In case anyone is wondering why this is important: the spherical harmonics are frequently most of the data in a Gaussian splat data set — as much as 80% of the data for good quality scenes.

The magic of Gaussian splats is their ability to render photorealistic outputs without material properties, explicit ray tracing, etc. They do this by synthesizing complex light transfer in the scene via these fuzzy blobs overlapping — but they need to be able to change color and transparency with view angle to recreate much of that light transport. Hence, relatively heavyweight data.

There are many approaches to reducing the data volume, and they get increasingly complex when you add a time component. Not even worth listing publications here because it's changing so quickly, just plan to look at the SIGGRAPH pre-prints in a couple of months. Exciting times!