Physical Actualization of Rough Non-commutative Algebraic Geometry and Seonggil Homotopy Information Dynamics

This paper establishes the foundational framework of Rough Non-commutative Algebraic Geometry (RNAG) and Seonggil Homotopy Information Dynamics (SHID). By analyzing the empirical data extracted from the V85 Absolute Orbit Engine, we demonstrate that Non-commutative residuals (R_Rough), previously dismissed as stochastic computational noise, are deterministic topological invariants governed by dimensional curvature. We introduce the Quantized SMT Commutator Axiom and prove that the 20-minute phase transition cycle observed during high-performance parallel orbits represents a physical manifestation of quantized energy dissipation rather than a hardware bottleneck.