So, I wonder what this is? By all accounts it's a Les Paul Junior Special, hence the four pots.(?)
Looking at the body and its been stripped and plugged with a wrap around added as opposed to the standard bridge and tail setup. Looking around the bridge humbucker and it also looks like it's been plugged, so maybe a standard p90 / P100 has been replaced by the humbucker. With no serial number on the back of the headstock and what looks like paint stripper running down the front of the headstock..(!!!) it's anybodys guess.
I'll have to check out a bit more. I do like the concept anyway.