The hard problem of consciousness has resisted solution for over three decades, with existing theories failing to bridge the explanatory gap between objective physical processes and subjective experience. This thesis presents Processual Experiential Realism (PER), a novel metaphysical framework that dissolves the hard problem through mathematical precision and empirical testability. Unlike previous approaches, PER makes experience itself fundamental while avoiding the ambiguities that have plagued earlier theories. PER introduces Primary Experiential Processes (PEPs) as the basic constituents of reality, characterized by temporal extension, qualitative valence vectors, selective integration functions, and causal projection capabilities. Consciousness emerges when Integration Complexity IC(S) = H(S) × C(S) × T(S) exceeds a critical threshold θc, where H represents Shannon entropy, C measures connectivity, and T quantifies temporal coherence. The framework addresses critical weaknesses in existing theories: it provides precise operational definitions that eliminate conceptual ambiguity, maintains explanatory differentiation without category collapse, offers falsifiable empirical predictions, and solves the causal exclusion problem through a unified ontology. PER distinguishes itself from neutral monism by specifying the nature of fundamental reality, from panpsychism by locating consciousness in integration rather than fundamental particles, and from process philosophy by providing mathematical formalization and testability criteria. Empirical predictions include specific correlations between neural connectivity measures and consciousness levels, testable interventions using optogenetics and brain stimulation, and novel architectures for artificial consciousness. The theory generates immediate research programs in neuroscience, artificial intelligence, and quantum mechanics while providing practical applications for clinical diagnosis, AI development, and ethical frameworks. This work demonstrates that consciousness can be understood scientifically through a properly formulated metaphysical foundation that takes experience seriously while maintaining rigorous empirical standards. The implications extend beyond consciousness studies to fundamental questions about the nature of reality, causation, and the unity of science.