Geometric Origin of Quark Flavour Mixing from Topological Twist Density on T³

We extend the Unified Quantum Gravity Architectural Framework (UQGAF) from static mass eigenstates to dynamic transition amplitudes. Using the Topological Twist Density (rho = Q/P) of the quark standing waves on a three-torus vacuum manifold, we perfectly rank-order all 9 CKM matrix transitions with zero free parameters. Applying a topological Gibbs measure with temperature T = 3²/2π², we derive the 5 primary real-valued CKM elements to approximately 1% precision, including the Cabibbo angle to 0.7%. The identical manifold constant (2π²) that determines particle masses in the UQGAF also determines the thermodynamic scale of flavour transitions, unifying statics and dynamics under a single geometric quantity. The four heavily suppressed corner elements are identified as the explicit boundary where real-valued torus geometry terminates and CP-violating complex topological phases begin. The Standard Model requires four hand-tuned parameters to describe quark flavour mixing. The UQGAF requires none.