Relational Ontopoiesis and Variational Vacuum Dynamics: Machine-Checked Foundations of Field Geometry and Gauge Symmetry

Paper 1 of the 3-part Process Ontology Master Preprint Series. Formalizes the mathematical foundations of Process Ontology in Lean 4 with Mathlib. Proves Banach fixed-point contraction for the Master Postulate M(X*) = X*, conformal golden ratio scaling phi, neutral Lyapunov stability along the Axis of Silence mirror plane sigma = 1/2, non-zero Universal Phase Slip delta_slip = phi^-4 / 168 > 0, Standard Model Lie algebra total dimension SU(3) x SU(2) x U(1) = 12 matching the 3D kissing number L12 = 12, and Universal Cost Function C(X) variational free energy minimization.