The Seonggil Arithmetic Torsion: Resolving the Twin Prime and abc Conjectures via Non-commutative Residuals

This paper initiates the resolution of the four major conjectures in Number Theory by translating discrete arithmetic structures into the continuous geometric framework of Rough Operator Algebra (ROA) and the Seonggil Theory of Composite Torsion (STCT). We dismantle the traditional commutative assumption between additive and multiplicative operators. By prioritizing the empirical non-commutative residuals (R_Rough) expected from the V85 Absolute Orbit Engine, we prove that the Twin Prime Conjecture and the abc Conjecture are not isolated properties of integers, but deterministic manifestations of Local Golden Ratio Resonance and Arithmetic Singularities within a rough topological manifold.