Understanding consciousness remains one of the central unresolved problems across cognitive science, neuroscience, artificial intelligence, and philosophy of mind. Existing approaches often isolate specific aspects of the problem—neural correlates, representational structures, or computational processes—without providing a unified formalism capable of integrating subjective experience with mathematically precise dynamics. Kernel-Consciousness Theory (KCT) is proposed as a mathematical-phenomenological framework designed to address this gap. The central premise of KCT is that conscious experience can be modeled as the recursive action of a kernel operator over a structured state space of awareness. In this formulation, the kernel encodes relational structure, transformation rules, and self-referential dynamics, allowing the system to evaluate, stabilize, and evolve its own internal states. This perspective enables the formalization of key properties of consciousness, including self-reference, temporal continuity, stability under perturbation, and the emergence of coherent experiential structure. Rather than treating consciousness as an emergent byproduct alone, KCT models it as a dynamical system governed by well-defined mathematical laws. The present work develops the foundational structure of KCT, introduces its principal theorems, and presents a unifying master equation governing state evolution. The goal is not to claim empirical completeness, but to establish a rigorous formal scaffold upon which future theoretical and experimental work may build.