SIT-Y Series, Paper I: Structural Spectrum Transform—A Generalized Fourier Theory for Structural ChangeThis paper introduces the Structural Spectrum Transform (SST), a mathematical framework that generalizes Fourier analysis from spatial domains to s

This paper introduces the Structural Spectrum Transform (SST), a mathematical framework that generalizes Fourier analysis from spatial domains to spaces of structured objects. Instead of decomposing functions by translation symmetry, the framework derives spectral coordinates from admissible structural transformations. Structural states are represented by objects, relations, and constraints, while transformation generators define structural harmonics analogous to Fourier modes. The paper develops the underlying theory using representation theory, Lie groups, spectral geometry, graph Laplacians, and functional analysis. It establishes conditions for structural derivatives, spectral decomposition, inversion, Parseval identities, heat flow, filtering, perturbation stability, and compositional spectra. A complete worked example on a finite structural state space demonstrates exact forward and inverse transforms, illustrating the computational realization of the proposed framework. The Structural Spectrum Transform is presented as a general mathematical framework whose concrete implementation depends on the chosen structural state space, admissible transformations, metric, measure, and spectral operator.