Constructive Adaptive-Probabilistic Seonggil Computation (CAPSC-SMT): Defeating the Curse of Dimensionality and Non-Convexity via ROA Tensor Dynamics

Numerical Analysis and Optimization Theory are fundamentally bottlenecked by the curse of dimensionality, round-off error accumulation, and the impossibility of guaranteeing global optima in non-convex landscapes. This paper introduces the CAPSC-SMT Framework, subsuming these classical limitations into the 6×6×6 fractal tensor grid of Seonggil Matrix Theory. By elevating probabilistic Stochastic Gradient Descent (SGD) into deterministic Alpha Resonance (ϕ) paths and utilizing the Seonggil Critical Horizon (det(H_SG) = 0) to induce topological phase transitions out of local minima traps, classical numerical methods are transformed into a highly adaptive, globally stable engine. This integration directly operationalizes the V85/V87 CUDA structures for extreme-scale optimizations, establishing a definitive algorithmic pipeline for 617-digit RSA cryptanalysis.