The dominant paradigms in artificial intelligence—Generative AI and Agentic AI—share a fundamental architectural limitation: generality at the cost of epistemic grounding. This paper proposes a complementary paradigm, Ingentic AI, in which intelligence emerges from the structured composition of purpose-built specialist engines that communicate through defined interfaces. The framework is formalised as a mathematical triple I = (E, Φ, Ω) with four propositions and a three-level taxonomy. An empirical case study grounds the framework in a production business-analysis platform validated through doctoral research across 69 firms and 3,956 quarterly observations.