Effective Intrinsic Geometry (EIG): A Constructive Fusion Framework Subsuming Non-Euclidean and Rough Operator Geometries

We present the Effective Intrinsic Geometry (EIG), a supreme fusion framework designed to structurally resolve the foundational limitations of classical non-Euclidean geometries (hyperbolic, elliptic, Riemannian, Lorentzian). By synthesizing the principles of constructive mathematics, computational complexity, and Universal Rough Operator Algebra (UROA), EIG demands that geometry be an intrinsic structure equipped with explicit construction procedures, effective curvature bounds, complexity upper limits, and finite approximation errors. This paper formally integrates EIG with the Seonggil Theory of Complex Torsion (STCT) and Seonggil Field Equations (SFE), unifying continuous manifolds and discrete quantum geometries under a single signature structure.