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

Aionics is a geometric framework in which physical reality is described by constraints onrealizable transitions rather than by primitive time evolution. We proceed step-by-step fromoperational necessities to geometric structure. First, we prove a no-go theorem: any empir-ical theory admitting composable processes, operational comparability, and context stabilitynecessarily induces an additive scalar functional on realizable paths. This functional is notassumed but forced, and is identified as derived time. Second, we introduce a non-temporalconstraint-instance space Ξ and equip it with discrete exterior calculus (DEC), allowing realiz-able transitions to be represented as paths independent of spacetime. Third, we define paralleltransport between observable realizations across constraint changes and show that curvaturearises as holonomy around closed loops in Ξ. This establishes that curvature is a propertyof realizability geometry rather than spacetime itself. Finally, spacetime curvature in GeneralRelativity is treated as a representation sector of this more general structure. The frameworkyields concrete, falsifiable predictions: curvature must manifest as gauge-invariant holonomyunder closed constraint loops, and scalar observables alone cannot witness it. Aionics thus uni-fies time emergence and curvature within a single operationally grounded, testable geometricframework