5.5 Geometric Factorization

This article proves that observables of the information field can be decomposed into the product of four geometric factors. The four-factor decomposition structure is jointly determined by the three-segment partition of the coding orbit and the closing step, with each factor corresponding to an algebraic structure jump point. This article provides a detailed derivation of the factorization formula, analyzes the physical meaning of each factor, and demonstrates the application of factorization to the fine-structure constant, mass ratios, and coupling constants.