Gap-protected spectral invariants on T^d/Z_2: dimensional rigidity at d = 4

Preprint of Gap-protected spectral invariants on T^d/Z_2: dimensional rigidity at d = 4. On certain flat orbifolds the spectral projector rank of the covering torus at a finite cutoff decomposes exactly into orbifold-topological invariants and their products; on T^d/Z_2 with the cubic lattice the decomposition exists if and only if d = 4 (dimensional rigidity). The deposit includes the manuscript and supplementary-material PDFs and the scripts reproducing the two computational steps (the substrate-uniqueness sweep and the spectral-radius / Krawtchouk-eigenvalue bound). Python 3 with NumPy, SymPy, mpmath.