Pith Number

pith:HIBBQWSI

pith:2000:HIBBQWSISUUSEJW3F7SVIOYV6F

not attested not anchored not stored refs pending

The cosmological lens equation in a universe with non zero cosmological constant

A.A. Marino (Osservatorio Astronomico di Capodimonte, Dipartimento di Scienze Fisiche, E. Piedipalumbo (Dipartimento di Scienze Fisiche, INFN, M. Demianski (Institute for Theoretical Physics, Napoli), R. de Ritis (INFN, Universita` di Napoli), University of Warsaw)

arxiv:astro-ph/0004376 v1 · 2000-04-27 · astro-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{HIBBQWSISUUSEJW3F7SVIOYV6F}

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	2026-05-17T23:44:10.706603Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a02185a4895292226db2fe5543b15f1690d718b4dad0a5415492aa4b216c0ff

Aliases

arxiv: astro-ph/0004376 · arxiv_version: astro-ph/0004376v1 · doi: 10.48550/arxiv.astro-ph/0004376 · pith_short_12: HIBBQWSISUUS · pith_short_16: HIBBQWSISUUSEJW3 · pith_short_8: HIBBQWSI

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/HIBBQWSISUUSEJW3F7SVIOYV6F \
  | 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: 3a02185a4895292226db2fe5543b15f1690d718b4dad0a5415492aa4b216c0ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1fa2008ea82d36baeb1d136964a27424d892b16771ef17f3561233694ce5dac6",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2000-04-27T10:01:34Z",
    "title_canon_sha256": "3694df3ff46ff668b239a6499c5c4d386f4910032a7c422a92d2585758def5df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0004376",
    "kind": "arxiv",
    "version": 1
  }
}