Pith Number

pith:RJRD654E

pith:2011:RJRD654EF5SJZFEWN4H2MYB3HS

not attested not anchored not stored refs pending

Lensing by Kerr Black Holes. I: General Lens Equation and Magnification Formula

Amir B. Aazami, A. O. Petters, Charles R. Keeton

arxiv:1102.4300 v2 · 2011-02-21 · astro-ph.CO · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RJRD654EF5SJZFEWN4H2MYB3HS}

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	2026-05-18T02:03:06.950752Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8a623f77842f649c94966f0fa6603b3ca71f20643ad231b9f980528798ddc216

Aliases

arxiv: 1102.4300 · arxiv_version: 1102.4300v2 · doi: 10.48550/arxiv.1102.4300 · pith_short_12: RJRD654EF5SJ · pith_short_16: RJRD654EF5SJZFEW · pith_short_8: RJRD654E

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/RJRD654EF5SJZFEWN4H2MYB3HS \
  | 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: 8a623f77842f649c94966f0fa6603b3ca71f20643ad231b9f980528798ddc216

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f507d8fc741cdc3277dad2b6719f67a31b29ca4c9ed82b69052f68a1e4fc2b8",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2011-02-21T18:25:52Z",
    "title_canon_sha256": "1ebfb57a0aaf926827d5ade3dab32b6b96a18e61a30ef682661fd1bcd79856de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.4300",
    "kind": "arxiv",
    "version": 2
  }
}