Symmetry-Protected Band Structure of Icosahedral Quasicrystals: A Bond Cohomology Prediction Tested Against Realistic Tight-Binding Models

Paper 14 in this series predicted that the tight-binding spectrum of an icosahedral quasicrystal decomposes into six bands transforming as exterior powers Λᵏ(H) of the five-dimensional H-representation of the icosahedral group, with irrep content determined by the bond cohomology lattice H¹ ≅ A₅. We test this prediction against three levels of increasingly realistic Hamiltonian models on a 47-atom periodic approximant: (1) on-site disorder up to σ = 2.0, (2) anisotropic hopping with up to 10-fold variation across the six parent-lattice axes, and (3) a species-dependent Al–Pd–Mn model with distinct on-site energies and hopping parameters inspired by Fujiwara (1989). The six-band structure with correct icosahedral irrep content survives all perturbation levels at moderate strength. At weak perturbation (σ ≤ 0.3, anisotropy ≤ 15%), all four checkable bands show exact irrep matches. Under Fujiwara-inspired Al–Pd–Mn parameters, six bands persist with 3/4 resolved bands matching. Degradation is graceful: bands merge but do not scramble, and the outermost bands (trivial and H representations) are the most robust. The highest predicted gap (IDS ≈ 0.964) is consistent with the experimentally observed pseudogap in i-Al₇₀Pd₂₀Mn₁₀. The topological constraint is complementary to Hume-Rothery and hybridization mechanisms: it determines the number of allowed gap families (five) and the symmetry content of each band, while dynamical mechanisms select which gaps open widest. Fifteenth paper in a series; companion papers at DOI 10.5281/zenodo.19028078, 10.5281/zenodo.19039170.