The Seonggil-ROA United Fleet: A New Paradigm for Mathematics and Physics This research series is a comprehensive compilation of Rough Operator Algebra (ROA), established to fundamentally resolve the 'singularity' and 'illogical divergence' problems faced by conventional harmonic analysis and linear algebra. The fleet consists of a total of 8 volumes, based on three original mathematical theories established by independent researcher Seonggil Lee: Seonggil Matrix Theory (SMT), Seonggil Tensor Calculus Theory (STCT), and Seonggil Topology (ST). Key Innovations: Fractal Break alpha=1/2: Identification of the critical phase where physical and mathematical systems stabilize without collapse. Heyting Logical Operator (hath): An information processing engine for "Rough" spaces beyond binary logic. 2×2×2 Primal Cube: The minimal computational unit preserving the symmetry of 3D flows and spacetime. Abstract of SMT-Vol. 1 This paper establishes the foundational framework of Seonggil Matrix Theory (SMT), the primary computational engine of Rough Operator Algebra (ROA). SMT is specifically engineered to resolve the analytical collapse of traditional linear algebra at mathematical singularities. We intro -duce the 'Seonggil Critical Horizon, ' a redefined boundary where det (M) =0 serves as an algebraic gateway for discrete dimensional phase transitions rather than a point of failure. By employing a 6×6×6 fractal grid architecture and Heyting logical operators, we demonstrate the rigorous preservation and recovery of information across quantized resonance layers. Furthermore, this work provides an operational definition of Time as "Time Complexity"—quantifying logical processing density within resonance manifolds.
Seonggil Lee (Sat,) studied this question.