Threshold T3 or T3i differences ?

Do the Threshold ("improved") "i" versions of the T3 preamp (aka T3i) actually state T3i on the preamp? Or if it has a separate power supply does that mean it is a T3i? Or is there a serial number after which all T3 preamps are T3i preamps? Thanks for any help in this regard!
The unit will actually have the "i" designation on the serial number tag... All of the T3s had outboard supplies, the "i" model had a larger supply than the non-"i" versions.
There may be other ways to tell.... but I do not remember all of them...
Thanks J_K for the follow up!