Pith Number

pith:HFUV7L6M

pith:2019:HFUV7L6MMFXQU4LOVULCIRSQLR

not attested not anchored not stored refs pending

The Lambert $W$ function: A newcomer in the Cosmology class?

Kazuharu Bamba, Subhajit Saha

arxiv:1908.11712 v2 · 2019-08-29 · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HFUV7L6MMFXQU4LOVULCIRSQLR}

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	2026-07-05T00:29:20.522187Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

39695fafcc616f0a716ead162446505c7b34be662f1bde7ef9d513e03410dd0d

Aliases

arxiv: 1908.11712 · arxiv_version: 1908.11712v2 · doi: 10.48550/arxiv.1908.11712 · pith_short_12: HFUV7L6MMFXQ · pith_short_16: HFUV7L6MMFXQU4LO · pith_short_8: HFUV7L6M

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/HFUV7L6MMFXQU4LOVULCIRSQLR \
  | 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: 39695fafcc616f0a716ead162446505c7b34be662f1bde7ef9d513e03410dd0d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b74b9e112b1b1119f18d2d86c471e741f5b48a23a1e468231e97e95e8b9f3c72",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2019-08-29T16:25:42Z",
    "title_canon_sha256": "a90554b98ed2ad4f8fda29f2dbb43e45a813344e4ad83f02272884e96d34c860"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.11712",
    "kind": "arxiv",
    "version": 2
  }
}