Global South countries possess over 60% of the world's critical green mineral resources yet capture less than 30% of global manufacturing value added. Africa accounts for less than 2% of global manufacturing output and only 1.4% of global manufactured goods exports. The transition from "resource curse" to "industrial autonomy" represents the most fundamental development challenge facing the Global South in the 21st century. Based on the eight-dimensional framework of Prim-Lex Theory (Economic Climatology)——Prim-Unity·Prim-Fire (industrial metabolic efficiency of the Global South), Two Principles·Yin-Yang (balance between resource export and local processing), Three Realms·GC⁴A (cross-scale integration from international rules to regional strategies to national industries), Four Phenomena·Four Colors (four-phase differentiated governance of industrialization), Five Elements·Five Models (coupling of metabolic deficit, phase-transition early warning, spatial zoning, resource balance sheet, and industrial resilience), Six Dimensions·Six Directions (spatial synergy of Global South industrial chains), Seven Luminaires·Seven Rhythms (multi-period synchronization of resource cycles and industrial upgrading cycles), and Eight Trigrams·Eight Information (entropy governance of Global South industrial information networks)——this paper constructs, for the first time, an eight-dimensional quantitative assessment system for Global South industrialization governance. It elaborates, dimension by dimension, the calculation principles, mathematical formulas, parameter meanings, and data sources. Using three empirical anchors——the African Green Minerals Strategy, the Southeast Asian electric vehicle industrial chain upgrade, and the resource-dependent economic transformation of Latin America——this paper demonstrates the application pathway of the eight-dimensional framework in identifying "phase differences" and "critical windows" in Global South industrialization, providing a quantifiable, programmable, and auditable mathematical language and governance tool for the Global South's transition from "resource dependency" to "eight-dimensional industrial autonomy."