What would count as cancellation

To discharge J2 by cancellation one would have to construct or control the complete grouped coefficient and prove that the dangerous configurations disappear throughout the retained noncoincident characteristic domain.

A single nonzero component does not disprove cancellation between components. A single vanishing component does not prove it. The rank relation above is uniform as geometric data on ${\mathcal{N}}^{\circ }$; it is not a uniform theorem about the summed numerical distribution.

The inherited existence of the $H$ contraction also does not define the $H_T$ contraction. The grouped difference (eq:formal) must remain grouped until a valid prescription or cancellation argument is supplied.