Pith Number

pith:XA4N5QHM

pith:2025:XA4N5QHMI626HTKSBXJISRL2KB

not attested not anchored not stored refs pending

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

Niyaz Uddin Molla, Sayan Naskar, Ujjal Debnath

arxiv:2507.13953 v1 · 2025-07-18 · astro-ph.GA · 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{XA4N5QHMI626HTKSBXJISRL2KB}

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	2026-07-05T11:39:25.965484Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b838dec0ec47b5e3cd520dd289457a5045552b46a912c788dc91ce872937ac47

Aliases

arxiv: 2507.13953 · arxiv_version: 2507.13953v1 · doi: 10.48550/arxiv.2507.13953 · pith_short_12: XA4N5QHMI626 · pith_short_16: XA4N5QHMI626HTKS · pith_short_8: XA4N5QHM

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/XA4N5QHMI626HTKSBXJISRL2KB \
  | 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: b838dec0ec47b5e3cd520dd289457a5045552b46a912c788dc91ce872937ac47

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9eb112505919b172c5d98002f73fe6c28b51941bccbf534f20ac9c184c5c52ba",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "astro-ph.GA",
    "submitted_at": "2025-07-18T14:21:03Z",
    "title_canon_sha256": "195bcdf0ef80cedcd092f017f520c312b83678671dc36c709cf9322ab0b0185c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.13953",
    "kind": "arxiv",
    "version": 1
  }
}