Pith Number

pith:7C3PE5HF

pith:2004:7C3PE5HF5XJLGZZQT2GYVSSBBV

not attested not anchored not stored refs pending

Safety in numbers: Gravitational Lensing Degradation of the Luminosity Distance-Redshift Relation

Daniel E. Holz, Eric V. Linder

arxiv:astro-ph/0412173 v1 · 2004-12-08 · 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{7C3PE5HF5XJLGZZQT2GYVSSBBV}

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	2026-05-18T04:22:20.978347Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f8b6f274e5edd2b367309e8d8aca410d53df8419471d7646ef8e04478e5ef024

Aliases

arxiv: astro-ph/0412173 · arxiv_version: astro-ph/0412173v1 · doi: 10.48550/arxiv.astro-ph/0412173 · pith_short_12: 7C3PE5HF5XJL · pith_short_16: 7C3PE5HF5XJLGZZQ · pith_short_8: 7C3PE5HF

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/7C3PE5HF5XJLGZZQT2GYVSSBBV \
  | 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: f8b6f274e5edd2b367309e8d8aca410d53df8419471d7646ef8e04478e5ef024

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "391d2b314d853c0929280be3bc15104874137071e16c17f7fa873d57d42d2665",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2004-12-08T02:36:37Z",
    "title_canon_sha256": "d5b4023ed5fd203720372a1753b954b3ccc1ce1b51eb34063165301c549443a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0412173",
    "kind": "arxiv",
    "version": 1
  }
}