Topological Venting and Dynamic Closure: A Unified Resolution of Hilbert's 16th Problem via Seonggil Field Equations

For over a century, Hilbert’s 16th Problem has remained fragmented, dividing algebraic geometry (Part 1: the topology of real algebraic curves) and differential equations (Part 2: the upper bound of limit cycles for polynomial vector fields). This paper unifies both parts through the Seonggil Field Equations (SFE). By redefining the real projective plane as a projection of a hypercomplex space under torsional equilibrium, we reveal that Harnack’s curve limit is an exact macroscopic manifestation of the Seonggil Topological Venting Law. Furthermore, we establish the existence of an absolute upper bound for limit cycles, H (d), by proving that limit cycles are dynamic event horizons governed by the Lie derivative of the Seonggil Density Tensor (LV ˆS_µν = 0) and quantized by the universal phase-lock constant CSMT.