This technical note formalizes the 2/3 geometric efficiency threshold as a fundamental principle of structural stability within the framework of lattice topology. By analyzing the ratio of confinement versus content—exemplified by the transition from a constrained 1D boundary (potential energy) to a liberated 3D spherical state (kinetic minimum)—we demonstrate that 2/3 represents the universal limit for optimized boundary-to-content configurations. This geometric signature provides a first-principles derivation for the Koide mass formula (Q≈2/3), interpreting it as the mathematical manifestation of the network's maximum load capacity, or "topological hoop rupture." In this model, leptonic masses are not arbitrary values but optimized geometric distortions that occupy two-thirds of the available configuration space, mirroring the classical Archimedean ratio of a sphere relative to its circumscribed cylinder. This document serves as a specialized technical supplement to the primary research on the 6Π4 Lattice Model and its applications in resolving the proton-to-electron mass ratio and the anomalous magnetic moment of the muon (g-2).