Pith Number

pith:UMF4WAZC

pith:2000:UMF4WAZC6DLBD2TXN25GISGEAU

not attested not anchored not stored refs pending

Perurbation expansions for the spiked harmonic oscillator and related series involving the gamma function

Nasser Saad, Richard L. Hall

arxiv:math-ph/0006024 v1 · 2000-06-27 · 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{UMF4WAZC6DLBD2TXN25GISGEAU}

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.

Cited by

1 paper in Pith

Landau levels in a gravitational field: The Schwarzschild spacetime case

Receipt and verification

First computed	2026-07-04T16:21:10.824390Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a30bcb0322f0d611ea776eba6448c40515f47d519baafc132c54de68389819a7

Aliases

arxiv: math-ph/0006024 · arxiv_version: math-ph/0006024v1 · doi: 10.48550/arxiv.math-ph/0006024 · pith_short_12: UMF4WAZC6DLB · pith_short_16: UMF4WAZC6DLBD2TX · pith_short_8: UMF4WAZC

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/UMF4WAZC6DLBD2TXN25GISGEAU \
  | 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: a30bcb0322f0d611ea776eba6448c40515f47d519baafc132c54de68389819a7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "739a80d1c3c927f2406d985a279a39ddeef57904a0cf700702fbd11dae871714",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2000-06-27T18:29:47Z",
    "title_canon_sha256": "d47d513a25c1b382b26cdfac78190865feaa7a5e5c4d738fe50a95b9429b39b8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0006024",
    "kind": "arxiv",
    "version": 1
  }
}