Pith Number

pith:DJPELXUJ

pith:2010:DJPELXUJWERLADPZGSDA745BKB

not attested not anchored not stored refs pending

Gravitational Lensing in Spherically Symmetric Spacetimes

Bonita de Swardt, Chris Clarkson, Peter K. S. Dunsby

arxiv:1002.2041 v1 · 2010-02-10 · gr-qc · 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{DJPELXUJWERLADPZGSDA745BKB}

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.

Cited by

1 paper in Pith

Inhomogeneous model with a space dependent Cosmological Constant

Receipt and verification

First computed	2026-07-04T17:21:41.776206Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1a5e45de89b122b00df934860ff3a150521702b5a39b1153aa0a077c0c929246

Aliases

arxiv: 1002.2041 · arxiv_version: 1002.2041v1 · doi: 10.48550/arxiv.1002.2041 · pith_short_12: DJPELXUJWERL · pith_short_16: DJPELXUJWERLADPZ · pith_short_8: DJPELXUJ

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/DJPELXUJWERLADPZGSDA745BKB \
  | 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: 1a5e45de89b122b00df934860ff3a150521702b5a39b1153aa0a077c0c929246

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4a18462eb56c8b0f5cd9ee3a2bbae9b45043b24d0606f81bd8575924ed2d0de",
    "cross_cats_sorted": [
      "astro-ph.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2010-02-10T09:59:03Z",
    "title_canon_sha256": "3ab9dc22b49b141950892911c1d0e25c3a70d62d33f55a7abf53b67a4b187d39"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.2041",
    "kind": "arxiv",
    "version": 1
  }
}