c9d6dae32b2361f

Aliases

arxiv: 1310.8498 · arxiv_version: 1310.8498v2 · doi: 10.48550/arxiv.1310.8498 · pith_short_12: ZND42GDO64NH · pith_short_16: ZND42GDO64NHXJ2W · pith_short_8: ZND42GDO

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/ZND42GDO64NHXJ2WWUP4U65NFR \
  | 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: cb47cd186ef71a7ba756b51fca7bad2c56de6745da4b3eed6c9d6dae32b2361f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba5e67ae100e54688e23c3f82d03bce09a0ea551c6a0918a1206629fae3d7d52",
    "cross_cats_sorted": [
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-10-31T13:45:23Z",
    "title_canon_sha256": "f57d98021ccd11e2bb20b0dec6fb0122a89dcaa1cdcb7fd507a5de1ddb163a88"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.8498",
    "kind": "arxiv",
    "version": 2
  }
}