Pith Number

pith:VFX5JJTR

pith:2024:VFX5JJTRBNNJ5WIMXCXO7WIGHB

not attested not anchored not stored refs pending

Twisting shadows: Light rings, lensing and shadows of black holes in swirling universes

Carlos A. R. Herdeiro, Lu\'is C. B. Crispino, Zeus S. Moreira

arxiv:2401.05658 v2 · 2024-01-11 · 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{VFX5JJTRBNNJ5WIMXCXO7WIGHB}

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

Spinning generalizations of Majumdar-Papapetrou multi-black hole spacetimes: light rings, lensing and shadows

Receipt and verification

First computed	2026-07-05T11:44:38.784791Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a96fd4a6710b5a9ed90cb8aeefd90638750163315c3406daaa6876c817b5c15f

Aliases

arxiv: 2401.05658 · arxiv_version: 2401.05658v2 · doi: 10.48550/arxiv.2401.05658 · pith_short_12: VFX5JJTRBNNJ · pith_short_16: VFX5JJTRBNNJ5WIM · pith_short_8: VFX5JJTR

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/VFX5JJTRBNNJ5WIMXCXO7WIGHB \
  | 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: a96fd4a6710b5a9ed90cb8aeefd90638750163315c3406daaa6876c817b5c15f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "906f171e291b52d1afff6f2eda7f6d180dcc4d81a9278fd3a0fe619cd43c3188",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2024-01-11T04:42:44Z",
    "title_canon_sha256": "6a33218fbff0793869220fb600bb2475eb73780fd8759c8ded33a91a386e55e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2401.05658",
    "kind": "arxiv",
    "version": 2
  }
}