Corollary: Actual ramp and qualified nonvanishing

On $h_{\ast }$, the time-only preparation jet gives

with every other component zero. This tensor is not identically zero.

Proof. Only $J_{00}$ survives, so the substitution in (eq:Ktable) gives the displayed formula. If ${\sigma }_{\epsilon }^{\prime \prime }$ were identically zero, the smooth ramp would be affine. Its constant value on $t\le 0$ would then force it to be constant everywhere, contradicting its value one for $t\ge \epsilon$.