Chapter 7: The Life Loop Class and Metabolic Geometry

The Life Loop Class Loop_L packages the two earned predicates—Distinction and SelfDesc—into a single homotopy-theoretic object: a triple (D, γ, h) encoding the distinction, the metabolic cycle, and the cycle’s homotopy class. The DecodeTarget operator extracts the phenotype target; the DecodeHorizon operator extracts the stable genotype. Source and Closure sub-classes on the metabolic fiber (γ, η) formalize the universal dichotomy of production and recycling. The Metabolic Fiber Theorem proves that every Life loop factors through these sub-classes. The Consumer Mixer Uniqueness theorem identifies the unique mixed sector on (γ, η), correcting the 1st Edition’s identification.