Observer L is in the rest frame of object L; consequently he measures its proper length. Observer C is not in the rest frame of object L, and therefore measures a shorter length. Your claim that L measures a shorter length than C indicates that you’re using something other than special relativity, that you’re using special relativity wrong, or that I didn’t understand your description. Please clarify which it is. A diagram may be helpful.
Additionally, this:
Distance only diminishes in transformation
is plain wrong, since you can always do the transformation in the other direction! It doesn’t diminish both ways! And this claim:
length increases when transformed towards a frame of reference closer to that of the object in question
appears to be meaningless; there’s no such thing as a frame of reference “closer to an object”. A frame of reference doesn’t have a location, it has a speed relative to an observer.
Sticks L and R are stationary in the frame of C; objects L and R just happen to be close to the other ends of the sticks at some time, and are stationary in their own reference frames.
At this point I have no idea what is supposed to be happening in your scenario. You’ve got sticks, objects, and observers, and it’s not clear whether any of them are the same or what frames they are in. Please draw a diagram.
Observer L is in the rest frame of object L; consequently he measures its proper length. Observer C is not in the rest frame of object L, and therefore measures a shorter length. Your claim that L measures a shorter length than C indicates that you’re using something other than special relativity, that you’re using special relativity wrong, or that I didn’t understand your description. Please clarify which it is. A diagram may be helpful.
Additionally, this:
is plain wrong, since you can always do the transformation in the other direction! It doesn’t diminish both ways! And this claim:
appears to be meaningless; there’s no such thing as a frame of reference “closer to an object”. A frame of reference doesn’t have a location, it has a speed relative to an observer.
Sticks L and R are stationary in the frame of C; objects L and R just happen to be close to the other ends of the sticks at some time, and are stationary in their own reference frames.
At this point I have no idea what is supposed to be happening in your scenario. You’ve got sticks, objects, and observers, and it’s not clear whether any of them are the same or what frames they are in. Please draw a diagram.