Pith Number

pith:KN7XUNZO

pith:2008:KN7XUNZOBYWXMFGXMNYRR7YEFI

not attested not anchored not stored refs pending

Multivariate Jacobi and Laguerre polynomials, infinite-dimensional extensions, and their probabilistic connections with multivariate Hahn and Meixner polynomials

Dario Span\'o, Robert C. Griffiths

arxiv:0809.1431 v2 · 2008-09-09 · math.PR · 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{KN7XUNZOBYWXMFGXMNYRR7YEFI}

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	2026-05-18T04:18:13.355752Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

537f7a372e0e2d7614d7637118ff042a37884ca379d1b1d261f02221cefca8ad

Aliases

arxiv: 0809.1431 · arxiv_version: 0809.1431v2 · doi: 10.48550/arxiv.0809.1431 · pith_short_12: KN7XUNZOBYWX · pith_short_16: KN7XUNZOBYWXMFGX · pith_short_8: KN7XUNZO

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/KN7XUNZOBYWXMFGXMNYRR7YEFI \
  | 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: 537f7a372e0e2d7614d7637118ff042a37884ca379d1b1d261f02221cefca8ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6f02ea8b2d0cba004d154774527eb1302605fb034178b15780b3c2cdbf4597e",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2008-09-09T16:34:19Z",
    "title_canon_sha256": "dcf167feaff8b28264513d435e268fc70f607db5e7ff64fd605153c140c33df3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0809.1431",
    "kind": "arxiv",
    "version": 2
  }
}