Everyone, I'm pleased to know how many voters are interested in this method. In my quest for searching for an organization, I have linked to this thread so that they can see the poll to know that people are actually interested. That should help out. This really means a lot!
(And please, if someone knows someone who can help me make this process go faster, I would greatly appreciate it.)
Did you edit the fact that you've written a paper which includes 3x3 and 4x4 example solves? I've could have sworn I saw that yesterday.
Yes. I have written a self-contained book (in LaTeX format which is about 350 pages of content + 550 pages of appendices) which contains a lot of hyperlinks for easy navigation within the document.
The first eight chapters of the book are regarding my proofs (I have proved it in multiple ways, in order to describe the structure of all possible single commutator solutions which can exist and to give the reader complete knowledge on the subject of commutators) of the following theorem:
All elements in the nxnxn supercube commutator subgroup (disregarding odd nxnxn supercube elements which rotate fixed centers) have a commutator length of one.
Chapters 9-11 are applications of the theory derived in these first eight chapters, and chapter 12 is all about this new solving method which is also an application of the theory I had to derive to prove the theorem.
Make no mistake, I'm not considering single commutator solves like for
this random 3x3x3 position and
this random 4x4x4 position to be categorized as the solves I described in this thread, despite that they appear to be solves similar to that 100x100x100 solve. These are commutators after all, and I claim that we don't need commutators at all to solve any size cube or any size minx.
If this approach doesn't produce near-optimal solutions for a completely scrambled cube could it do it for e.g. LL or move reduced cases?
Although I have not explored fewest moves with this method, I believe that the answer is yes for a subset of last layer positions.
I think this might turn out to be something similar to the algebraic solutions to cubic and quartic equations, i.e. something that looks like a holy grail from afar, but turns out to be a whole bunch of work for not a whole lot of satisfaction.
If you like to do any of the following, you will get a lot of satisfaction from this approach.
- solving Sudoku puzzles
- balancing chemical equations
- decoding ciphers
- simplifying algebraic expressions
- solving math problems which have long solutions
- optimizing the efficiency of software
Make no mistake, when this method is released, it is not a method where I give you an abstract formula which is so complicated that you just merely need to figure out how to use it. With this method, there is so much freedom (there are multiple ways to handle any portion of the solving process), and it requires thinking, planning, and creativity.
