5 gen God's number?

[guysensei1]

I concur that the "incomplete cubes" solver in Cube Explorer is much slower than its regular optimal solver. Obviously, it is not creating a "huge" pruning table for use in this mode, or even using the existing huge table when no face restrictions are imposed.

Yes, whatever superflip requires, will be a lower bound. Because of its symmetry, it doesn't matter what orientation of the cube we use (or which face we make restricted). As I said in my previous post, we have that 5-gen superflip gives us a lower bound of 21, but the actual value could be higher, and thus could provide a better lower bound.

How did you know that all optimal superflips require the use of all 6 faces?

 

[cuBerBruce]

How did you know that all optimal superflips require the use of all 6 faces?

Mike Reid determined all optimal superflip maneuvers a long time ago.

These are the only minimal maneuvers for superflip in FTM, up to cyclic shifting, inversion, and conjugation by symmetries of the cube. They both require all six faces.

U R2 F B R B2 R U2 L B2 R U' D' R2 F R' L B2 U2 F2
U R2 F B R B2 R U2 L B2 R U' D' R2 F D2 B2 U2 R' L

EDIT: I've found a 27-move maneuver for superflip. It's probably not 5-gen optimal.

U R2 F B R B2 R U2 L B2 R' U2 B2 U F B L2 F R2 F' B' U' R L F2 B2 R2

EDIT 2: I've now found a 23-move maneuver for superflip. Optimal 5-gen superflip is now known to be in the range of 21-23.

U2 R U F R2 F B2 L' U F2 R2 B R L' U' L2 B2 R2 B' R2 F' U2 R2

EDIT 3: I've now ruled out any 21f 5-gen solution for superflip. 22 is a lower bound for the 5-gen God's number in FTM.

I am also very doubtful of a 22f solution for superflip. I should have that ruled out soon.

 

[cuBerBruce]

Using Rokicki's RubSolv solver - modified so that it does not use D-layer moves - I have verified that there are no 5-gen solutions for superflip with less than 23 face turns.

So 23 face turns is a lower bound for God's number for solving the cube using only 5 face layers. This lower bound is valid whether or not you're allowed to pick the restricted face separately for each position.

I have found the following 23-move solutions for superflip (unique up to conjugation by cube symmetries, inversion, and cyclic shift):

U2 R U F R2 F B2 L' U F2 R2 B R L' U' L2 B2 R2 B' R2 F' U2 R2
U2 R U F' R2 B U F2 L' U' B L' U' R' L2 F' U' L2 F2 L' B U2 R
U2 R F U F R2 U' R B2 U' F B' L2 B2 R' U' F' L' B' L2 F' B R2
U2 R F' U' F2 L B U B2 R2 U L' F R' L2 U B2 U2 F2 R' L' F L2
R L' U R2 B2 L2 F' B R' F2 U2 R2 L' U F2 R2 L2 B2 U' F' L2 F B
R L' U R2 B2 L2 F' B R' F2 U2 R2 L' U B2 R2 L2 F2 U' F' L2 F B
R L' U R' B2 U' F' R B R L' U' B2 R2 L' F2 U L2 B R2 U' R' F2
R L' U2 F R2 U' F2 R2 L2 B2 U B2 U2 R' F2 B2 L' F' B U2 R2 U' F2
R L' U2 F R2 U' B2 R2 L2 F2 U B2 U2 R' F2 B2 L' F' B U2 R2 U' F2

There could be additional 23f* solutions.

 

[qqwref]

Ooh, cool! A lower bound of 23 is interesting, definitely higher than I expected. Would you be willing to try the same thing (a) in qtm, and (b) with the superflip + 4spot (in 2 orientations) and some asymmetric 20f* position (in 6 orientations)?

 

[cuBerBruce]

Ooh, cool! A lower bound of 23 is interesting, definitely higher than I expected. Would you be willing to try the same thing (a) in qtm, and (b) with the superflip + 4spot (in 2 orientations) and some asymmetric 20f* position (in 6 orientations)?

My "database" of 26q* maneuvers has several that are 5-gen. For example:

U U F D D L U' F D' R' L F L' U F' U D' R D R' L' D R F R L

However, all such maneuvers for the superflip plus "equatorial" 4-spot require both U and D layer turns (according to my "database").

Thus, some orientation of superflip + 4-spot will require at least 28q if you're not allowed to pick the restricted face (assuming my "database" is not missing any maneuvers).

As for finding a 5-gen (no D moves) 28q* for the superflip + "equatorial 4-spot position, I can give it a try, as well as your other suggestions. I'm also attaching a ZIP file containing my FTM and QTM versions of rokicki's solver (executables) so you or others can also do so.

EDIT: Some more maneuvers without D-layer moves:

superflip:
U L' U' F' R B L' B L' F' U' R' F B U R U R U L B' L F' R' L U (26q)

"equatorial" 4-spot composed with superflip

U U F B' R B' U F L' B R' U R L' F R L' U F L F' R B U' R L' F R' (28q)
U U F B' R' F U' B' L F' R U' R' L B' R' L U' B' L' B R' F' U R' L B' R (28q)