Theorem: Anchored-null obstruction

For a fixed event $p$ in the unchanged component carrier,

has at most two elements. A convergent sequence in $F_p$ is eventually constant. Consequently no fixed original event approximates the entire nonzero null boundary by its comparable event differences.

Proof. Proposition prop:order bounds the strict future by two events. A finite set is closed and its distinct elements have positive minimum separation. The nonzero Lorentz null boundary contains infinitely many vectors.