Remark: An added scalar can reproduce the normal component

When ${\partial }_{s}F>0$, define $S_F$ locally by $U=F(S_F(U,x),x)$. Implicit differentiation gives

Thus numerical or functional equality is possible after the schedule-defined scalar is explicitly added. This does not identify $S_F$ with an inflaton, supply its rods, or derive $F$ from matter dynamics. It prevents an overstrong claim that kinematic and scalar lapses can never coincide.