The Origin of Factor '2': First-Principles Derivation of the Schwarzschild Metric from k=6/k=3 Topology

Einstein’s 1915 derivation of the Schwarzschild metric determined the factor '2' by back-calculating for consistency with the Newtonian limit. This paper derives this factor '2' for the first time from first principles, independently of Newtonian mechanics. The factor is identified as the topological ratio between the vacuum grid (k=6) and the matter defect (k=3) —a simple geometric necessity of 6/3 = 2. By redefining spacetime curvature solely through grid topology, k-Foam Theory unifies General Relativity and Quantum Mechanics within a single axiomatic framework.