Inqury about equation 9 and according CUDA implementation

[Zhanpeng1202]

Hi, thanks for opening source this great work.

I just have some questions about the 4d covariance.

For the mean, at each time we are computing a displacement proportional to $\Delta t$, which is $\mu_{xyz | t} = \mu_{1:3}$ + a time varing term. But for the rotation, it seems like it would not change by time? i.e. for each timestamp, we are using the exact same quaternion product?

That is, at each timestep, there is only displacement and opacity change accoring to timestamp. But the covariance would be the same? Or did I miss something here?