On the Ontological Foundations of Cosmological Update Dynamics: Distinguishability as the Minimal Condition for Structure Formation

This work presents a minimal ontological foundation for Cosmological Update Dynamics (CUD), a framework describing the universe as a process of probabilistic structural updates. In CUD v2.5, structure formation is governed by the update flux (ρ), structural potential (u), and instability (φ). However, the conceptual meaning of the update flux ρ has remained unspecified. This work introduces an interpretative extension in which ρ is defined as a distribution of distinguishability, understood as the minimal condition under which differences can be established. Within this framework: - Structural potential u is interpreted as accumulated distinguishability - Flow emerges from gradients of u (Flow ∝ -∇u), not from ρ itself - Structure is understood as the result of accumulated differentiation This formulation preserves the mathematical structure of CUD v2.5 while clarifying its conceptual foundation. This work serves as a bridge between CUD v2.5 and future developments (CUD v3), where the origin of distinguishability and the nature of update processes remain open questions.