Comment to Comment to Black Hole in Dehnen $\left(1,4,\frac{1}{2}\right)$ Dark Matter Halo: Exact Solution, Lensing, Light Ring, and Thermodynamics

Abstract

The claim in \cite{Al-Badawi:2025ipr} that *"the errors in the foundational components (3) and (5) of Ref. [1] invalidate all subsequent analyses, numerical results, and physical interpretations that depend on them"* is **entirely unfounded**. This statement reflects a fundamental misunderstanding of the typographical nature of the error and appears to be a misplaced critique originating from a competing author, rather than a substantive assessment of the results, which remain fully valid.

The comment letter we comment for (arXiv:2511.15748) has been retracted