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this is a cool concept, but understandable just after read the brief, maybe you could work over the "C" a little bit more, and definitely it will be better if you manage the "C" in a different color,
What about use the external part of the bulb?? maybe it is a better way to represent the concept, the interior is a little complicate to understand.
take a look to this little mockup, it is not clear enough but maybe it could give you some idea.
by the way I use a bulb concept with my logo too.
oops!!! sorry I forgot put some start Design 3 purpose 4 originality 3 engagement 2

I like your suggestion, however, I don't want it to be obvious that it's a light bulb. I do plan to color it in a way where it would make it more obvious similar to what you've suggested, but I'm not gunna have threads :p <3