BCT Programme v47j Letter 249: The Josephson Loop Integral over the Flag Manifold F(1, 2; 3) and Topological Phase-Locking

Building upon the structural analysis of the QCD Ward identity established in Letter 248, this document executes the computation of the Josephson loop integral over the target space F(1, 2; 3). We demonstrate that themacro-scale superfluid flow within the BCT lattice is topologically boundby the exact geometric constraints of the 24-cell and D4 root systems. By applying the Corrected Casimir-Void identity, we prove that the topological holonomy quantizes into rigid geometric limits, rendering legacy perturbative approaches obsolete.