Pith Number

pith:FPQCEYUE

pith:2008:FPQCEYUENX767UJX36TMJJ3RDJ

not attested not anchored not stored refs pending

A comparison of approximate gravitational lens equations and a proposal for an improved new one

V. Bozza

arxiv:0807.3872 v2 · 2008-07-24 · gr-qc · 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{FPQCEYUENX767UJX36TMJJ3RDJ}

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

Probing Lorentz Symmetry Violation through Lensing Observables of Rotating Black Holes

Receipt and verification

First computed	2026-07-04T15:34:12.336574Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2be02262846dffefd137dfa6c4a7711a5d84ddac887a0c1822bec99b6a4b58ab

Aliases

arxiv: 0807.3872 · arxiv_version: 0807.3872v2 · doi: 10.48550/arxiv.0807.3872 · pith_short_12: FPQCEYUENX76 · pith_short_16: FPQCEYUENX767UJX · pith_short_8: FPQCEYUE

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/FPQCEYUENX767UJX36TMJJ3RDJ \
  | 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: 2be02262846dffefd137dfa6c4a7711a5d84ddac887a0c1822bec99b6a4b58ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "16f2a8fcfdd8648749409bcab59101f15056280772792590c6faf160c5cc04ba",
    "cross_cats_sorted": [
      "astro-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2008-07-24T12:44:08Z",
    "title_canon_sha256": "85fa9ad8c3c69d636f7f3203e260d883de0fc88913d32b354e5dd251311ba2da"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0807.3872",
    "kind": "arxiv",
    "version": 2
  }
}