Pith Number

pith:V4H4HGIF

pith:2021:V4H4HGIFWSD65LLBVCGNXNIVBE

not attested not anchored not stored refs pending

Investigating strong gravitational lensing effects by suppermassive black holes with Horndeski gravity

Jitendra Kumar, Shafqat Ul Islam, Sushant G. Ghosh

arxiv:2109.04450 v2 · 2021-09-09 · 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{V4H4HGIFWSD65LLBVCGNXNIVBE}

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	2026-07-05T04:27:45.332453Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af0fc39905b487eead61a88cdbb5150916e6742e5a708596a07d89610a0ea44c

Aliases

arxiv: 2109.04450 · arxiv_version: 2109.04450v2 · doi: 10.48550/arxiv.2109.04450 · pith_short_12: V4H4HGIFWSD6 · pith_short_16: V4H4HGIFWSD65LLB · pith_short_8: V4H4HGIF

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/V4H4HGIFWSD65LLBVCGNXNIVBE \
  | 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: af0fc39905b487eead61a88cdbb5150916e6742e5a708596a07d89610a0ea44c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "267833af29230c585a769f9f3f7952b7b6d623223ed40e9b90d25b84e6a9e8c1",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2021-09-09T17:49:26Z",
    "title_canon_sha256": "0796e8d2723fb95f8ab213ec814691ca35fcd53b66442f431de89adad8f6595f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.04450",
    "kind": "arxiv",
    "version": 2
  }
}