AGDAU: Existential Admissibility as a Foundation for Safe Post-Turing Artificial General Intelligence

Abstract The transition from narrow artificial intelligence to Artificial General Intelligence (AGI) constitutes a fundamental break in the theory of computation. Post-Turing agents do not merely operate within predefined state spaces; they actively generate new representations, actions, and causal structures. In such systems, syntactic constructs are no longer passive data but potential actions with physical consequences. This paper introduces AGDAU (Admissible Growth-Defining Action Universe), a foundational formalism that reframes safety as an ontological condition of existence rather than a behavioral constraint. AGDAU defines an explicit existential admissibility predicate that determines which informational constructs may exist as executable reality. Constructs that fail this predicate are not prohibited, penalized, or avoided—they are non-existent within the operational semantics of the system. We show that existential admissibility resolves several foundational pathologies of post-Turing systems, including combinatorial explosion, reward hacking, self-referential collapse, and unbounded simulation loops. Unlike alignment, ethics, or policy-based approaches, AGDAU operates upstream of control and optimization, establishing a necessary condition for physically interpretable computation. We argue that existential admissibility represents a missing primitive in the foundations of AGI, analogous to causality constraints in physics, and provides a viable structural path toward a stable and safe future for artificial general intelligence. This record includes the following attached materials: (1) a final PDF version of the paper, (2) the complete LaTeX source compatible with Overleaf, and (3) a plain-text UTF-8 version for archival integrity and long-term reproducibility.