Generative Mapping of Mathematical Structures in Infferus: Unifying Linear, Nonlinear, and Calculus Forms through Eigenvalue Structure in Triogenesis

Building on the generative framework established in Native Language of the Universe, this work develops a structured mapping between classical mathematical representations and the underlying alignment mechanisms of Triogenesis. The focus is on advancing the interpretation of linear and differential structures as consistent manifestations of pure length alignment, recursive propagation, and Replica Tiering closure.

A unified mapping strategy is introduced to relate finite and infinite-dimensional systems within a single generative perspective. In particular, discrete finite, discrete infinite, and continuous eigenvalue spectra are interpreted as different observable states of the same alignment tree, distinguished by the degree of concealment and revelation of structural variation under Replica Tiering.

The classical eigenvalue problem is used as an initial demonstration, showing that both matrix-based and operator-based formulations arise naturally from the same generative process. These results support the view that exact mathematical forms are stabilised and abundant patterns emerging from the underlying system, rather than constructed abstractions, and suggest a more coherent and transferable foundation for mathematical learning and abstraction development.