【英語版タイトル】 Gamma Theory v80〜v150-2/3-EX_1: Complete Enhanced Unified Hierarchical Theory — Full Integration of Mathematical and Physical Corrections (EX-1 Final Public Edition)

【英語版説明】This paper integrates the entire system of Gamma Theory v80〜v150-2/3, presenting a coherent mathematical framework encompassing recognition mathematics, cosmology, axiomatic systems, phase transition theory, and hierarchical unification. It provides rigorous definitions of the projection mapping Φ from recognition manifold to physical spacetime, derives extended Einstein and Friedmann equations, establishes observational protocols for external noise ‖ξ(z)‖², axiomatizes the triadic structure (noise-responsiveness-stability), theoremizes the Ebihara-Go Boundary ν ≷ ‖ξ‖²/(4η), predicts cosmic phase transitions via the critical surface Σ_u, and unifies the universe-life-mind-society hierarchy through the functor F with natural transformations. Complete dimensional analysis across all hierarchies is provided.