Pith Number

pith:WIGADR6I

pith:2010:WIGADR6I4WEKTXTO4BVPM6PPEZ

not attested not anchored not stored refs pending

Precise analytic treatment of Kerr and Kerr-(anti) de Sitter black holes as gravitational lenses

G. V. Kraniotis

arxiv:1009.5189 v1 · 2010-09-27 · gr-qc · astro-ph.GA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WIGADR6I4WEKTXTO4BVPM6PPEZ}

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	2026-05-18T04:24:52.931507Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b20c01c7c8e588a9de6ee06af679ef26524fa3de608ecc8830b08d053ace14d5

Aliases

arxiv: 1009.5189 · arxiv_version: 1009.5189v1 · doi: 10.48550/arxiv.1009.5189 · pith_short_12: WIGADR6I4WEK · pith_short_16: WIGADR6I4WEKTXTO · pith_short_8: WIGADR6I

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/WIGADR6I4WEKTXTO4BVPM6PPEZ \
  | 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: b20c01c7c8e588a9de6ee06af679ef26524fa3de608ecc8830b08d053ace14d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36d96b4e65e971da716b8201fa851d4600c6dfa91749a971ebb692011076ca01",
    "cross_cats_sorted": [
      "astro-ph.GA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2010-09-27T08:48:25Z",
    "title_canon_sha256": "f8cf1b340c8ff4af750173c24f9615b2b6228e5634db90a55a3856bbdcd55666"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.5189",
    "kind": "arxiv",
    "version": 1
  }
}