Pith Number

pith:4EO7PJU6

pith:2011:4EO7PJU6UTF3ZMCTVWJNT7CJUW

not attested not anchored not stored refs pending

Direct Measurements of the magnification produced by galaxy clusters as gravitational lenses

Alessandro Sonnenfeld, Giuseppe Bertin, Marco Lombardi

arxiv:1106.1442 v2 · 2011-06-07 · astro-ph.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4EO7PJU6UTF3ZMCTVWJNT7CJUW}

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	2026-05-18T02:01:41.028395Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e11df7a69ea4cbbcb053ad92d9fc49a59c3dab16a0630cbccc092067713589c6

Aliases

arxiv: 1106.1442 · arxiv_version: 1106.1442v2 · doi: 10.48550/arxiv.1106.1442 · pith_short_12: 4EO7PJU6UTF3 · pith_short_16: 4EO7PJU6UTF3ZMCT · pith_short_8: 4EO7PJU6

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/4EO7PJU6UTF3ZMCTVWJNT7CJUW \
  | 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: e11df7a69ea4cbbcb053ad92d9fc49a59c3dab16a0630cbccc092067713589c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aae85c030aa316a5902a3af8d2d49327c456bf324fbfc73972e0d8dabd5cbd8a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2011-06-07T20:04:21Z",
    "title_canon_sha256": "677ab7f86c4a4441cb8bb9b9b68baddfde29a109f3df53ae296ed9c425d00cd1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.1442",
    "kind": "arxiv",
    "version": 2
  }
}