Causal Structure, Nonlinear Accumulation, and Cosmology: Curvature Coherence as a Structural Invariant

This work proposes a causal structure framework in which the universe is described as an evolving network of realizable relations rather than a collection of independent physical components. A central mechanism is nonlinear accumulation, expressed in minimal measurable form as Δφ = Ah + Bh² with T² scaling. This mechanism is extended to cosmology through a coarse-grained structural field, the causal cloud C(x,T), representing the accumulation and interaction of relational constraints. Within this framework, spacetime geometry, thermodynamic irreversibility, quantum correlations, cosmic expansion, and large-scale structure are interpreted as manifestations of accumulated causal structure. Dark energy-like and dark matter-like phenomena are not directly replaced, but reinterpreted as emergent effects of latent relational constraints. To enable empirical testing, we introduce two largely model-independent observables: the Relational Curvature Invariant (RCI) and the Sign-Coherence Statistic (SCS). These quantities characterize the second-order structure of cosmological observations, particularly the distance modulus–redshift relation μ(z). The central prediction is curvature sign coherence across the observable redshift range. If curvature signs fluctuate randomly, SCS approaches zero; if curvature maintains a consistent direction, |SCS| approaches one. This provides a minimal, reproducible, and falsifiable criterion distinguishing parameter-driven curvature behavior from accumulation-driven structure. The framework does not rely on specific parameter choices or introduce new fundamental fields. Instead, it identifies structural invariants within observational data, shifting the focus from parameter fitting to structural interpretation. This work aims to provide a bridge between microscopic interaction, nonlinear accumulation, and macroscopic cosmological structure within a unified framework. All figures and conceptual frameworks presented in this work are original and protected under copyright.