Pith Number

pith:WUPNK73M

pith:2012:WUPNK73M6UXY62THHRNNAIPHUE

not attested not anchored not stored refs pending

Convergence in $\C$ of series for the Lambert $W$ Function

David J. Jeffrey, German A. Kalugin

arxiv:1208.0754 v1 · 2012-08-02 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WUPNK73M6UXY62THHRNNAIPHUE}

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	2026-05-18T03:49:22.922210Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b51ed57f6cf52f8f6a673c5ad021e7a110152bf69b8fd231ad4788d176d65b4c

Aliases

arxiv: 1208.0754 · arxiv_version: 1208.0754v1 · doi: 10.48550/arxiv.1208.0754 · pith_short_12: WUPNK73M6UXY · pith_short_16: WUPNK73M6UXY62TH · pith_short_8: WUPNK73M

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/WUPNK73M6UXY62THHRNNAIPHUE \
  | 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: b51ed57f6cf52f8f6a673c5ad021e7a110152bf69b8fd231ad4788d176d65b4c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "54fe11ca9b0c5c29b9628024cb236ac1763cdbfdfb4299723f5cf85016b690d1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-08-02T14:04:30Z",
    "title_canon_sha256": "8773dd0c70ed98d13ad60fe6f4cebf71017b02707888004db83869f38b0da9f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.0754",
    "kind": "arxiv",
    "version": 1
  }
}