Hour builder, I think you're only partly correct!
I forgot (mea culpa) to add that the skills test has to be succesful otherwise it is Pu/t. Most skills tests are successful otherwise the applicant wouldn't have been put up for it in the first place so you haven't really added much to my point that Pilot In Command Under Supervision is still P1 time, not dual.
If a skills test has been failed it is logged as Pu/t; if it was passed it is logged as P1u/s (or PICUS), therefore, PICUS is never Pu/t!
Cheers
Whirls