This article presents an investigation into the transition from traditional Euclidean latent space to Riemannian manifolds with constant curvature in neural networks. The central innovation lies in the integration of the Golden Ratio ($\phi \approx 1.618$) as a dynamic curvature regulator ($c = \phi^{-1}$) and weight initialization.

The study compares three topological paradigms using the MNIST dataset:

1. Hyperbolic Geometry (Negative Curvature): Implemented via the Poincaré Disk Model to capture hierarchical structures.

2. Spherical Geometry (Positive Curvature): Used for cyclic data mapping and intrinsic normalization via hypersphere.

3. Euclidean Architecture (Control): Baseline using traditional Xavier initialization.

Main Results: The experiments demonstrate the superiority of the Golden Hyperbolic Geometry, which achieved an accuracy of 97.70%, surpassing the Euclidean baseline (92.06%). The results indicate that the use of non-Euclidean manifolds regulated by $\phi$ allows for more efficient class separation, stabilizes gradients during training, and accelerates convergence compared to conventional artificial market methods.