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I don't think your proof is actually a proof. Essentially I am just not convinced that all theoretically possible parity algs which are more optimal than the pure edge flip one can be ruled out. Perhaps explaining exactly how you have covered all cases would be helpful. It is clear that any optimal parity alg which keeps the puzzle reduced would start and end with a slice move, but I don't agree that this means the pure edge flip is the best way to do it.

Also, your post directed at deadalnix was indeed pretty arrogant (e.g. the part where you're like "find the shortest pure edge flip in the world by hand, and then we will talk").

Well what I would do is imagine in my mind what the PLL would look like if that edge was flipped.

If I can't seem to recognise any PLL case, then that probably means that I have a double parity case. However, if it seems like a PLL case I know, then I probably have just an OLL parity.
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What I'm really starting to think is that a combination of both systems (depending on the OLL case with parity) is the way forward.

reThinking the Cube,
I actually was on the same page you were on. You and I do see eye to eye. And thanks for your appreciation! Well, if you really want me to try to find the "dirtiest" alg that does what you want, I will try. I will not use a computer in my attempts (I refuse to). The reason I first discouraged the idea is because you said the current dedge flip algorithms stink. That to me implied that you prefer the cleanest algorithms possible.

qqwref,
I am glad you agree with me with the slice at the beginning and end of the alg. Maybe it is possible to consider a non-pure algorithm to be the shortest.

Dang it Lucas! Thanks for the nice alg courtesy Grandmaster P, but you are seriously frustrating me when you make r' = (Rr)' = r' . How can you specify a single slice turn on a big cube with this notation method? I never know for sure with your algs to slice or not to slice. Stop it, or, or, or..... I might be revenge driven to post gobs and gobs of mystery algs using a combination of face color names, arrows, and compass headings!

Yeh, its a good thing that I did, or that earlier post might have contained a few too many 4-letter algorithms. It's actually funny how I tried doing that a couple of times and was getting rather peaved, before I spotted the problem with the notation, and then also watched his applet to confirm my hunch. Lucas knows far too much to not know that (Rr) = r = (Rr) notation is confusing people wherever it is found.

Lucas usually uses the SiGN notation, which is not in any way ambiguous or confusing (although you do have to know it is being used to follow it, since it's not the same as the other notation). Unlike the notation you're familiar with, it is actually consistent with the 3x3 notation, in that r is a double-layer turn.

In SiGN, by the way, turns of single slices (on the R face, say) are labeled R, 2R, 3R, ... and turns of multiple slices (on the R face) are labeled R, r, 3r, 4r, .... So if Lucas wanted to use a slice turn in his alg he would write 2R.

reThinking the Cube,
I actually was on the same page you were on. You and I do see eye to eye. And thanks for your appreciation! Well, if you really want me to try to find the "dirtiest" alg that does what you want, I will try. I will not use a computer in my attempts (I refuse to).

Yeh, I WOULD use a computer to help me, but there aren't any programs (yet) that will solve this. Acube and CubeX find some 4x4x4 algs by limiting moves and setup, but not this one. These algorithm(s) are destined to become the new standards for flipping single edgepairs. Naming rights should go to the finder. Maybe even do a trademark funny like Petrus did with Sune™

There is no need for a parity algorithm to be used before the last slot. It is pointless. There are a large amount of people with official sub-50 solves. As far as I know, they all use a form of reduction. They don't need a new parity algorithm to get fast. They get fast by practise. A new parity algorithm that messes up your last layer is not a 'new standard.' It is pointless.

Even if somebody wrote up a long list of algorithms to solve OLL on the 4x4x4 in one step (including the cases with 1 and 3 oriented edges), that would not be a new standard. Even if somebody wrote up a long list of algorithms to solve PLL on the 4x4x4 in one step (including odd parity), that would not be a new standard. It would be impressive that they made the algorithms, learnt them, and put them into practise, but it would not be a new standard, and it would not be significantly faster.

Why on Earth are you looking for a 'new standard' parity algorithm?

It does NOT mess up the LL since F2L is not even done yet, and that IS the point of this algorithm - which should be faster, quicker, and cheaper than what we have now.

