Trace-reversal simplification

For $I=00$, $N^{\mu \nu }{}_{00}={{\delta }^{\mu }}_0{{\delta }^{\nu }}_0-{\eta }^{\mu \nu }/2$, and the kinetic combination is ${{\delta }^{\nu }}_0{\partial }_{2,0}d$. For $I=01$, ${\vartheta }_I=0$ and

This checks both a diagonal and an off-diagonal endpoint. The generic result follows from the same exact numerator calculation, not a component truncation.