This paper introduces the Ochometric Theory of Economical Finance and Sustainability as a diagnostic and prescriptive framework for Africa’s structural transformation. Historically, African economies have operated within the "extractive trap," exporting low-value raw commodities and importing expensive finished goods. This structural imbalance drains capital, exports employment opportunities, and accelerates ecological degradation without commensurate financial returns. The Ochometric framework evaluates the mathematical velocity of capital, domestic resource retention metrics, and long-term sustainability yields to model economic outcomes. The theory demonstrates that the only viable path forward for Africa’s development is an absolute transition to domestic mining, processing, and exporting exclusively finished goods. By calculating the "Ochometric Value Gap" across critical sectors—such as West African cocoa, Central African cobalt, and Southern African platinum—we prove that raw material exportation guarantees net-negative sustainable development. Conversely, a legally enforced, continent-wide ban on raw exports, paired with unified industrial zones, creates self-sustaining capital pools. This paper models how end-to-end local processing maximizes domestic credit multiplication, builds climate-resilient manufacturing infrastructure, and establishes African economic self-reliance.