Torsion-Order Infinity Spectrum (TOIS): A Topological-Causal Classification System for Structured Infinity with Spacetime and Narrative AI Applications

The classical mathematical classification of infinite sets relies exclusively on cardinality-based dichotomies: countable infinity and uncountable infinity. This paradigm treats infinity as a static quantitative property of sets and completely ignores the generative structure, topological orientation, causal directionality, and recursive nesting behavior of infinite topological spaces. In this work, we propose a novel, axiomatically grounded hierarchical framework — the Torsion-Order Infinity Spectrum (TOIS). We establish a two-dimensional orthogonal classification system based on topological torsion (T) and causal recursive order (O), systematically defining five fundamental classes of structured infinity. Unlike traditional set-theoretic infinity, TOIS categorizes infinite spaces according to their manifold gluing rules, orientability breaking mechanisms, causal curve structures, and iterative generation depth. We further establish rigorous correspondences between each TOIS infinity class and non-orientable Lorentzian spacetime structures, providing a new topological interpretation for closed causal curves, self-consistent causal loops, and non-singular recursive causal hierarchies. Finally, we transplant the TOIS topological axioms into generative artificial intelligence, constructing a formal topological layer for narrative generation that resolves inherent logical paradoxes in traditional graph-based story generation. This work establishes a new unified research paradigm bridging topological infinity theory, causal spacetime mechanics, and structural narrative intelligence.