One does need to compute the traditional position of the pieces to determine which ones need to be rotated for a given move, but the total state is significantly reduced.
Tell me this isn't news to the cube world. It cant be. Can it?
I don't know anything about the cube world as I'm just a noob in this.
You didn't really define what "cube coordinates" or "piece coordinates" are.
If you're trying to reduce the size of the state needed to represent the entire state of the cube, you can represent it as the operations needed to transform a solved cube into that state.
Each possible permutation of legal state in a rubiks cube can be achieved in 20 operations (moves) or less.
But that's expensive to calculate if you are only given the target state without the list of operations to generate that state.
It also doesn't let you represent illegal states (e.g. someone has spun a single corner piece on the spot) or know if a given state is illegal without trying to brute-force solve the cube.
Needing to represent the state of a cube without knowing the operations that generate that state is far more useful than being given a state that's already the solution to solve a cube.
> the total state is significantly reduced.
The minimal "state space" of a rubiks cube is a constant value. Any "reduction" would imply the model being reduced was inefficient.
On the topic of cool "alternative" views of rubiks I recently saw this and thought it was novel.
https://old.reddit.com/r/gifs/comments/z3okyv/the_only_way_t...
I put together something looking at a rubik's cube as a permutation of numbers a while back. https://taeric.github.io/cube-permutations-1.html I remember realizing that my representation essentially had some permutations of numbers that it would never hit, but wasn't sure it was worth trying to more directly model the pieces of the cube. Curious if there are advantages here that I'm ignoring.
I blather about the permutation matrix of a rubiks cube for a long while at https://www.hgreer.com/TwistyPuzzle/