Gravity Field Dynamics: Complete Field Closure from Stellated Octahedron Topology

Every formulation of gravity contains two elements: the geometric structure of the gravitational field, and the requirement that the field must extend completely through space. We demonstrate that both follow from a single equation in combinatorics, 2(d+1) = 2^d, whose only positive integer solution is d = 3. This solution fixes two structural constants: K = 4 vertices per simplex and D = 3 spatial dimensions. Binary encoding in three dimensions produces two interlocking tetrahedra (the stellated octahedron) whose face structure yields the (3+1) spacetime decomposition and whose face normals are identically the tetrad of general relativity. The requirement that the field close through this geometry determines the coupling polynomial f(k,s) = 1 + ks + k^2, the gravitational constitutive law mu(x) = x/(x+1), and the complete covariant scalar-tensor action, all with zero free parameters. Expressed in bimetric language, the topological coupling fixes the five previously free Hassan-Rosen coefficients to {1, 0, 16, 0, 1} (companion letter). Every numerical constant in the theory reduces to K = 4 and D = 3. Different coupling depths yield constitutive laws that differ by approximately 12% at the transition acceleration scale, measurable in galaxy rotation curves. The binary structure validated here was independently encoded in the I Ching trigram system (c. 2800-1000 BCE), predating formal binary arithmetic by millennia.