Realizability and the Origin of Causality

We show that spacetime causality—light cones and an invariant maximal speed—follows from a realizability axiom: a fundamental variational law must admit an attained minimum on the temporally persistent, spatially nontrivial admissible class ($\Delta t = T > 0$, $\Delta r \neq 0$). In positive-definite geometry, the infimum over this class is $0$ but unattained, with minimizing sequences collapsing toward the trivial process. Realizability therefore enforces nontrivial zero-cost (null) directions; under a minimal local quadratic ansatz this excludes Euclidean signature and yields a Lorentzian null cone with slope $dr/dt=\pm c_{\max}$. Special Relativity emerges as the minimal geodesic dynamics compatible with this constraint.