The Noetic Model: A Spectro-Topological Framework for Structure-Preserving Prediction and Mimetic Discretization Patrice Portemann Abstract—The Noetic Model is a unified spectro-topological framework for the prediction and governance of complex systems. Its master hydrodynamic equation preserves structural invariants under mimetic discretization, enabling stable, multi-scale and certifiable computation. We formalize the operator, prove key preservation theorems, derive structural predictions, and provide comparative tables. An extended appendix includes full demon- strations of invariance, stability, and discretization coherence. Epistemological implications and institutional considerations are briefly discussed. I. INTRODUCTION The Noetic Model proposes a master equation for complex systems based on a spectro-topological operator LST . Unlike classical PDE or machine-learning approaches, the model en- forces structural preservation at both continuous and discrete levels. […]