You don't get it, reThinker. Even if there is an algorithm that ignores last slot + last layer and is more efficient than any pure edge flip, it's not going to be by much - maybe two or three turns at most. It's not like there's some really awesome 10-move parity alg that, when found, will completely revolutionize bigcube solving. That is, although I'm not convinced by cmowla's proof, I don't think there is likely to be a parity alg that is "faster, quicker, and cheaper than what we have now" - and even if there is, I really don't think it will be by very much.

The thing is, as you can see in the video, the fastest speedcubers perform the already-known alg in under 4 seconds. At best, you're talking an improvement of a fraction of a second, and that's without factoring in how annoying a parity alg that messed with the last slot would be. Not only would recognition get slightly harder, but if you had a solved (or really nice) last slot case as well as parity you'd have to abandon that in order to do your special alg. I'm not saying you should completely stop looking, but don't think your idea is going to substantially change how 4x4 solves are done.

That is, although I'm not convinced by cmowla's proof, I don't think there is likely to be a parity alg that is "faster, quicker, and cheaper than what we have now" - and even if there is, I really don't think it will be by very much.

Even if it is just a little faster - then its still gonna be faster.
Even if it is just a little quicker - then its still gonna be quicker.
Even if it is just a little cheaper - then its still gonna be cheaper.

SO IF GIVEN A CHOICE -
Which one would you prefer?
Which one would most prefer?

Seems to me that it certainly WOULD make a difference.

This new algorithm should also be simpler, and hopefully much easier to learn. Try teaching the 4x4x4 solve to someone not familiar with these parity algs, and then come back and tell me this won't make much of a difference. The existing parity algs are relatively hard for most to learn and master.

I did not say that it would substantially change how the whole of 4x4x4 solves are done. My idea here is that this specific parity issue (only one component of the solve) could be dealt with in a new and better way. It would then become standard practice to use that new "way", or technique to fix just this dedge flip parity.

This new algorithm should also be simpler, and hopefully much easier to learn. Try teaching the 4x4x4 solve to someone not familiar with these parity algs, and then come back and tell me this won't make much of a difference. The existing parity algs are relatively hard for most to learn and master.

It can't get any simpler than that. If you want more of a proof, deadalnix, find the shortest pure edge flip in the world (in block quarter turn moves) by hand, and then we will talk.

You can't prove I'm wrong so I'm right ? That's a very strange way to apply logic.

Anyway, each time you post here, a rabbit dies somewhere on the planet. And as long as you cannont prove me that I'm wrong, I will continue to say that I'm right. See the flawed logic ? You do the same. Arogance have nothing to do with that.

The experience show that you are proabaly right, but you cannot have any proof of that at this moment, so don't call this a proof.

reThinking the cube, for a start I have utilized the algorithm which you have seen in this thread already: (Rr)' U R U [(Rr)' U2] * 3 (Rr)2 U R' U' (Rr)2 U' R' U (Rr)' I will refer to this as the base.

Here is a 36 Block Quarter turn alg: The base + a 3 edge cycle.

(Rr)' U R U [(Rr)' U2] * 3 (Rr)2 U R' U' (Rr)2 U' R' U (Rr)' z' R' U R' U' R' U' R' U R U R2 z

Here is a 34 Block Quarter turn alg: The base + some moves I previously came up with in one of my threads. (Rr)' U R U [(Rr)' U2] * 3 (Rr)2 U R' U' (Rr)2 U' R' U (Rr)' F' L' U' L F U R2 U R'

These algs have a lot of moves don't they? And they are more complicated. However, if there exists and alg around 25q that accomplishes both tasks simultaneously, then maybe that alg is less complicated as well (but I doubt it).

These two algs are perfect examples of what my "proof" speaks of. They do satisfy your constraints, but their format and length, as well as overall beauty is poor. Notice that I had to add a lot of outer-layer turns to satisfy your constraints (just as my proof said). The last inner-layer turn (Rr)' by no means occurs at the end here.

This new algorithm should also be simpler, and hopefully much easier to learn. Try teaching the 4x4x4 solve to someone not familiar with these parity algs, and then come back and tell me this won't make much of a difference. The existing parity algs are relatively hard for most to learn and master.

OK. I am cyclily stumped. He uses K4 hybrid, and is working towards a Dr. of Music. This is a parity paradoxical to me. Please post your link to this familiar song.