Topological Fractional State-Space Modeling Overcoming Statistical Induction via Causal Geometric Priors Proprietary Technical Briefing Patrice Portemann | Noetic Industries R&D 1. The Epistemological Bottleneck of Modern AI The current paradigm in Artificial Intelligence—driven by Deep Learning and massive stochastic approximations—has reached an asymptotic limit. While architectures like Graph Neural Networks (GCNs) or LSTMs excel at pattern recognition, their computational graphs are fundamentally arbitrary regarding the physical laws governing the system being modeled. This architectural arbitrariness leads to three critical industrial failures: • The Markovian Assumption: Standard algorithms assume the state at tn+1 depends only on tn. This fails catastrophically when modeling complex physical systems (turbulent fluids, non-Newtonian materials, biological signals) that exhibit long-range temporal memory (heavy-tail asymptotics). • The Parameter Curse: To approximate missing physics, models require millions of parameters, resulting in exorbitant computational costs, rendering Edge AI deployment impossible. […]