Aionic IV: Theory of Structure

We present Aionic IV, a foundational framework that isolates the minimal structural condi-tions required for coherent empirical science. Rather than introducing new dynamics, particles,or forces, Aionics identifies the constraints that any empirically consistent physical theory mustsatisfy in order for experimentation, comparison, and refinement to be possible at all. Fromcomposability of processes, stability under refinement, and context-stable comparability, wederive the necessity of additive ordering, equilibrium structure, unitary interference representa-tions, and redundancy-induced entropy corrections. These results are independent of spacetimegeometry, quantum postulates, or microscopic assumptions. Physical theories such as classicalmechanics, general relativity, and quantum theory are understood as distinct representationsectors instantiating the same underlying structure. Aionic IV thus characterizes the structuralskeleton that makes cumulative physics possible, and provides precise criteria for what wouldconstitute genuinely new physics as violations of realizability itself.