Preservation of the F-bound under flips

Let $Y$ and $Y^+$ be terminal threefolds related by a flip, written

$$Y \dashrightarrow Y^+.$$

Let $F$ denote the invariant used in the source.

Flip F-bound conjecture. If $F(Y)\leq 24$, then

$$F(Y^+)\leq 24.$$

This claim is intended to control the invariant $F$ during the inductive study of flips. The supplied text gives no resolution status.