Unary Field Theory: Solar System Tests with α ∼ 10⁻¹² Suppression

The Unary Field Theory (UFT) predicts that all deviations from general relativity (GR) in the Solar System are doubly suppressed: by the dimensionless coupling α ∼ κ²v²/M_Pl² ∼ 10⁻¹² and by the kinematic factor (m_φ r)². For Solar System scales (r ∼ 1 AU, m_φ = 1.1 × 10⁻²² eV), the product α(m_φ r)² ∼ 10⁻¹⁰⁷, rendering scalar field corrections completely negligible. This paper provides the step-by-step derivation of the three classical Solar System tests—Mercury's perihelion precession, the Shapiro time delay, and light deflection—from the UFT metric. All predictions reproduce GR values within current measurement precision: Mercury precession = 42.98″/century (observed: 42.977±0.044″), Shapiro delay = 131.3 μs (Cassini: 131.3±10 μs), light deflection = 1.756″ (VLBI: 1.745±0.015″). Crucially, the UFT achieves this GR agreement without screening mechanisms (unlike f(R) or chameleon theories), relying instead on the universal parameter α that also governs galactic dark matter and cosmic acceleration. This provides a seamless transition from local to cosmological scales within a single framework. This is UFT Prediction Paper XIII; the unified framework is in the main paper: Zou (2026), doi:10.5281/zenodo.21186809.