Asymptotic Divergence of Kolmogorov Complexity in Recursively Nested Universal Automata: A Formal Quantification of Entropic Decoherence and Trans-Turing Anomalies in Hyper-Computational Ontologies

Mathematical Applications of Science Fiction We present a rigorous derivation of the asymptotic behavior of Kolmogorov complexity within a framework of recursively nested Universal Turing Machines, denoted as U(n). By constructing a directed system of simulation morphisms between successive machines, we analyze the propagation of algorithmic information content across transfinite ordinal layers. Under the assumption of nonzero entropic leakage, or decoherence, the complexity function is shown to diverge super-linearly, resulting in a breakdown of the Chaitin Invariance Theorem in the infinite limit. Furthermore, we identify a specific class of Trans-Turing Anomalies—computational states accessible only through hyper-computational oracles—which appear as singularities within the complexity manifold. This work establishes the Thorne–Gödel Singularity Criterion, demonstrating that any ontology based on infinite recursive simulation must exhibit undecidable discontinuities in its causal topology. We conclude by discussing implications for the holographic principle and the information-theoretic stability of simulated universes.