Emergence XXVIII: The Emergence of Tensor Properties from Primitives

General relativity describes gravity as the curvature of spacetime, with the stress-energy tensor sourcing the Einstein tensor. This paper proves that none of these tensor quantities are fundamental. Every tensor in general relativity—the stress-energy tensor, the Riemann curvature tensor, the Einstein tensor, and the metric—emerges from the eight primitives of the canvas model. The dynamic primitives generate the energy-momentum of matter through the unified wave equation. The property primitives provide the dimensional stage on which tensor quantities exist. The stress-energy tensor is the organized energy-momentum of the primitive fields. The Riemann tensor is the discrete curvature of the voxel lattice, encoded in the deficit angles at lattice hinges. The Einstein equations are the equilibrium condition between the compression of the lattice and the energy of the primitives. Nothing in general relativity is fundamental. Geometry is not fundamental. The metric is not fundamental. Curvature is not fundamental. They are emergent descriptions of how the eight primitives behave at scales much larger than the Planck length. This paper completes the reduction of general relativity to the canvas model.