Pith Number

pith:25N7IINS

pith:2021:25N7IINSVOMD7QP62ZSRQ774N3

not attested not anchored not stored refs pending

Strong field gravitational lensing by hairy Kerr black holes

Shafqat Ul Islam, Sushant G. Ghosh

arxiv:2102.08289 v5 · 2021-02-16 · 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{25N7IINSVOMD7QP62ZSRQ774N3}

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

Strong gravitational lensing by black hole in F(R) Euler Heisenberg Gravity's Rainbow

Receipt and verification

First computed	2026-07-05T02:53:35.849918Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d75bf421b2ab983fc1fed665187ffc6ed69bdef8ff651aa0414001841a19655a

Aliases

arxiv: 2102.08289 · arxiv_version: 2102.08289v5 · doi: 10.48550/arxiv.2102.08289 · pith_short_12: 25N7IINSVOMD · pith_short_16: 25N7IINSVOMD7QP6 · pith_short_8: 25N7IINS

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/25N7IINSVOMD7QP62ZSRQ774N3 \
  | 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: d75bf421b2ab983fc1fed665187ffc6ed69bdef8ff651aa0414001841a19655a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7cbb0b38a3b0684a244b0b11687bdf316ac49126194399a919bcfaca53332b5",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2021-02-16T17:19:12Z",
    "title_canon_sha256": "b11946d7d6ff5c25a9d2202c074232def8ebb9c0f2c98b3f81d70a3f5de1de09"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2102.08289",
    "kind": "arxiv",
    "version": 5
  }
}