Self-Consistent Many-Mode Dynamics and Emergent Atomic Structure in the Scalar Temporal Field Ontology

This work extends the Scalar Temporal Field Ontology (STFO) to include self-consistent many-mode dynamics, enabling the description of multi-mode bound configurations beyond the hydrogenic approximation. Previous work established localized matter-core solutions, hydrogen-like bound modes, and non-Coulomb corrections responsible for shell splitting. However, these results were derived in a fixed-background approximation in which fluctuations do not backreact on the temporal field. In this paper, we derive a self-consistent mean-field formulation in which occupied bound modes source the temporal field and modify the effective potential. This leads to the emergence of screening, occupation-dependent coupling, and nonlinear mode–mode interactions. We analyze the minimal two-mode system and demonstrate the appearance of an effective screening potential that reduces binding strength. We further show that competition between binding energy and interaction energy produces an emergent exclusion mechanism and shell structure without explicitly imposing external statistical rules. The resulting framework provides a unified description of atomic structure in which binding, screening, shell formation, and exclusion behavior arise dynamically from a single scalar temporal field.