Pith Number

pith:SCJ5G2O4

pith:2004:SCJ5G2O4RVKADIRUUWZB7QVMVK

not attested not anchored not stored refs pending

Strong gravitational lensing by braneworld black holes

Richard Whisker

arxiv:astro-ph/0411786 v3 · 2004-11-30 · astro-ph · gr-qc · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SCJ5G2O4RVKADIRUUWZB7QVMVK}

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

Astrophysical environment around a black hole in the braneworld and its optical signatures

Receipt and verification

First computed	2026-07-04T16:45:19.463924Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9093d369dc8d5401a234a5b21fc2acaaa7eb6a7383a721748b35dd86030369ea

Aliases

arxiv: astro-ph/0411786 · arxiv_version: astro-ph/0411786v3 · doi: 10.48550/arxiv.astro-ph/0411786 · pith_short_12: SCJ5G2O4RVKA · pith_short_16: SCJ5G2O4RVKADIRU · pith_short_8: SCJ5G2O4

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/SCJ5G2O4RVKADIRUUWZB7QVMVK \
  | 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: 9093d369dc8d5401a234a5b21fc2acaaa7eb6a7383a721748b35dd86030369ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b5236e561b374a683a72b811b1cb26ee0b269f7c1ebd84eac796b33da43600a",
    "cross_cats_sorted": [
      "gr-qc",
      "hep-th"
    ],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2004-11-30T09:29:21Z",
    "title_canon_sha256": "e1ac483bdeb9741106bcadcbe4452d88446165456cfd5c744eb771f8acdb8a13"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0411786",
    "kind": "arxiv",
    "version": 3
  }
}