Cosmic Fabric:A spherical soliton proof -of-concept model for Dark-Matter-like phenomena.

We present the Cosmic Fabric Unified Field Model (CF-UFM v11), a proof-of-concept numerical model in which a localized phase transition of a scalar field s(r), coupled to an auxiliary structural field h(r), is triggered by high-density baryonic cores. Through a symmetry-consistent coupling modification (s(s² - s₀²)ρ_b) and logarithmic potential protection, we obtain a numerically stable coupled-field soliton configuration with s(0) = 0.307649 < 0.5. The total mass is M_total ≈ 1.93403 (natural units), equivalent to 4.45 × 10¹¹ M⊙, within the typical mass range of spiral galaxy dark matter halos. The model is tested on 129 galaxies from the SPARC database, achieving an 89.1% success rate in reproducing observed rotation curves. The model naturally produces cored density profiles, offering a possible mechanism for addressing the core-cusp tension. An emergent baryonic Tully-Fisher relation (M_b ∝ v^4) is derived directly from the field dynamics without any ad hoc tuning. This work is a preprint submitted for open access. The full Python code used to generate the results is available upon reasonable request from the author.