And here is the reconstruction that I posted in FB.
Commified alg.garron link http://tinyurl.com/algx2UU-LUM2z-x
My first reconstruction!
Scramble: R2 B R2 B' L2 D2 U2 F2 D2 U2 F D U' F' D2 R' B2 U L2 F' L' Uw
Memo:
Starting position:
x2
Edges:
Buffer(DF)
BL UL FU BD BU DR BR...

http://orthotope.com/orthotope/bh-translator.php
It may kill the idea because BH list is mainly speed optimal and not move optimal, translating would make it not speed-optimal. But works as some reference for the few cases which one couldn't come up with an alg for.

I can't agree more to what Mike Hughey says. But for those who want to refer to a list and use BH for a different buffer, I wrote a quick dirty script to do the job. You can check it here.
http://orthotope.com/orthotope/bh-translator.php
It may kill the idea because BH list is mainly speed...

Try l2 instead of L2. This would work since it's a corner comm.
Instead of l2, you can write x2 R2. This will cancel an R.
L2 R' D' R U2 R' D R U2 L2 becomes x2 R2 R' D' R U2 R' D R U2 R2 x2. And this on cancelling R becomes x2 R D' R U2 R' D R U2 R2 x2. Now if you want to remove the x2, you...

You can do this
http://alg.garron.us/?alg=[M,E-]%0A[F-_L-:[R_U-:[R_U_R_U_R,_z-_y2]]]%0A[x2_y-:[F-_L-:[R_U-:[U_R_U_R_U,_z-_y2]]]]
http://alg.garron.us/?alg=[R_U-:[R_U_R_U_R,_z-_y2]] and http://alg.garron.us/?alg=[R_U-:[U_R_U_R_U,_z-_y2]] may be replaced by convenient U perms
One don't have to...

R' B2 U' B' U = D B' D' B2 R'
I don't know how one can arrive at this logically, but I found this by comparing two V perms
R' U R' U' B' R' B2 U' B' U B' R B R
R' U R' U' B' D B' D' B2 R' B' R B R
This is how my thought process went from here on.
R' B2 U' B' U R B2 D B D' = Identity (Modifying...

5x5 BLD
Memo : 28:53.23
Solve : 29:37.64
Total : 58:30.87
L' Uw D' F Fw' Bw' B' Uw2 D2 F Bw2 Lw B R Fw Rw' Fw Rw2 U' B R2 Dw' Fw' Bw U L2 R' Fw R Dw2 Bw Dw Bw2 R2 B U Dw' Fw Lw2 Dw' Rw2 U' Uw2 Lw' Rw2 U R' Dw2 Fw U B' U D2 L Fw' Uw' Bw Uw2 D B'
My first 5x5 BLD and it was a success...

There have been so many posts since I have last seen this thread! And looks like cmowla's proof is 14 pages! This is going to take a while for me to go through it completely! A lot of work. Hats off just for the amount of it and the detail in which it is written.

4x4x4 blindfolded
13 Sep, 2012 11:09:46 AM - 12:30:42 PM
Mean: 23:32.09
Average: 23:26.93
Best time: 23:07.25
Median: 23:26.93
Worst time: 24:02.10
Standard deviation: 22.69
1. 24:02.10 U2 L Uw2 U2 B' D Uw2 U F Uw Fw F' U2 Fw2 D' R D L Rw2 Uw' F Uw2 L' Fw' F' Rw' D Uw' R' Uw2 L' Fw2 L Fw F2 D'...

I do this.
1. Solve opp centers.
2. Solve three dedge pairs of one of the solved centers and put them around the corresponding center
3. Solve the remaining centers
4. Solve the fourth dedge pair of the same colour as the first three pairs.
5. Key hole, the eight dedges and four courners. The...

Realized I didn't cover everything I intended to.
Reducing the Maneuver :
-Always write R before L, U before D and F before B when consecutive recursively till no change in the maneuver
-Replace all X X' / X X2 combinations to "nothing" / X' respectively
-Replace all X4 kind to "nothing"
and...