Pith Number

pith:3353FBXF

pith:2003:3353FBXF3LSCWU6VALBAJQNUDP

not attested not anchored not stored refs pending

Gravitational Lensing Statistics in Universes Dominated by Dark Energy

C. R. Keeton, M. Kuhlen, P. Madau

arxiv:astro-ph/0310013 v1 · 2003-10-01 · 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{3353FBXF3LSCWU6VALBAJQNUDP}

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	2026-07-04T16:51:47.406019Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

defbb286e5dae42b53d502c204c1b41bfee301e3ad35f3b0a0a921e96053e474

Aliases

arxiv: astro-ph/0310013 · arxiv_version: astro-ph/0310013v1 · doi: 10.48550/arxiv.astro-ph/0310013 · pith_short_12: 3353FBXF3LSC · pith_short_16: 3353FBXF3LSCWU6V · pith_short_8: 3353FBXF

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/3353FBXF3LSCWU6VALBAJQNUDP \
  | 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: defbb286e5dae42b53d502c204c1b41bfee301e3ad35f3b0a0a921e96053e474

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "92b194d95ae757e564c513040ebc1c7c9abd6041ece27e82c759fef55a75b398",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2003-10-01T00:56:09Z",
    "title_canon_sha256": "3512f24f068f66d33234c5f481d178a34d2479eebb5a450e62c154d19243f3ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0310013",
    "kind": "arxiv",
    "version": 1
  }
}