Pith Number

pith:ZA33CUEM

pith:2006:ZA33CUEMRBRIYGHSYT2MNFG4RR

not attested not anchored not stored refs pending

Three Gravitational Lenses for the Price of One: Enhanced Strong Lensing through Galaxy Clustering

(2) Kapteyn Institute, (3) UC Santa Barbara, (4) KIPAC, (5) OCIW), C. D. Fassnacht (1), D. Wittman (1) ((1) UC Davis, J. P. McKean (1), L. M. Lubin (1), L. V. E. Koopmans (2), M. W. Auger (1), R. D. Blandford (4), T. E. Jeltema (5), T. Treu (3), V. E. Margoniner (1)

arxiv:astro-ph/0603445 v1 · 2006-03-17 · 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{ZA33CUEMRBRIYGHSYT2MNFG4RR}

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	2026-05-18T04:36:21.602520Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c837b1508c88628c18f2c4f4c694dc8c5f98a549026349ffb5a9a7a146d25ac5

Aliases

arxiv: astro-ph/0603445 · arxiv_version: astro-ph/0603445v1 · doi: 10.48550/arxiv.astro-ph/0603445 · pith_short_12: ZA33CUEMRBRI · pith_short_16: ZA33CUEMRBRIYGHS · pith_short_8: ZA33CUEM

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/ZA33CUEMRBRIYGHSYT2MNFG4RR \
  | 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: c837b1508c88628c18f2c4f4c694dc8c5f98a549026349ffb5a9a7a146d25ac5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6ca7b1ed9288606b7daf406954c6f8fa1f5e8f07aedc169c6ef35b62047ec85e",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2006-03-17T01:14:48Z",
    "title_canon_sha256": "ed9290f4e5cccbb9ccdb6dab09690363bd2f95f768fd3aaad1790280fb162e22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0603445",
    "kind": "arxiv",
    "version": 1
  }
}