Structural Collapse Geometry: A Deterministic Framework for Emergent Curvature and Cosmological Structure

A deterministic field model is presented in which curvature, entropy, and causal geometry emerge from local threshold dynamics on a discrete spatial lattice. Sites evolve synchronously and undergo irreversible collapse when local gradients exceed a fixed threshold. Collapse propagates as directional fronts, encodes structural memory, and produces monotonic entropy growth. The resulting freeze-time field defines geodesic flow and scalar curvature, while collapse frequency scales quadratically with excitation amplitude—yielding a deterministic analog of Born-rule statistics. All features arise from local articulation rules alone, without stochastic inputs, observer dependence, or wavefunction formalism. Simulations confirm that collapse is finite, directional, and structurally irreversible, producing stable curvature and information-preserving articulation cores. The model realizes the foundational hinge-and-step structure introduced in Articulation Cosmology, supporting irreversible articulation as a substrate for measurement-like behavior, causal geometry, and logical computation within the Structural Collapse Geometry (SCG) framework.