Mathematical Foundations of Structured Space Theory (SST)

We present the axiomatic and mathematical structure of Structured Space Theory (SST), a geometric–gravitonic framework in which all physical constants and field equations emerge from a vertex-transitive tetrahedral–octahedral graviton lattice characterized by three parameters: graviton density GD, graviton frequency GF, and geometry constant k_geo. Starting from three lattice identities (E1–E3), we derive the speed of light c, Planck’s constant h, Newton’s gravitational constant G, vacuum permittivity ε₀, vacuum permeability μ₀, and the Planck scale. We show that Maxwell equations emerge from the transverse vector mode of the lattice equations of motion, with c = 1/√(ε₀μ₀) recovered as an internal consistency condition. We demonstrate that Lorentz invariance emerges in the continuum limit from isotropic wave propagation enforced by the O_h point-group symmetry of the cuboctahedral coordination shell, with residual violations suppressed by (d/λ)² ~ 10⁻³⁸ at observable scales. Weak-field general-relativistic behavior is recovered via potential-form solutions (E7–E8). A broad set of empirical validations, spanning laboratory to cosmological scales, confirm numerical agreement with established physics within current experimental precision.