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This method was developed for the Method Development Competition January 2021. Because I was running the competition, I submitted the method not as a competitor. This method takes advantage of a flaw that exists within EPLL, ELL, and some L5E and LSE cases. Take for example any EPLL case. Almost all of the common algs for those cases start and end with an M2 move. The first M2 places dM at uM then the second M2 places those pieces back. That is a waste of two moves. So this method is designed around having the two edges on the U layer already solved. That way the end of the solve can permute the remaining four edges without having to break something that was already built.
Step 1
Solve dL.
Step 2
Create two pairs on the U layer. These are the pairs that go to UFl and UBl. The two edges within the pairs don't have to be the correct ones that align with the two corners. The two edges can be a pair of edges from elsewhere in the M slice. The two corners can also have pseudo techniques applied to shorten this step even further. The user can also choose to solve the two pairs that contain the UL+UR edges. This way, later in the solve, if the final step is to permute the four edges of the M-Slice then there will be no final AUF.
As for building the two pairs, various methods can be used depending on the case. Blockbuilding techniques, two corners paired then the edges slotted, or two edges paired on the D layer then the corners placed with the edges are all viable.
Step 3
Solve the R layer corners using ÆCLL (Thanks to Blobinati Cuber for the name idea). If the corners in Step 2 were solved with pseudo techniques, methods such as EG or L5C can be also be used.
Step 4
Solve the remaining edges. There are many variants available for this step. A few that stand out are:
1
a: Solve a triplet of redges.
b: Solve the remaining four edges in a single algorithm.
Note: The first step doesn't always have to be to solve three redges. It can be two redges and any other edge and possibly have good algorithms for L4E.
2
a: Solve two redges
b: L5E (~400 algs)
3
a: Solve any two edges.
b: Solve any other two edges.
c: L3E.
Note: In steps a and b, it is likely best to solve at least one D layer edge and at least two redges. This leads to easy L3E solutions.
4
a: Solve two redges.
b: Place a third redge while orienting the remaining edges.
c: Permute remaining four edges.
Note: This method is particularly good to use if the user is neutral in solving pairs in the second step that contain either UF+UB or UL+UR edges. And any pseudo applications along with that.
5
a: Solve a single redge.
b: Place two redges while orienting the remaining edges.
c: Permute remaining four edges.
6
a: Solve two redges.
b: Solve the remaining two redges or the UL edge + one redge while orienting the remaining edges.
c: L3EP. This would be three cases with a high skip chance. The cases are two three cycles and the skip.
7
a: Solve EO and two redges
b: Permute the last 5 edges
Note: This edge method idea is by Blobinati Cuber
L9E Variant - Æther (Ætherman as an Edge Technique)
An alternative would be to use the Ætherman bar technique for Waterman and Corners First methods. This may be easier than building two pairs as in the original Ætherman method. For Waterman, the method would become like below:
Step 1: dL 1x2x3.
Step 2: Solve remaining corners. This can be to place the two corners at UL then R layer CLL, place the two corners at DR then U layer CLL, place a single corner then L5C, or any other method.
Step 3: Solve the bar of edges.
Step 4: L7E.
Notes
An interesting thing is that the slots that the edges fill in Step 2 don't affect the typical corners first solve at all. Corners first doesn't need those two slots free. When slotting edges in corners first methods, the moves are almost always U M' U', U M2 U', and variations. These moves happen to do nothing to the edges at UF+UB, so it is beneficial to place edges here early in the solve.
Having the two edges on the U layer solved greatly reduces the number of cases for solving a pair or triplet of Redges in Step 4.
Look-ahead is also improved versus other corners first methods.
If all edges are oriented early in the solve, as in EOFB or somewhere else, it would reduce the number of cases for the remaining edges. Ergonomics would be a bit worse though because of the increase in the number of required M2 moves.
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