Pith Number

pith:RKUHSRFY

pith:2014:RKUHSRFYAUIC3AIZHNPR3QV3HG

not attested not anchored not stored refs pending

Explicit Evaluations of Matrix-variate Gamma and Beta Integrals in the Real and Complex Cases

A.M. Mathai

arxiv:1409.7561 v1 · 2014-09-26 · math.ST · math.PR · 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{RKUHSRFYAUIC3AIZHNPR3QV3HG}

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	2026-05-18T02:41:52.418605Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8aa87944b805102d81193b5f1dc2bb398f6bac237cda621c621fd88507e47eb3

Aliases

arxiv: 1409.7561 · arxiv_version: 1409.7561v1 · doi: 10.48550/arxiv.1409.7561 · pith_short_12: RKUHSRFYAUIC · pith_short_16: RKUHSRFYAUIC3AIZ · pith_short_8: RKUHSRFY

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/RKUHSRFYAUIC3AIZHNPR3QV3HG \
  | 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: 8aa87944b805102d81193b5f1dc2bb398f6bac237cda621c621fd88507e47eb3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31d931b1a1b57a558d5e4ce28a7d988875623f8a9c62ba646ec90460a2a5022c",
    "cross_cats_sorted": [
      "math.PR",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2014-09-26T13:02:53Z",
    "title_canon_sha256": "ff45ed71383fa4ab4f89743887a9c77cc1610bc751e1550ccc6e70fb9fc048ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.7561",
    "kind": "arxiv",
    "version": 1
  }
}