A Minimal Cyclic Structure for Epistemic Closure Across Physical Theories

Contemporary physical theories — General Relativity, Quantum Mechanics, Quantum Field Theory, Thermodynamics, and Cosmology — exhibit strong internal consistency within their respective domains yet leave specific conceptual cycles open when considered in relation to one another. These open cycles are not empirical failures but structural discontinuities: each theory identifies a domain of manifest form without providing the epistemic operator that closes the transition back to potential. This paper introduces the Kiawe Epistemological Framework (KEF), a non-ontological cyclic structure designed to identify and close these open cycles without modifying the physical theories themselves. The framework distinguishes two complementary structural states — G6 (centripetal, pre-temporal, latent potential) and Q9 (centrifugal, temporally extended, manifest form) — and two transition operators: eXopia (X), governing the passage from potential to manifestation, and Entropy (N), governing the return toward coherence. The algebraic foundation of the framework — including the derivation of the self-composition law (N∘X) ·A·UK = A²·UK and the Möbius topological identification as a direct consequence of X² = −IdV — is established in an accompanying paper (Authors, 2026b). The present paper applies this structure to five foundational physical theories, demonstrating that each instantiates a recognizable phase of the G6–X–Q9–N cycle and that each leaves open a structurally homologous gap. The convergence of this pattern across independent theories is the paper's central epistemological claim.