Part II: Taxonomy and Structural Symmetries of Transient Rational Locking

Building on the torus-sawtooth dephasing law, this paper systematically classifies the transient geometric structures of modular logarithmic orbits. We formalize two universal structural laws---the Inversion Theorem and the Base-Shift Identity---that strictly preserve canonical locking data under algebraic transformation. By separating intrinsic toral persistence from extrinsic rendering commensurability, we classify transient skeletons into strict visual archetypes. Finally, we show that many apparently new structures are inherited shadows of existing canonical classes, and that these shadows can be algorithmically collapsed to reveal a taxonomy of genuinely distinct Diophantine resonances.