Pith Number

pith:4UON4OAB

pith:1995:4UON4OABEZJAFCVZ2WMBX2UBBL

not attested not anchored not stored refs pending

COSMOLOGICAL PARAMETERS AND GRAVITATIONAL LENSING STATISTICS

Phillip Helbig

arxiv:astro-ph/9502041 v1 · 1995-02-07 · 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{4UON4OABEZJAFCVZ2WMBX2UBBL}

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	2026-05-18T04:24:26.608151Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e51cde38012652028ab9d5981bea810ac4a6dfbc36243d40f2599f20f0a90b6b

Aliases

arxiv: astro-ph/9502041 · arxiv_version: astro-ph/9502041v1 · doi: 10.48550/arxiv.astro-ph/9502041 · pith_short_12: 4UON4OABEZJA · pith_short_16: 4UON4OABEZJAFCVZ · pith_short_8: 4UON4OAB

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/4UON4OABEZJAFCVZ2WMBX2UBBL \
  | 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: e51cde38012652028ab9d5981bea810ac4a6dfbc36243d40f2599f20f0a90b6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc42ae496adc5a2ca7a4ac17ae04524e78cbe963b198888e18bcba8184e1d89d",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "1995-02-07T09:55:40Z",
    "title_canon_sha256": "236e5e234e5d10f0f33513d9750453aa9f83ac68f8ea0e8cc194550aab521287"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/9502041",
    "kind": "arxiv",
    "version": 1
  }
}