This work introduces a minimal Lagrangian framework describing the stabilization of a scalar difference field through coupling to a retention field. The model includes kinetic, spatial, and retention terms, leading to a non-trivial equilibrium configuration in which the difference field acquires a stable non-zero value proportional to the retention field. A stability criterion is derived, separating regimes of structural persistence from collapse. The framework further introduces spatially localized retention domains and predicts observable signatures such as suppressed decay, enhanced spatial coherence, and domain-like structure formation. The formulation is presented as an effective field-theoretic description applicable to systems exhibiting retention-mediated stabilization.
Logacheva Yulia (Sun,) studied this question.