Ontological Incompleteness of Closed Theories: The Necessity of a Latent Domain

The observable domain (N}_0) of foundational theories is structurally incomplete and necessitates a latent domain ({N}_1) to account for stability and selection without circularity. This paper formalizes the {N}_1 -> {N}_0 projection, demonstrating that purportedly self-sustaining frameworks implicitly rely on hidden structural remainders. Modern foundational discourse often pursues ontological closure by restricting reality to operational outcomes, yet fails to explain why specific possibilities are realized over alternatives. By analyzing standard quantum interpretations—including Copenhagen, Many-Worlds, and Decoherence—we show that latent structures such as measurement contexts or environment-induced selection are consistently present but unacknowledged. The necessity of this latent domain is presented not as a metaphysical addition, but as a structural requirement analogous to Gödelian incompleteness, where a system cannot justify its own conditions of validity from within. Ultimately, the transition from possibility to realization is reframed as an ontological projection under constraint, providing a path toward structural honesty and clarity in theoretical physics Video Abstract — Intuitive overview of ontological incompleteness in closed theories. Two physicists discuss why any theory confined to observable structures (N₀) necessarily presupposes a latent structural domain (N₁) to account for selection, stability, and necessity. https://vimeo.com/1157867642?share=copy&fl=sv&fe=ci