Semantic Gravitation V: Semantic Field Dynamics in Complex Systems — From Neural and Latent States to Semantic State Spaces

Semantic Gravitation is an open research programme that investigates whether meaning can be modelled as a dynamical entity with its own geometry, stability properties, and flow laws—analogous to how physical field theories describe the evolution of states and structures. This fifth paper provides the operational bridge between the abstract semantic field theory developed in Papers I–IV and concrete, data-bearing complex systems. It shows how semantic field dynamics can be instantiated for neural networks, large language models, and other high-dimensional dynamical agents by mapping their internal state spaces into a shared semantic Hilbert space. Starting from raw neural or latent-state dynamics, the paper introduces semantic encoders that induce semantic trajectories governed by an effective potential. It develops a principled pipeline from internal representations to semantic gradient flows, free-energy functionals, and alignment metrics. In doing so, it formulates empirically accessible protocols for inferring semantic geometry, potentials, and robustness properties directly from observed system behaviour. Conceptually, this work reframes alignment, control, and interpretability questions as problems of semantic field organisation and stability. Methodologically, it provides a reproducible template for analysing complex systems through the lens of semantic dynamics, preparing the ground for empirical validation and for the global semantic field structures developed in the final paper of the series.