Pith Number

pith:BEIDFLWS

pith:2026:BEIDFLWSE7MMM7L7N5XXYIG5YQ

not attested not anchored not stored refs pending

Photon Propagation and Black Hole Imaging in Kruglov Nonlinear Electrodynamics

A. Sulaksono, D. A. Witjaksana, H. S. Ramadhan, M. F. Fauzi

Kruglov nonlinear electrodynamics produces stable photon orbits outside black hole horizons for small positive q, changing the appearance of relativistic images.

arxiv:2604.22309 v3 · 2026-04-24 · gr-qc · hep-th

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BEIDFLWSE7MMM7L7N5XXYIG5YQ}

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.

Claims

C1strongest claim

sufficiently small positive values of q generate stable photon orbits outside the event horizon, together with significant modifications to the range of impact parameters supporting multiple photon trajectories. These effects produce observable modifications in the relativistic images

C2weakest assumption

The effective null geometry derived from the Kruglov Lagrangian correctly governs photon propagation, and the fully numerical geodesic integrations accurately capture all qualitative features without hidden approximations or instabilities that would alter the reported stable orbits and image changes.

C3one line summary

In Kruglov nonlinear electrodynamics, small positive values of the parameter q produce stable photon orbits outside the event horizon and modify black hole shadows and relativistic images even when the spacetime metric stays close to Reissner-Nordström.

Receipt and verification

First computed	2026-07-01T01:17:51.206532Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

091032aed227d8c67d7f6f6f7c20ddc42a4c3b15a183510b696c9b707413af67

Aliases

arxiv: 2604.22309 · arxiv_version: 2604.22309v3 · doi: 10.48550/arxiv.2604.22309 · pith_short_12: BEIDFLWSE7MM · pith_short_16: BEIDFLWSE7MMM7L7 · pith_short_8: BEIDFLWS

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/BEIDFLWSE7MMM7L7N5XXYIG5YQ \
  | 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: 091032aed227d8c67d7f6f6f7c20ddc42a4c3b15a183510b696c9b707413af67

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4c7a5ab2e7ff68d785afb13f35f5ccf5cf45bc43c215c76850eef5fcd4f2477",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-04-24T07:41:22Z",
    "title_canon_sha256": "211338725832fdc9fc67e0afaccaf11defee95a86769cbf134c7d7d65558a0fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.22309",
    "kind": "arxiv",
    "version": 3
  }
}