some info on AHTA
First step: EO
Second step: equator
Third step: corner orientation
Fourth step: corner permutation
There are only 5 cases, I generated my own algs for these but it would be very easy to generate others if you do not care for these
Fifth step: edges
Final step: edges
THX for sharing; HTA needs more love!
Some feedback/questions on your steps:
Second step: equator
I always look at this step as "solving U/D corners"
Do you think one of the "mindsets" has advantages over the other?
Third step: corner orientation
LCBM has been briefly discussed further up the thread.
My personal feelings though are that using such a large alg set goes a little against the spirit of Human Thistlethwaite.
Do you actually use this alg set or do you use regular OLL and or Heise's two twist?
I use both.
In some cases like Pi OLL the Heise alg with set up actually saves moves!
Fourth step: corner permutation
Props for finding your own algs but please have a look at these common Ortega algs, they may save you some moves
Double J: (place the correct corners on L)
F2 U' R2 U D R2 D' F2
Ortega: (place the correct corners on F) R2 U R2 U2 F2 U F2 or the left handed version
Double Y: (no setup needed)
F U' R' B' L2 B R U F'
Ortega: (no setup needed) R2 F2 R2 or any variation of it
YJ: (place the correct pair on top left)
F' L U L F D2 F' L' U' L' F
Ortega (place correct corners on top F): R U' R F2 R' U R' or the left handed version
Why the alternative versions?
I prefer to pick the versions that cancel moves with the previous step
Fifth step: edges
" you can use things along the lines of M2 U2 M2 U2"
I suppose you mean "fix bad edges"
Typically you would use single move turns on U / D at this stage to bring the edges into the right orbit and exchange with M2.
Unless you perhaps use set up moves including F and B to enable edge pair swaps to fix edges? I sometimes do something similar with R2 U2 R2 U2 R2 U2.
You will find some in my example solves.
I will keep M2 U2 M2 U2 in mind as it provides an extra opportunity to cancel moves.
Final step: edges
yep, this is all about edge cycles and edge swaps including H-perm
When solving for Fewest Moves I like to insert the edge cycles to save extra moves.
Especially the equator edges are very likely to cancel moves as they are (obviously) in the same orbit for most of the solve. As a result you will have multiple situations where they can be cycled.
But to end the solve in true Thistlethwaite it is sometimes nice to end in all double turns.
Unfortunately this adds two moves to the edge 3-cycles...