TUM versions 10.0 : Geometric Projection of 8D Structures to 3D via Clifford Algebra Cl(8)

Abstract

A geometric projection model from an 8-dimensional space, represented using Clifford algebra Cl(8), to observable 3-dimensional structures is presented. The process unfolds in four fundamental stages: base algebraic iteration, formation of coupled toroidal structures, dimensional projection to the fundamental axis system A, B, C, D, and application to observational phenomena at stellar and cosmic scales. The fundamental rule C ≠ D is established, defining the separation and stability of reality domains. Model v10.0 extends v9.0 by adding falsifiable predictions for pure torsion black holes, including modifications to Hawking temperature, additional gravitational wave ringdown modes, and black hole shadow signatures. The experimental evidence of the "Half-Möbius" molecule from IBM [March 2026] confirms Physics #5: Geometric Coherence at the molecular scale, validating the 8D→3D projection. This converts the interpretation into a testable scientific theory based on geometric principles without requiring additional hypotheses.