The actual compact geometric gauge group

Let $\xi \in {C_c}^{\infty }(\mathcal{M};T\mathcal{M})$, and let the infinitesimal admitted diffeomorphism be generated by $s\xi$. Put

The coefficientwise jet transformation is

The corresponding off-shell coefficient operation is

It acts on classical configurations, not on an already assumed physical quantum quotient.

Compact diffeomorphisms preserve the spatial asymptotic labels. They transform the geometric rod construction covariantly; they need not leave each unpulled rod function numerically unchanged in a fixed coordinate chart.