The copied common-space release

The common space is

where the four factors are open spacetime neighborhoods. The supplied XIV-G text copies the retained characteristic configuration in the form

This is the selected retained locus, with its copied neighborhood restrictions. It is not the assertion that every characteristic configuration of the global selected pair is represented by this local formula.

The dimensions have the stated bookkeeping interpretation: $a$ contributes four parameters, $\mathbf{n}$ contributes two, and $\alpha ,\beta$ contribute two. The attachment equality determines $z$. Thus the copied local locus has eight parameters in the sixteen-dimensional common space. No transverse degree follows from this count, and no amplitude order is assigned to a future extension by subtracting the dimensions.