Causal Structure as a Dynamical Framework: Nonlinear Accumulation and Curvature Coherence (v4)

We propose a causal structure framework in which physical reality is described as a system of realizable relations and their accumulation over structural time. In this view, the universe is not composed of objects, but emerges from the accumulation of relations. A minimal and testable nonlinear mechanism is identified: Δφ = A h + B h², with B (T) ∝ T², indicating that nonlinear effects arise from feedback-driven accumulation rather than higher-order perturbative corrections. We introduce the concept of a causal cloud C (x, T) as a coarse-grained representation of relational density. Geometric structure, including curvature, is shown to emerge from spatial variations in this accumulated structure. A key prediction of the framework is curvature coherence: the sign of curvature remains consistent across observational scales. This is quantified through the Relational Curvature Invariant (RCI) and the Sign-Coherence Statistic (SCS), providing a model-independent and falsifiable test. This work does not replace ΛCDM, but introduces a structural diagnostic beyond parameter fitting, offering a new pathway toward understanding the origin of cosmic structure. This work is part of an ongoing series on causal structure and accumulated observables.