Proposition: Fixed-source null-boundary obstruction

For a representation of the unchanged carrier, fix $p\in E_D$. There are at most two nonzero comparable differences

If comparable differences from this source converge to $v\ne 0$, they are eventually equal to $v\in F_p$.

Therefore the entire nonzero future-null boundary of a Lorentz cone cannot be approximated from one unchanged component by such differences.

Proof. Equation (eq:future) bounds the nonzero set by two. Allowing $q=p$ adds only zero. A convergent sequence in this finite set has its limit in the set and is eventually constant: take a ball about the limit excluding all other points. A nonzero limit belongs to $F_p$.

The Lorentz cone has infinitely many nonzero null directions when $m\ge 3$. An invertible linear map preserves that fact.