Proposition: Division reverses global magnitude protection

Suppose a global exact-count rule removes the lowest scores and divides a designated recurrent group's magnitudes by $b>1$, leaving other scores fixed. The number of retained coordinates in that group cannot increase solely because of this division.

It can decrease strictly.

Proof. Every designated score weakly decreases relative to unchanged scores. With fixed deterministic tie breaking, its group cannot gain positions in the top-retained ranking.

For a strict example, take one recurrent magnitude 2 and one other magnitude $3/2$, and delete one coordinate. Without division the other coordinate is deleted. At $b=2$, the recurrent score is 1 and is deleted instead.