Pith Number

pith:KQJQU7KW

pith:2026:KQJQU7KW6NV5QYNBJVJZNSPTTE

not attested not anchored not stored refs pending

The conditional expectation of the product of the first $n-1$ Hermite polynomials in a multivariate normal distribution with respect to the $n$-th variable. A fresh perspective on the Kibble-Slepian formula

Pawe{\l} J. Szab{\l}owski

arxiv:2606.22526 v1 · 2026-06-21 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KQJQU7KW6NV5QYNBJVJZNSPTTE}

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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	2026-06-23T02:13:40.827861Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

54130a7d56f36bd861a14d5396c9f3990d45849512b6e2ab66d4b20c75dd6bba

Aliases

arxiv: 2606.22526 · arxiv_version: 2606.22526v1 · doi: 10.48550/arxiv.2606.22526 · pith_short_12: KQJQU7KW6NV5 · pith_short_16: KQJQU7KW6NV5QYNB · pith_short_8: KQJQU7KW

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/KQJQU7KW6NV5QYNBJVJZNSPTTE \
  | 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: 54130a7d56f36bd861a14d5396c9f3990d45849512b6e2ab66d4b20c75dd6bba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a68a06f8c3d213fd86cc33f8be715d0f610195206c7bebcec7df195722077dc",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-06-21T14:25:16Z",
    "title_canon_sha256": "4cb98b8aa4be90af6d77fbeb9ba30678c155151339abdd6eeee5e9a6cbbee7ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.22526",
    "kind": "arxiv",
    "version": 1
  }
}