Latent Geometric Emergence and the Necessity of Topological Capacity Bounds

We prove tha tbehavioral alignment of neural systems is type-theoretically unsound when the latent representation space admits geometric structures not detectable by weight-level inspection.The theorem requires a type theory capable of expressing non-trivial fiber structure while maintaining coherent interpretation. Martin-L¨of Type Theory fails because UIP collapsesall path structure. Homotopy Type Theory fails because the rigidity constraint on ML-algebras (Eden,2025) shows that univalent universes with non-trivial symmetry do not admit coherent interpretation. We work instead in Linguistic Ontological Type Theory (LoTT), which resolves both obstructions by grounding type formation in the simply connected profinitesite Pro(FinSet) where πsite 1=0 (Eden,2025). On this site,descent collapses, locally constant sheaves are constant, and linguistic expression of mathematical structure constitutes identical transport to formal notation. The central theorem establishes that profinite capacity bounds on the latent space are the unique sound safety mechanism,and that the simply connected site provides the only coherent foundation for proving this.