Pixel Theory (PT) predicts c(t) = c₀(t/t₀)^{-λ}, with λ₀ = 0.277. Combined with the PT foundational constraint ℓ_P = const, this immediately implies ℏG = ℓ_P²c³. We show that four independent observational datasets uniquely determine how every fundamental constant varies with c. Lunar laser ranging constrains |Ġ/G| < 7.1×10⁻¹³/yr, forcing G = const and ℏ∝c³ to within 1%. ESPRESSO quasar spectroscopy constrains |Δα/α| < 1.3×10⁻⁶, requiring e∝c. Molecular hydrogen absorbers constrain μ = m_e/m_p = const. The CMB recombination redshift z_rec = 1089 constrains E_H = const, giving m_e and m_p ∝ c⁻². The solution is internally consistent: α and μ are exactly constant (falsifiable null-hypothesis predictions for ANDES/ELT), atoms were larger in the early universe (Bohr radius ∝ c⁴), and the Planck energy was higher (E_P ∝ c⁴). The varying-constants problem is transformed from speculation into a systematic observational constraint on PT's single parameter λ.