--- original/manuscript.tex
+++ build_repaired/manuscript.tex
@@ -17,6 +17,7 @@
 \usepackage{listings}
 \usepackage{xcolor}
 \usepackage{tikz}
+\usetikzlibrary{shapes.symbols}
 \usepackage[margin=1in]{geometry}
 
 % --- Theorem Environments ---
@@ -27,9 +28,6 @@
 \newtheorem{definition}{Definition}[section]
 
 % --- Custom Commands ---
-\newcommand{\Phi}{\Phi}
-\newcommand{\Psi}{\Psi}
-\newcommand{\Omega}{\Omega}
 \newcommand{\golden}{\varphi}
 \newcommand{\fib}[1]{F_{#1}}
 
@@ -175,7 +173,7 @@
 
 We also employ the golden angle:
 \begin{equation}
-\theta_g = \frac{2\pi}{\golden^2} \approx 137.508°
+\theta_g = \frac{2\pi}{\golden^2} \approx 137.508^{\circ}
 \end{equation}
 
 This angle appears in phyllotaxis (leaf arrangement) and ensures maximal spacing between successive elements, minimizing overlap and interference \citep{adam2011mathematics}. We hypothesize that golden angle timing similarly minimizes destructive interference in information processing.