The present paper continues the programme initiated in DGDCG I–II. The Coverage Principle, defined on the unique admissible arena R4 (DGDCG II), generates an isostatic configuration of Voronoi cells whose perimeter functional converges, in the large-scale limit (or in the effective continuum description), to the Hilbert– Einstein action. The Einstein equations Gµν = 8πGNTµν are derived as the stationarity condition δJ /δgµν = 0 without additional postulates. The gravitational constant GN is expressed through the algorithmic Planck scale r∗: GN ∼ r∗2. The cosmological constant vanishes at the classical level. The energy-momentum tensor Tµν arises from defects of the isostatic configuration; geodesic motion follows from covariant conservation ∇µT µν = 0, which is itself a consequence of the diffeomorphism invariance of J . The equivalence principle is a structural result of the theory, not a postulate. All classical gravitational results follow from the single axiom — the Coverage Principle — without additional assumptions.
Andrei Okhremenko (Sun,) studied this question.