  Conventional wisdom dictates that $\mathbb{Z}_N$ factors in the integral
cohomology group $H^p(X_n, \mathbb{Z})$ 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 $\mathbb{Z}_N$ gauge symmetry realised by a St\"uckelberg-like action, and
calibrated torsion cycles to BPS objects that source the massive fields
involved in it.
