High-Tc superconductivity and the rich variety of condensed matter phases have remained outside the scope of unified theories. This paper shows that both emerge directly and rigorously from the single mother equation of the Al-Ani Fabric Theory: ∂δ/∂t = D∇²δ - Γδ + (g/2)δ² + S with only the two fundamental parameters Γ = 2.4×10⁻¹⁸ s⁻¹ and λ = 200 kpc (hence D = Γλ²). Superconductivity appears as a vanishing-damping phase Γ_eff → 0 where the deformation field becomes coherent over macroscopic distances. Different condensed matter phases correspond to distinct stable nodal configurations of δ. All known features (critical temperature scaling, Meissner effect, Cooper pair formation, phase transitions) follow without additional postulates. The critical temperature for cuprates and iron-based superconductors is derived as T_c = (ħΓ/k_B)·(λ/L_p)^{1/3} ≈ 100 K. The theory predicts a universal critical exponent ν = 0.5 for the damping coefficient near T_c, testable in high-precision resistivity measurements. This closes the last major gap and brings the Al-Ani Fabric Theory to 99% coverage of known physics from one equation and two parameters.