Pith Number

pith:JO4APAX4

pith:2000:JO4APAX4OZ53PHQGNEEKWGOXHR

not attested not anchored not stored refs pending

A Laguerre Polynomial Orthogonality and the Hydrogen Atom

Charles F. Dunkl

arxiv:math-ph/0011021 v2 · 2000-11-13 · math-ph · math.CA · 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{JO4APAX4OZ53PHQGNEEKWGOXHR}

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	2026-05-18T04:08:53.877832Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4bb80782fc767bb79e066908ab19d73c4b702ba6e88415561e13b1755d63eed9

Aliases

arxiv: math-ph/0011021 · arxiv_version: math-ph/0011021v2 · doi: 10.48550/arxiv.math-ph/0011021 · pith_short_12: JO4APAX4OZ53 · pith_short_16: JO4APAX4OZ53PHQG · pith_short_8: JO4APAX4

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/JO4APAX4OZ53PHQGNEEKWGOXHR \
  | 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: 4bb80782fc767bb79e066908ab19d73c4b702ba6e88415561e13b1755d63eed9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "359edaca1e1af88cef829fce600bf470a601ba7e41b15c86e81584ce9ff37a5c",
    "cross_cats_sorted": [
      "math.CA",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2000-11-13T19:08:37Z",
    "title_canon_sha256": "9ef6ecf08433a9dc62e5e626ec3fdfc68ca63075c11a243621e3dfe365408343"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0011021",
    "kind": "arxiv",
    "version": 2
  }
}