Pith Number

pith:2N4CXDXP

pith:2024:2N4CXDXPRYBKKQDBP4VXBEM623

not attested not anchored not stored refs pending

Strong Gravitational Lensing by Static Black Holes in Effective Quantum Gravity

Amnish Vachher, Qiang Wu, Sushant G. Ghosh, Tao Zhu, Yiyang Wang

arxiv:2410.12382 v1 · 2024-10-16 · 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{2N4CXDXPRYBKKQDBP4VXBEM623}

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	2026-07-05T09:21:18.147840Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3782b8eef8e02a540617f2b70919ed6d6e3b6606bbf8029a9dc6159d82314a1

Aliases

arxiv: 2410.12382 · arxiv_version: 2410.12382v1 · doi: 10.48550/arxiv.2410.12382 · pith_short_12: 2N4CXDXPRYBK · pith_short_16: 2N4CXDXPRYBKKQDB · pith_short_8: 2N4CXDXP

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/2N4CXDXPRYBKKQDBP4VXBEM623 \
  | 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: d3782b8eef8e02a540617f2b70919ed6d6e3b6606bbf8029a9dc6159d82314a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ba9652f60abd3288731321666cd2c470432d76ddb1adef965e9c3bbfdb80799",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2024-10-16T09:05:09Z",
    "title_canon_sha256": "04da1f41a7426a24eaae5e78832ff3d68157e0028d7924060ed0a509802a3aa0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2410.12382",
    "kind": "arxiv",
    "version": 1
  }
}