We propose a structural completion framework in which observable physical dynamics arise as projections of an invariant closure structure. Deviations from established physical theories are modeled through a closure deficit parameter ε = 1 − C, where C ∈ [0,1] represents the completion state of the underlying structure. The framework introduces correction terms that:- Preserve the backbone of standard theories- Vanish in the completion limit (C → 1)- Generate falsifiable deviations under specific projection protocols We demonstrate cross-domain instantiations in cosmology and open quantum systems. This work does not replace existing theories but provides a conservative structural completion mechanism with explicit recovery limits.