Electroconvergence: Emergent Spacetime and the Geometric Limit of the Mach-Maxwell Force.

This article presents a formal derivation of the spacetime metric and Einstein's field equations as geometric limits of the electroconvergent phase-field dynamics formulated in the foundational works of the electroconvergent framework. The derivation uses the relational formalism (the Kess matrix, the persistence operator, and the primitive distinction δ = Φ_G - Φ_L) as its primary deductive tool. The organizational network S0-S5 is defined for a generic stellar system. The metric tensor is derived as a deterministic property of the phase interaction between the observer S2 and the Mach references S4/S5. The energy-momentum tensor is obtained as a projection of the Kess matrix onto the persistent body C. The variational principle applied to the phasic field recovers Einstein's equations in the appropriate limit, with the Newtonian gravitational constant G identified as the inverse of the phase rigidity. The derivation is scale-independent and does not rely on observational data from any specific natural system.