The second-order composition formula

The shape agrees with the supplied classical formulas in XX-A and Em02-E. Equality of this algebraic shape is not identification of every clock normalization, background coordinate, raw coefficient, or boundary condition in those manuscripts.

A formal two-jet is also not, by itself, an exact positive lapse or an exact Einstein solution. When an exact smooth input family is supplied, positivity and local coordinate invertibility persist on a fixed compact comparison region for sufficiently small $\epsilon$. When only formal data are supplied, the conclusion of Theorem thm:lapse-composition remains a formal one.