Question What input and output color spaces does external tonemapping expect?

The color science documentation is pretty unclear on what actual color spaces are used, so it's difficult to determine what exactly is going on.

We did some digging to try to figure it out, and I'm posting our answers here to help others out, as well as to hopefully get some official confirmation from whoever's implemented Unity's color pipeline and perhaps nudge the documentation to be more explicit.

Input Primaries: ARRI Wide Gamut 3 (this is a guess, maybe it should be sRGB?)
Input Transfer Function: ARRI Alexa LogC EI 1000
"Input" means the stage of the color pipeline immediately before the LUT is applied.

Output Primaries: ARRI Wide Gamut 3 (this is a guess, maybe it should be sRGB?)
Output Transfer Function: Scene Linear
"Output" means the expected state of the image immediately after the LUT is applied.

Some additional questions: do the output primaries or other things change depending on the player's output color gamut? So, for example if the display is P3, do you need to have a different LUT for that case. And how does it work when you have "Use display in HDR mode" selected.

Any and all details on this would be appreciated!