Classical Tests of the Fractal-Temporal Framework: Perihelion Precession, Light Deflection, Shapiro Delay, and Gravitational Redshift from the τ -Field

Any alternative theory of gravity must pass four tests: Mercury's perihelion precession (42. 99"/century), light deflection by the Sun (1. 751"), the Shapiro time delay (~240 μs), and the Pound-Rebka gravitational redshift. This paper demonstrates that the fractal-temporal Lagrangian passes all four — exactly. The proof is structural: the τ-field vacuum equation ∇² (τ²) = 0 admits the solution τ = √ (1 − rₛ/r), which produces the exact Schwarzschild metric in the Jordan frame. No approximation is needed. The PPN parameter γ = 1 identically in vacuum, satisfying the Cassini constraint |γ − 1| < 2. 3 × 10⁻⁵ by construction. The theory is observationally indistinguishable from general relativity at first post-Newtonian order. Where the theory departs from GR is at higher precision, through the fractal texture tower Φₙ. The texture fields introduce log-periodic corrections to all four classical observables, with modulation period ln√2 ≈ 0. 347 in log-radius. For Mercury's perihelion precession, the predicted fractal correction is δφ ~ 3 × 10⁻⁴ "/century — within an order of magnitude of the current measurement precision from Messenger radar ranging (±0. 002"/century). The BepiColombo mission, currently in transit to Mercury, provides a near-term test capable of detecting or excluding this correction. The paper establishes three results: (1) the τ-field reproduces all classical GR tests exactly at leading order, (2) the fractal sector generates distinct, computable corrections at higher order, and (3) these corrections are approaching the sensitivity of current and planned missions. This positions the framework as not merely compatible with GR but as a testable extension with specific predictions for next-generation precision gravitational measurements.