Emergent Gravity from the PhiMDL Field: Einstein Equations, Kink Sources, and Quantum Gravity Scale

Starting from the -symmetric Klein-Gordon field with V = (mₚhi²/49) (1- 7) and mₚhi = m_ = 1776. 86\, MeV, we derive six gravitational results. (1) T_ = _\, _ - L is machine-certified in Lean 4 (zero sorry; symmetry, vacuum-vanishing, and gravity prerequisites in StressEnergyTensor. lean). (2) The linearized Einstein equations G_ = 8 GN T_ follow from MDL-Lovelock correspondence (P35) combined with minimal coupling. (3) The BPS kink is a gravitational source: T₀0\, dx = Mₖink = 290. 10\, MeV (relative error 1. 410^-6) ; conservation holds to 610^-12. (4) The classical cosmological constant vanishes at all seven vacua; the one-loop correction VCW -1. 710⁷\, MeV⁴ exceeds the observed dark-energy scale by 10⁴2 — identified but not resolved. (5) The quantum gravity scale is MPlᵗot = /3 1. 81 lattice units from the Nyquist residual ₀ (M) = ²/ (3M²). (6) The three-tape CMCA c gradient-kick mechanism recovers Newtonian gravity F = GₑffM/ (4 b²) in the continuum limit (, P45 SpivackCMCA). Newton's constant GN is derived via the gravitational hierarchy formula ().