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

Starting from the -symmetric Klein-Gordon field with V = (m_phi^2/49)(1- 7) and m_phi = 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 G_N T_ follow from MDL-Lovelock correspondence (P35) combined with minimal coupling. (3) The BPS kink is a gravitational source: T_00\,dx = M_kink = 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 V_CW -1.710^7\,MeV^4 exceeds the observed dark-energy scale by 10^42 — identified but not resolved. (5) The quantum gravity scale is M_Pl^tot = /3 1.81 lattice units from the Nyquist residual _0(M) = ^2/(3M^2). (6) The three-tape CMCA _c gradient-kick mechanism recovers Newtonian gravity F = G_effM/(4 b^2) in the continuum limit (, P45 SpivackCMCA). Newton's constant G_N is derived via the gravitational hierarchy formula ().