This deposit contains the PDF version of the article “Canonical Structural Decomposition and Orthogonalization of Dynamical Modes in Measure Evolution”. The work formulates a canonical affine structural decomposition for evolving densities by separating mass, translation, global linear deformation, and residual shape. Its central contribution is to show that these components can be defined in a mathematically coherent way through an affine normalization procedure, yielding a structural coordinate system in which transport and informational modes can be projected and analyzed separately. Within this framework, the article establishes uniqueness of the affine structural decomposition under a canonical gauge, defines projected transport and informational modes, and proves a diagonalization result for the kinetic action once the residual transport is orthogonalized against the affine modes. The work also develops an abstract structural closure principle for the residual dynamics and explains how the isotropic theory appears as a special case of the affine regime. Main mathematical themes:- measure evolution;- affine structural decomposition;- dynamical mode orthogonalization;- affine normalization;- residual dynamics;- kinetic action decomposition.
Francisco Anderson de Sousa Oliveira (Sat,) studied this question.