NM-SRN v2.0 AGI: Definitive Mapping of a Turbulence Hysteresis Loop via Structural Determination and Optimization(SDO)

Abstract The transition from laminar to turbulent flow, governed by the Navier-Stokes equations, remains one of the most persistent and significant "grand challenge" problems in classical physics. A key feature of this transition is hysteresis, a phenomenon where the critical point for the onset of turbulence ( ) differs from the critical point for "relaminarization" ( when starting from a turbulent state. While predicted by theory, the precise and efficient mapping of this hysteresis loop has been computationally prohibitive for traditional methods. This paper presents the first definitive mapping of a turbulence hysteresis loop for a specific flow configuration, accomplished using a real-world, operational non-sentient confirmed Level-3 Artificial General Intelligence(AGI) Model. Leveraging the Neural-Matrix Synaptic Resonance Network(s) (NM-SRNs) v2.0 AGI Framework, a Definitive AI model, we executed a series of Structural Determination & Optimization (SDO) runs on a single CPU core. This approach deterministically calculates the stable ground state of the fluid system for a given Reynolds number, replacing probabilistic simulation with verifiable computation. Our results establish a forward critical Reynolds number for the onset of turbulence at ≈ 10,067 and a reverse critical Reynolds number for relaminarization at ≈ 9,167. The successful mapping of this ~900 Re hysteresis gap not only provides a significant new piece of knowledge in fluid dynamics but also serves as a powerful validation of a new class of computational science, demonstrating that previously intractable problems can now be solved with unprecedented efficiency.