Exact Periodic Global Closure Beyond Singular and Infinite Endpoints in Six-Throat Directed Geometry

Abstract

We construct an explicit smooth global completion of the regular six throat spacetime on a single periodic Lorentzian manifold. The original six throat core and the central Zero Region are preserved exactly, while a smooth outer connector produces one finite global maximum without introducing an additional throat, singular surface or physical radial boundary.The completed geometry has bounded curvature invariants, a finite closed radial null circuit, an accessible critical optical sector and a conservative circulation with zero net flux. The construction replaces the formal infinitely distant core endpoints with a finite smooth periodic continuation while retaining exactly six throats.