Mathematical Mechanism Report on SRE-Based Möbius Embedding of Number Axis and Orthogonal Truncation Topological Inversion

This report systematically constructs the rigorous algebraic mechanism for embedding a one-dimensional discrete real number axis sequence into a three-dimensional continuous Möbius manifold space, and quantitatively demonstrates the non-trivial manifold collapse induced by a specific two-dimensional orthogonal projection matrix. Through parameter elimination via double-angle trigonometric identities, this report corrects the previous geometric misconception of a “parabolic envelope” and rigorously derives the analytical geometric characteristic of the collapse boundary as an “oval/circular envelope.” Furthermore, utilizing the Poincaré-Hopf Theorem and congruence measure theory, we complete the mathematical proof of the spatial concentration probability distribution under Mod 6 congruence, alongside the algebraic derivation of the chiral vacuum bandgap width. This framework establishes a rigorous mathematical foundation for the degenerative inversion of discrete number-theoretic structures into continuous topological entities.