Canonical Nonlinear Global-Chart Structural Decomposition in the Penalized Quadratic Regime

This deposit contains the PDF version of the article “Canonical Nonlinear Global-Chart Structural Decomposition in the Penalized Quadratic Regime”. The work develops the next structural regime beyond the affine theory by introducing a canonical nonlinear global-chart formulation for evolving densities. Its central goal is to determine how far a single global chart can be extended beyond the affine level while still preserving a coherent structural decomposition of the dynamics. Within this framework, the article formulates a penalized quadratic regime in which nonlinear corrections are incorporated into the structural coordinates, allowing curved and folded residual geometries to be represented within a single-chart ontology. The work studies the corresponding structural variables, the role of penalization in controlling the chart, and the way this regime extends the affine decomposition while remaining simpler than a fully multichart description. Main mathematical themes:- structural decomposition;- nonlinear global charts;- penalized quadratic regime;- measure evolution;- structural model extension;- single-chart nonlinear dynamics.