Analytical Supplement: Parallel Transport of the Polarization Vector in the IKBL Framework and the Derivation of Topological Birefringence.

This supplement provides the first-principles derivation of achromatic topological birefringence within the Iterated Klein Bottle Lattice (IKBL) framework. By distinguishing between the torsion-immune electromagnetic field strength (F_μν) and the torsion-sensitive parallel transport of the polarization vector (Aᵘ), we resolve the apparent 'Nieh-Yan Paradox.' We derive a frequency-independent rotation of β_int ≈ 31.5° per junction, providing a unique observational signature for non-orientable cosmic architectures falsifiable by upcoming LSST and SKA tomography.