Pith Number

pith:4QJL4XWY

pith:2001:4QJL4XWY4AYOWNTWMKAX2W54FN

not attested not anchored not stored refs pending

The Integral Representation for the Product of Two Parabolic Cylinder Functions $D_\nu (x) D_\nu (-x)$ at $Re \nu <0$ by Means of the Fundamental Solution of a Landau-Type Operator

C. Malyshev

arxiv:math/0106142 v2 · 2001-06-17 · math.CA · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4QJL4XWY4AYOWNTWMKAX2W54FN}

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	2026-05-18T00:05:41.179783Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e412be5ed8e030eb367662817d5bbc2b50f27255a374920ef52acf6aa82fc8bf

Aliases

arxiv: math/0106142 · arxiv_version: math/0106142v2 · doi: 10.48550/arxiv.math/0106142 · pith_short_12: 4QJL4XWY4AYO · pith_short_16: 4QJL4XWY4AYOWNTW · pith_short_8: 4QJL4XWY

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/4QJL4XWY4AYOWNTWMKAX2W54FN \
  | 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: e412be5ed8e030eb367662817d5bbc2b50f27255a374920ef52acf6aa82fc8bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef1a5ada562f353aef07cfc8e49299ae9f75d9c9b9eaf7092b91bbc5f94b6282",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.CA",
    "submitted_at": "2001-06-17T13:32:57Z",
    "title_canon_sha256": "4874ab570262fb00d5d801da1e95a929f4090d0dcf34c5381763855162dce211"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0106142",
    "kind": "arxiv",
    "version": 2
  }
}