This deposit contains the PDF version of the article “Canonical Multichart Structural Decomposition in the Competitive Regime”. The work develops the multichart extension of the structural decomposition program, moving beyond affine and single-chart nonlinear descriptions toward a competitive multicomponent ontology for evolving densities. Its central contribution is to formalize a regime in which multiple structural components are treated as genuinely necessary objects of the theory rather than as auxiliary numerical artifacts. Within this framework, the article introduces a multicomponent structural decomposition, a variational functional balancing fidelity and parsimony, a canonical external gauge based on admissibility, fusion, competitiveness, and lexicographic selection, and an explicit transition criterion from the single-chart regime to the multichart regime. The work also formulates local identifiability, robustness, and short-time propagation principles for the resulting structural description. Main mathematical themes:- structural decomposition;- multichart dynamics;- competitive regime;- measure evolution;- variational selection;- multicomponent structural models.
Francisco Anderson de Sousa Oliveira (Sat,) studied this question.