Pith Number

pith:XH3NS4VK

pith:2012:XH3NS4VKZ4D4XIZLGA3YL7IFKP

not attested not anchored not stored refs pending

Holonomic gradient method for the distribution function of the largest root of a Wishart matrix

Akimichi Takemura, Hiroki Hashiguchi, Nobuki Takayama, Yasuhide Numata

arxiv:1201.0472 v4 · 2012-01-02 · 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{XH3NS4VKZ4D4XIZLGA3YL7IFKP}

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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.

Receipt and verification

First computed	2026-05-18T03:28:17.663127Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b9f6d972aacf07cba32b303785fd0553f3752b0006306e7250dd9ffd4151f1de

Aliases

arxiv: 1201.0472 · arxiv_version: 1201.0472v4 · doi: 10.48550/arxiv.1201.0472 · pith_short_12: XH3NS4VKZ4D4 · pith_short_16: XH3NS4VKZ4D4XIZL · pith_short_8: XH3NS4VK

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/XH3NS4VKZ4D4XIZLGA3YL7IFKP \
  | 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: b9f6d972aacf07cba32b303785fd0553f3752b0006306e7250dd9ffd4151f1de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c8ce5061245a7664779465c3c4e0a707b92e66faadc7408941ce1bcc28acdaf",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2012-01-02T14:28:37Z",
    "title_canon_sha256": "bb826cf163bdee7e6cdbf063edffd464487c72843430d91d62bbc52afab901d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.0472",
    "kind": "arxiv",
    "version": 4
  }
}