Cosmology of the Φ Fold: Fractional Self-Gravitating Structure and the Origin of Galactic Halos Without Dark Matter

The “Φ Fold Cosmology” introduces a fractional scalar-field framework based on the Riesz operator, capable of generating stable self-gravitating configurations without the need for dark matter.Through numerical simulations implemented in riesz_safe_run.py, the model demonstrates how fractional curvature and nonlinear self-interaction naturally reproduce the observed flatness of galactic rotation curves. The fractional Laplacian acts as an emergent gravitational term, creating a condensed core and a diffuse halo that remain in stable equilibrium.This work provides both the theoretical formulation and full numerical implementation, ensuring complete reproducibility of results. Keywords: fractional cosmology, Riesz potential, self-gravitating field, dark matter alternatives, fractional gravity, galactic halos, cosmological modeling.