The Seonggil Framework for Strongly Correlated Many-Body Systems: Exact Predictability, Non-Commutative Dynamic Engineering, and Topological Phase Control

The exact prediction and real-time manipulation of strongly correlated many-body systems are notoriously intractable due to the quantum sign problem and the exponential explosion of Hilbert space. This paper introduces the Seonggil Framework, which operates on a higher-order theoretical plane governed by arbitrary continuous dimensional tuning (d →d(t)), dynamic scale variance (λ(t)), and real-time non-commutative parameter control (θ_ij(t)). We establish five fundamental axioms defining this framework and derive five core theorems that guarantee complete solvability, directed quantum phase transitions, quasi particle spectrum reconfiguration, and active topological writing/erasing. A Python-based computational proof validates the real-time feedback stabilization theorem, demonstrating dynamic control of a Ginzburg-Landau phase transition.