cubing
4x4x4 Centers-Only: How to properly solve when no piece to "fix"?
Last night before I switched to 5x5x5 centers, I was hoping to find god's number for 4x4x4 centers-only. However it hits the same problem as triangles-only FTO. There is no piece to fix the orientation and it would solve the 24 center pieces into their particular faces, instead of any of the 24 whole cube orientations are possible. It might be possible to fix a single center piece, but that would still leave 4 possible orientations and not properly solve the problem.
In triangles-only FTO, fixing a (non-existent) corner separates the two orbits, but forces solving into one of the 12 possible orientations instead of any. If I put in the effort to redefine with a single triangle piece fixed, then it still forces solvign into one of 3 possible orientations instead of any. (I did not test if puzzle-geometry-bin.js is capable of fixing center since it is not a complete solution.)
This seems to support my earlier request to be able to define multiple solved states. Having this would certainly solve this issue. It would also allow things like searching for color-neutral cross on 3x3x3. In addition, I was hoping to tackle questions like god's number between phases, such as with centers-only 5x5, with 4 faces of centers solved, to find god's number for last two centers with that initial condition (starting with the adjacent face case, then perhaps the opposite face case). It can solve SOME of these types of questions if the new problem can be formated as a different puzzle definition. For example, adding --moves U,R to megaminx solves the <R,U> 2-generator problem on it which some multi-stage solvers use as a last stage. (Btw, this problem is uses too much memory, and another person wrote a solver that uses disk to work around it.) The effort on the megaminx problem actually lowered the upperbound for megaminx to something like 113.
Getting back to this issue... I wonder if it's possible to workaround it by having fake orientation moves that (sort of) cycle the colors around. Does it know to treat a "Move" as an orientation move as long as it ends in a lower-case "v"? But if I have a 4x4 center piece fixed, that piece is no longer in the piece set and how do I cycle into or out of it? Perhaps someone knows of a viable workaround for this issue I'm facing.
