Composition of Dilations and Structural Closure in the Family N (a, b) = ab ± a ± b

This work develops the structural behavior of the numerical familyN(a, b) = ab ± a ± b under positive linear dilations.It establishes full invariance and closed composition under all dilation factors, forming a stable multiscale semigroup.The results show that modular classifications, structural graphs, and induced numerical systems remain coherent across scales.The document includes both the English and Spanish versions for accessibility.