Part 5: Dynamics, Screening, and Deviation from Geometric Attractors

Previous work within the Origin Geometry (OG) framework established the existence of geometric eigenmodes and attractors in discrete aperiodic four-dimensional geometry, providing a structural mechanism for stability prior to any physical interpretation. A natural question then arises: if geometric attractors stabilize baseline configurations, why do experimentally inferred values generally differ from these idealized states?

In this paper, we introduce dynamics at a strictly controlled, pre-physical level to address this question. We argue that generic fluctuations—thermal, quantum-like, or environmental—induce dynamical screening that shifts systems away from geometric baselines while preserving attractor structure. This process is shown to admit a geometric interpretation analogous to renormalization flow, driven by coarse-graining and information-theoretic loss of structural coherence rather than by perturbative field-theoretic corrections.

We further demonstrate that this flow is intrinsically directional and irreversible, biasing effective configurations toward lower stiffness and lower-energy descriptions. No numerical evaluation, specific dynamical model, or physical coupling identification is introduced. The role of this paper is to establish how dynamics modifies—but does not generate—values, thereby preparing the ground for subsequent analysis of numerical emergence.