Aionics I: Realizability Geometry, Derived Time, and Curvature Beyond Spacetime

Aionics is a geometric framework in which physical reality is described by constraints on realizable transitions rather than by primitive time evolution. We proceed step-by-step from operational necessities to geometric structure. First, we prove a no-go theorem: any empirical theory admitting composable processes, operational comparability, and context stability necessarily induces an additive scalar functional on realizable paths. This functional is not assumed but forced, and is identified as derived time. Second, we introduce a non-temporal constraint-instance space $\Xi$ and equip it with discrete exterior calculus (DEC), allowing realizable transitions to be represented as paths independent of spacetime. Third, we define parallel transport between observable realizations across constraint changes and show that curvature arises as holonomy around closed loops in $\Xi$. This establishes that curvature is a property of realizability geometry rather than spacetime itself. Finally, spacetime curvature in General Relativity is treated as a representation sector of this more general structure. The framework yields concrete, falsifiable predictions: curvature must manifest as gauge-invariant holonomy under closed constraint loops, and scalar observables alone cannot witness it. Aionics thus unifies time emergence and curvature within a single operationally grounded, testable geometric framework.