Pith Number

pith:FOMPXTB7

pith:2016:FOMPXTB7RWAHIIBQZT5N3QWPQK

not attested not anchored not stored refs pending

Distribution of ratio of two Wishart matrices and evaluation of cumulative probability by holonomic gradient method

Akimichi Takemura, Hiroki Hashiguchi, Nobuki Takayama

arxiv:1610.09187 v1 · 2016-10-28 · 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{FOMPXTB7RWAHIIBQZT5N3QWPQK}

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	2026-05-18T00:16:45.675152Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b98fbcc3f8d80742030ccfaddc2cf8297f1efa88e857e389abaffbbde8991dc

Aliases

arxiv: 1610.09187 · arxiv_version: 1610.09187v1 · doi: 10.48550/arxiv.1610.09187 · pith_short_12: FOMPXTB7RWAH · pith_short_16: FOMPXTB7RWAHIIBQ · pith_short_8: FOMPXTB7

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/FOMPXTB7RWAHIIBQZT5N3QWPQK \
  | 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: 2b98fbcc3f8d80742030ccfaddc2cf8297f1efa88e857e389abaffbbde8991dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ace8d03a0c22dee9fc9a5ef26a3ca3de82dc97c7e471ba76b8efae3efaeedcc4",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2016-10-28T12:38:48Z",
    "title_canon_sha256": "23d64e9e1e74fa0474a5405ec4ee80f3a805c709a0b895e89664ecd4b8c77582"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.09187",
    "kind": "arxiv",
    "version": 1
  }
}