ADDENDUM v2.41-A: The Mechanical and Geometric Derivation of the Lattice Invariant α

Abstract

This addendum delivers a strict deterministic, mechanical, and geometric derivation of the fine-structure constant (α) and the Rydberg constant (R_infinity) within a superfluid lattice paradigm. By deconstructing α from an empirical ad hocparameter into an intrinsic gear-mesh transmission ratio between the rotational velocity of medium vortices (v_gear) and the transversal shadow-wave velocity of light (c), we resolve the physical mechanism governing the ground-state Bohr velocity. Furthermore, the Rydberg constant is mathematically mapped directly to the local three-dimensional scaling configuration of the medium interacting with the toroidal boundary surface of the electron knot (4π · r_e). Finally, we demonstrate that the long-standing theoretical boundary at element Z = 137 is not an abstract relativistic quirk, but a rigid hydrodynamics-enforced cavitation limit where the local medium grid matches the ultimate transversal wave speed c, precipitating immediate structural fracture and localized fluidic collapse into the underlying 4D substrate.