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I figured it would be useful to have a megathread for this. We can post requests for reconstructions (of WR solves and the like), cool reconstructions we've done, techniques, and so on.

A few useful links to start off with:
- Lucas Garron's reconstruction index
- Cube Explorer to track stickers when you don't have a scramble
- alg.garron.us to make sure your sequence solves the puzzle

It took an lot of work and trial/error (even the high quality video was pretty grainy/blurry on the cube section, and there were reflections on the stickers, and fingers and subtitles in the way), but:

scramble: U L2 D' B2 U' R2 B2 F2 D' F2 L2 R2 F R2 D L2 R2 B' L' D' R F'

inspection: x2 y
FL corners + 1 edge: D' R u D R' y' D' R D R'
FL center + 2nd edge: y D r' E' L
CLL: z2 U y l D R' z' R' x z' r' R2 U2 z D R2 D2
FL 3rd edge: R' l' z M D2 M'
LL 1st edge: z2 y R z' M z R'
LL 2nd edge: z' r' L' z D R' E R
LL 3rd edge: U' u' R E' R'
LSE hax: u R' E' R E2 R E R'
centers: R2 E E' r2 E M2 E'

It took an lot of work and trial/error (even the high quality video was pretty grainy/blurry on the cube section, and there were reflections on the stickers, and fingers and subtitles in the way), but:

scramble: U L2 D' B2 U' R2 B2 F2 D' F2 L2 R2 F R2 D L2 R2 B' L' D' R F'

inspection: x2 y
FL corners + 1 edge: D' R u D R' y' D' R D R'
FL center + 2nd edge: y D r' E' L
CLL: z2 U y l D R' z' R' x z' r' R2 U2 z D R2 D2
FL 3rd edge: R' l' z M D2 M'
LL 1st edge: z2 y R z' M z R'
LL 2nd edge: z' r' L' z D R' E R
LL 3rd edge: U' u' R E' R'
LSE hax: u R' E' R E2 R E R'
centers: R2 E E' r2 E M2 E'

As far as I can tell the method is roughly:
- first layer corners and then center, try to add in an edge if you see it
- last layer corners in one step
- insert first layer edges until 3 are done
- use the keyhole in the first layer to insert 3 last layer edges
- solve the last 6 edges and centers (not sure what his strategy here is)

I agree. The 'LSE hax' is a Roux trick for solving UL/UR edges and orientation in one, but I think it's unlikely he used the orient -> permute technique and he probably just did UL/UR then midges.

You could always reconstruct his other solves for more info

More or less that. I use Cube Explorer and fill in stickers on an empty cube until I know enough. I always try to find as much of the initial scramble as possible, but sometimes I can't get it all from the start. In that case I'll play along with a real cube and see if any previously unknown stickers come into view as the solution is executed. Once I have the starting state (and, if it's 2x2 or 3x3, a scramble to go with it), I can watch what's going on and do moves on my own cube to try to match what I can see at any given time. It's not always possible to figure out what moves are being done just by watching the hands and cube twist.

Got Piti's solve. Neither of the vids had a good enough view of the scrambled cube, so it took a few tries to get the right scramble.

scramble: F2 R2 D R D L2 R F2 L D F2 D2 R F L D' U' B

inspection: y' x'
cross: r' F' D
F2L1: U' R' U' R2 U R'
F2L2: U R' U2 R U R' U2 R
F2L3: y' U y' U R' U' R y U' L' U L
F2L4: U' R U2 R' U2 R U' R'
OLL: R' U' F U R U' R' F' R
PLL: U' R2 U R U R' U' R' U' R' U R' U

A megaminx reconstruction will be quite hard to do. In this case we have the scramble, but who can really say if it was scrambled correctly. The notation will also be a b*tch to do.