Dynamics of Urban Landscapes in a Unified Framework: A QFT-Inspired Compositional CW-Complex Formalism

Urban landscapes combine physical fields, built structures, mobility, ecological processes, economic activity, institutions, and historical practices. Their interactions can change both present conditions and the possibilities for subsequent transformation. This paper proposes a compositional mathematical language for studying such heterogeneous urban dynamics. The structural carrier comprises typed, potentially linked CW complexes with cell-associated internal state spaces; interfaces and typed events govern coupling, resource transfer, structural rewriting, and changes to the active event registry. Classical stochastic creation–annihilation operators describe selected counted processes, while action-weighted histories and group-field-theoretic constructions motivate optional accounts of structural generation. A distinct epistemic layer relates realized trajectories and observations to contextual interpretations and heterogeneous valuations. The framework separates cellular admissibility from physical constitutive laws, stochastic well-posedness, and evidential justification. For explicitly restricted subclasses, the paper establishes compatibility results for simplicial refinement, cell attachment, variable-dimensional state transfer, coupled physical balances, finite-rate hybrid processes, and selected rule-changing events. It also derives finite-state criteria for preserving dynamics, historical queries, and observation laws under exact or approximate coarse-graining. Worked urban examples expose cases in which structurally equivalent configurations retain different dynamics or histories. The contribution is the integration of established mathematical tools into an auditable specification of urban generation and interaction, together with its conditional results and explicit proof obligations. General closure for arbitrary heterogeneous CW rewrites, field-theoretic emergence, and empirically validated semantic or value models remains a subject for further research.