We present a unified derivation of three fundamental quantum phenomena from the Al-Ani Fabric Theory. Starting from a single master equation, we derive: (1) the visibility function for wave-particle duality V(I) = 1/[1 + e^{(I-I_c)/ΔI}], (2) the collapse probability for the measurement problem P(r) = |ψ₀|²/[1 + (δ_meas/δ_c)²], and (3) the CHSH correlation S = 2√2. Using three double-slit experiments (Jönsson 1961, Tonomura 1989, Arndt 1999) for calibration, we determine I_c = (2.1±0.3)×10⁶ and ΔI = (1.8±0.4)×10⁶. The predicted CHSH correlation matches modern experiments (Giustina 2015, Shalm 2015) within 1σ. We then make a testable prediction for future high-precision experiments: S = 2.828 ± 0.005.