Thanks for playing, and I'm glad you had fun with it!
w is not in fact anything, and 0004 is where I've seen a few people getting stuck, so I probably did not design it very well. It has a lot of overlapping rules and it's not that clear what order you're supposed to do them in, so maybe it would have been better if there was a previous lock that taught you about the solve order unambiguously.
"Finding part of the word and then guessing the rest" is very much intended though, as a sort of release valve for people who don't find the logic very clear!