Pith Number

pith:3NCSGQDW

pith:1996:3NCSGQDWVK4SUZEUMC2F2VOZS3

not attested not anchored not stored refs pending

Convergence Behavior of Variational Perturbation Expansions

FU Berlin), Hagen Kleinert (JGU Mainz, Wolfhard Janke

arxiv:quant-ph/9609027 v1 · 1996-09-28 · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3NCSGQDWVK4SUZEUMC2F2VOZS3}

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	2026-05-18T01:05:02.041294Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db45234076aab92a649460b45d55d996d821067fb0d8ede457eb1fa14b7bbb0f

Aliases

arxiv: quant-ph/9609027 · arxiv_version: quant-ph/9609027v1 · doi: 10.48550/arxiv.quant-ph/9609027 · pith_short_12: 3NCSGQDWVK4S · pith_short_16: 3NCSGQDWVK4SUZEU · pith_short_8: 3NCSGQDW

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/3NCSGQDWVK4SUZEUMC2F2VOZS3 \
  | 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: db45234076aab92a649460b45d55d996d821067fb0d8ede457eb1fa14b7bbb0f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06ad0ea22d832dd295e7716e1d922ca9996830a2ba8ecaa93128c915fb85ec48",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "1996-09-28T22:57:51Z",
    "title_canon_sha256": "54bcff0139b01ba1c814c7b690046bdbdff8e0f7a4b2da375d527d76f9b01383"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/9609027",
    "kind": "arxiv",
    "version": 1
  }
}