Geometric Unification of Matter Structures via M¨obius Topological Fibers

A geometric framework based on M¨obius topological fibers is presented to describe matter structures across multiple physical scales. The theory postulates that stable matter configurations arise from coherent resonance of M¨obius fibers distributed on the z = 0 reference plane, with intrinsic torsion angle θ 0 = 90 .4732◦ governing all coupling strengths. Comparative analysis reveals advantages of the topological approach in providing unified descriptions of confinement, quantization, and chirality, alongside limitations in addressing high-energy scattering and renormalization. Five precision experimental measurements are selected for quantitative validation, each accompanied by complete analytic derivation and numerical evaluation. The results demonstrate agreement at the sub-percent level or better across hadronic, atomic, optical, and astrophysical domains, supporting the geometric fiber paradigm as a candidate for unified description of fundamental matter.