This theoretical paper presents a rigorous mathematical derivation of the effective spacetime metric within a single-walled carbon nanotube (SWCNT) operating under crossed electric and magnetic (E×B) fields. Moving beyond the classical paradigm of point particles moving through an empty void, we model the system using the framework of 4D superfluid continuum hydrodynamics. In this model, the SWCNT acts as a Kaleidoscopic Interactive Fractal Structure (KIFS) geometric attractor that structurally confines the vacuum medium. By applying crossed electromagnetic fields, an azimuthal flow is induced directly within the vacuum continuum, generating a macroscopic Lense-Thirring effect (acoustic metric dragging). We formulate the effective acoustic metric tensor gμνeff and derive the exact topological phase transition boundary (cut-off limit) for traversing analytes. Rather than treating analytes as classical masses, they are modeled as macroscopic quantized topological defects (vortices) with intrinsic circulation. The derived mathematical inequality demonstrates that molecular and chiral separation at the nanoscale is fundamentally governed by the resonance between the defect's intrinsic vorticity and the helical flow of the superfluid vacuum. This tensor formulation provides the exact mathematical foundation for field-tunable nanohydrodynamic filtration, directly linking anomalous macroscopic trajectory corrections (such as the W parameter in Orbitrap analyzers) to quantum-level metric dragging.