Chapter 12: Linear τ-Einstein: Weak-Field Regime and Classical Tests

The τ-Einstein equation R^H = κ_τ · T^mat is a boundary-character identity valid at all scales. This chapter extracts its linear regime: the weak-field, slow-motion limit in which the frame holonomy gap is small compared to the identity. The linear regime recovers all classical tests of general relativity—the Newtonian gravitational law, Mercury’s perihelion precession, the deflection of starlight, gravitational redshift, and gravitational waves—as linear readouts of the full τ-Einstein identity. No approximation beyond linearity is needed. Every prediction matches the orthodox GR result to the precision of the measurements, because the chart shadow of the linearized τ-Einstein equation is the linearized Einstein equation.