A bstract Conventional wisdom dictates that ℤ N factors in the integral cohomology group H p ( X n , ℤ) of a compact manifold X n cannot be computed via smooth p -forms. We revisit this lore in light of the dimensional reduction of string theory on X n , endowed with a G -structure metric that leads to a supersymmetric EFT. If massive p -form eigenmodes of the Laplacian enter the EFT, then torsion cycles coupling to them will have a non-trivial smeared delta form, that is an EFT long-wavelength description of p -form currents of the ( n − p )-cycles of X n . We conjecture that, whenever torsion cycles are calibrated, their linking number can be computed via their smeared delta forms. From the EFT viewpoint, a torsion factor in cohomology corresponds to a ℤ N gauge symmetry realised by a Stückelberg-like action, and calibrated torsion cycles to BPS objects that source the massive fields involved in it.